Apttitude

Compiled by
Dr.C.Sekar
Professor of Mathematics,
PG Extension Centre,
M S University.

A contract is to be completed in 56 days and 104
men were set to work, each working 8 hrs a day.
After 30 days, (2/5)th of a work is completed.
How many additional men may be employed, so
that the work may be completed in time, each
man now working 9 hrs a day?
(a) 60 (b) 56 (c) 70 (d) 42
Ans : is a constant.
=> ? = 160
Additional men to be employed = 160-104 = 56
W
MXDXT
3
926?
2
830104 XXXX


If 27 Kg of corn would feed 42 horses for 21 days,
in how many days would 36 Kg of it feed 21
horses?
(a) 28 (b)42 (c)56 (d)32
Ans :
=> ? = 5636
?21
27
2142 XX


2 men and 7 boys can do a piece of work in 14
days; 3 men and 8 boys can do the same in 11
days; 8 men and 6 boys can do 3 times the amount
of this work in :
(a) 21 days (b) 18 days (c) 24 days (d) 36 days
Ans : (2M + 7B) x 14 = (3M + 8B) x 11
i.e., 5M = 10 boys
(2M + 7B) x 14 x 3 = (8M + 6B) x ?
11B x 14 x 3 = 22B x ?
? = 21 days.

A can do 1/3 of a work in 5 days and B can do 2/5
of the work in 10 days. In how many days both A
and B together can do the work?
(a) 7 (b) 8 (c) 9 (d) 10
Ans:
A can do full work in 5 x = 15 days
B can do full work in 10 x = 25 days
A and B together can do it in =
= 9 days
1
3
2
5
2515
2515

X
8
75
8
3

A is thrice as good a work man as B, and is
therefore able to finish a piece of work in 60 days
less than B. Find the time in which they can do it ,
working together,
(a) 20 days (b) 22 days
(c) 25 days (d) 40 days
Ans : Time ratio = 1:3  2 units = 60 days
Working together they can do it in
= unit time = 22 days
13
13

X
4
3
2
1
2
1

A and B together can do a piece of work in 6
days and A alone can do it in 9 days. The
time taken by B alone to do the work is:
(c) 12 days (d) 7.5 days
Ans : = 18 days
69
69

X

A can complete a job in 9 days, B in 10 days and
C in 15 days. B and C started the work and are
forced to leave after 2 days. The time taken by A
to complete the remaining work is:
Ans: The total work can be taken as L.C.M of 9,
10, 15 which is equal to 90 units. Therefore one
day work of A, B, C are respectively 10, 9, 6 units.
Two days work of B and C is 2X(9+6)=30 units.
Remaining work=60 units. A alone can complete
it in 6 days.

A can do a piece of work in 24 days while B alone
can do it in 16 days. With the help of C, they
finish the work in 8 days. C alone can do the work
in:
Ans: If the total work is the L.C.M of 24, 16, 8 =
48 units then
A+B+C’s one day work = 6 units
A+B’s one day work = 5 units
C’s one day work = 1 unit
Time taken by C = 48 units

Two pipes A and B can fill a tank in 36 min and 45 min
respectively. A waste pipe C can empty the tank in 30
min. First A and B are opened. After 7 min, C is also
opened. In how much time the tank is full?
(a) 39 min (b) 46 min (c) 40 min (d) 50 min
Ans: Total work = L.C.M of 36, 45, 30 = 180 units
1 min. work of A,B,C is +5, +4, -6 units respectively.
Work done in first 7 min = 7x(5+4) = 63 units
Remaining work = 180 – 63 = 117 units
Time taken to fill 117 units =117/3 = 39 min
Total time taken = 39 + 7 = 46 min

Three pipes A, B and C can fill a cistern in 6 hrs.
After working at it together for 2 hours, C is
closed and A and B can fill it in 7 hrs. The time
taken by C alone to fill the cistern is:
(a) 10 hrs (b) 12 hrs (c) 14 hrs (d) 16 hrs
Ans:
In 2 hours 1/3rd of work is done
C alone can do 2/3rd of work in hrs.
Therefore C alone can fill the cistern in 14 hrs.
47
47

X

•Find the number of factors of
540.
1) 24 2) 20 3) 30
4) none of these.

Solution
540 =2 x 2 x 3 x 3 x 3 x 5
=22x33x51
Therefore total number of factors of
540 is ( 2 + 1) ( 3 + 1 ) ( 1 + 1 ) = 24

The total number of divisors of
10500 except 1 and itself is
1) 48 2) 50 3) 46 4) 56

•10500 = 2x2x3x5x5x5x7
= 22x31x53x71
Therefore total number of
divisors of 10500 is
(2+1)(1+1)(3+1)(1+1) = 48 But
we have to exclude 1 and 10500.
So 46 is the correct answer.

If n = p1
a x p2
b x p3
c then
number of divisors is
(a+1)(b+1)(c+1).

Find the sum of factors of
270.
1) 670 2) 700
3) 720 4) 840

• 270 = 21 x 33 x 51
Therefore sum of factors of 270 is
(21+1-1)(33+1-1)(51+1-1)
----------------------------- = 720
(2-1)(3-1)(5-1)

Product of divisors of 7056 is
1) (84)48 2) (84)44
3) (84)45 4) None of these

Solution
7056 = 24x32x72
Number of divisors of 7056 =
(4+1)(2+1)(2+1) = 45
Product of factors =
= (84)45
)7056( 2
45

Number of odd factors of a given number
Number of odd factors of 90
is
1) 3 2) 5 3) 6 4) 8

Solution
90 = 21x32x51
Number of odd factors
= (2+1)(1+1)
= 6

If n = p1
a x p2
b x p3
c x ……
where p1, p2 , p3 ….. are odd
prime factors then the total
number of factors is
(a+1)(b+1)(c+1)……..

Number of ways of
expressing 180 as a product
of two factors:
180 = 22x32x51
No. of factors =
(2+1)(2+1)(1+1) = 18

Hence there are = 19 ways
in which 180 can be expressed
as a product of two factors.
2
18

Suppose N is a square number.
The number of divisors of N is an odd
number.
In this case
( i ) number of ways expressing N as a
product of two factors is
Number of factors + 1
-----------------------------------------------
2

( ii ) Number of ways of expressing as
a product of two distinct factors is
Number of factors - 1
-------------------------------------------
2

Examples
In how many ways can 576 be
expressed as the product of two
distinct factors?
576 = 26x32
Number of factors = (6+1)(2+1)
= 21

Number of ways of
expressing 576 as a product
of two distinct factors =
= 10
2
121

Find the number of zeros at
the end of the product of
2222x5555
Ans: 222

Find the number of zeros
at the end of the product
of the expression
10x100x1000x...x10000000000
a) 10 b) 100 c) 50 d)55

solution
Product is
10(1+2+3+…+10) =1055
Ans: 55

The age of a father 10 years ago was thrice the
age of his son. Ten years hence, the father’s age
will be twice that of his son. The ratio of their
present ages is :
(a) 8:5 (b) 7:3 (c) 5:2 (d) 9:5
Ans: Ten years ago Ratio=3:1
Ten years hence 2 : 1 = 4 : 2
Present ratio = 3. 5 : 1. 5 = 7 : 3

The age of a man is 4 times that of his son. 5 years
ago, the man was nine times as old as his son was
at that time. The present age of the man is:
(a) 28 years (b) 32 years (c) 40 years (d) 44 years
Ans:
Present ratio 4:1 = 32:8
5 years ago 9:1 = 27:3
5 unit difference = 5 years
Present age of the man is 32 years

The sum of the ages of a father and his son is 45
years. Five years ago the product of their ages
was 4 times the father’s age at that time. The
present ages of the father and son respectively
are
(a) 35yrs, 10yrs (b) 36yrs, 9yrs
(c) 39yrs, 6yrs (d) none of these
Ans: 5 years ago the son’s age was 4 years.
At present son’s age is 9 yrs and hence father’s
age is 36yrs

Jayesh is as much younger to Anil as he is older
to Prashant. If the sum of the ages of Anil and
Prashant is 48 years , what is the age of
Jayesh?
(a) 20 yrs (b)24 yrs
(c) 30 yrs (d) cannot be determined
Ans: 48/2 = 24 yrs

Ten years ago A was half of B in age. If the
ratio of their present ages is 3:4, what will be
the total of their present ages?
(a) 28 yrs (b) 20 yrs (c) 35 yrs (d) 49 yrs
Ans:
Ten years ago 1:2
Present ratio 3:4
Difference = 2 units = 10 years
Sum of their ages = 7 units = 35 years

Which number is less than 80 by 60% of 80 ?
(a)50 (b)42 (c)48 (d)32
Ans:
40% of 80 = 32

A number exceeds 20% of itself by 40. The
number is
(a)50 (b)60 (c)80 (d)320
Ans:
80% = 40 => 100% = 50

Rakesh credits15% of his salary in his fixed
deposit account and spends30% of the
remaining amount on grocers. If the cash in
hands is Rs.2380, what is his salary?
(a)Rs.3500 (b) Rs.4000
(c) Rs.4500 (d) Rs.5000
Ans: If his salary is S then
(1- ) x (1 - ) x S = 2380
i.e., 85 x 70 x S = 2380 x 100 x 100
Therefore S = 4000
100
15
100
30

From the salary of an officer, 10% is deducted
as house rent, 15% of the rest he spends on
children’s education and 10% of the balance,
he spends on clothes. After this expenditure, he
is left withRs.1377. His salary is
(a) Rs.2000 (b) Rs.2040 (c) Rs.2100 (d) Rs.2200
Ans : ( 1- ) x (1- ) x ( 1 - ) S = 1377
90 x 85 x 90 x S = 1377 x 100 x 100 x 100
S = 2000
100
10
100
10
100
15

The price of cooking oil has increased by 25%.
The percentage of reduction that a family
should effect in the use of cooking oil so as not
to increase the expenditure on this account is:
(a)15% (b) 20% (c) 25% (d) 30%
Ans: D = % , I = 25% => D = 20%
I
I
100
100

A student who scores 20% marks in an
examination fails by 30 marks. Another
student who scores 32% marks gets 42
marks more than those required to pass. The
percentage of marks required to pass is
(a)20 (b)25 (c)28 (d)30
Ans:
The difference in marks is 72 which is 12%
i.e., 30 marks is 5%
Passing percentage = 20 + 5 = 25%

75% of a number when added to 75 is equal
to the number. The number is
(a)150 (b)200
(c)225 (d)300
Ans:
25% = 75 => 100% = 300

On decreasing the price of T.V sets by 30% its
sale is increased by 20%. What is the effect on
the revenue received by the shopkeeper?
(a)10% increase (b) 10% decrease
(c)16% increase (d)16% decrease
Ans:
20 – 30 - = - 16% => 16% decrease
100
3020X

The population of a town is 8000. It increases by
10% during the first year and by 20% during
the second year. The population after 2 years will
be:
(a)10400 (b)10560
(c)10620 (d)none of these
Ans: Net increase = 10 + 20 + % = 32%
Population = 132% of 8000 = 10560 (or)
8000 x ( 1 + ) x ( 1 + ) = 10560
100
2010X
100
10
100
20

The value of a machine depreciates 10%
annually. If its present value is Rs.4000, its
value 2 years hence will be :
(a)Rs.3200 (b)Rs.3240 (c)Rs.3260 (d)Rs.3280
Ans:
4000 ( 1 - ) x ( 1 - ) = 4000 x x
= Rs.3240
100
10
100
10
100
90
100
90

3 liters of water is added to 15 liters of a
mixture of a 20% solution of alcohol in water.
The strength of alcohol is now:
(a)12% (b) 16% (c) 24% (d)16 %
Ans:
15 x 20 = 18 x ? => ? = = 16 3
2
3
2
18
2015X

A man spends 75% of his income. His income
is increased by 20% and he increases his
expenditure by 10%. His savings are
increased by:
(a)10% (b)25% (c)37 % (d)50%
Ans:
10 + x 100 = 50%
Is = IE + x 100
2
1
25
1020
S
II EI 

The length of a rectangle is increased by 10% and
breadth decreased by 10%. Then , the area of
new rectangle is:
(a) neither decreased or increased
(b) increased by 1%
(c) decreased by 1%
(d) decreased by 2%
Ans: 10 - 10 - = -1% => 1% decrease
100
1010X

A reduction of 21% in the price of wheat
enables a person to buy 10.5Kg more for
Rs.100. What is the reduced price per Kg?
(a) Rs.2 (b)Rs.2.25
(c) Rs.2.30 (d) Rs.2.50
Ans:
Cost of 10.5 Kg = Rs.21 =>
Reduced Price/Kg = Rs. 2

A mixture of 40 litres of milk and water
contains 10% water . How much water should
be added to this so that water may be 20% in
the new mixture?
(a) 4 litres (b) 5 litres
(c) 6.5 litres (d) 7.5 litres
Ans:
Quantity x concentration = constant.
40 x 90% = ? x 80% => ? = 45 (new quantity)
Water to be added = 5 litres

By selling a watch for Rs.1140, a man loses
5%. In order to gain 5% the watch must be
sold for :
(a)Rs.1311 (b)Rs.1197
(c)Rs.1254 (d)Rs.1260
Ans: 1140 : ? = 95 : 105 => ? = 1260

The selling price of 12 articles is equal to the
cost price of 15 articles. The gain percent is :
(a)16% (b) 20% (c)25% (d)80%
Ans:
x 100% , B = 15, S = 12;
x 100% = 25%
S
SB 
12
1215

If I purchased 11 books for Rs.10 and sold all the
books at the rate of 10 books for Rs.11, the profit
percent is:
(a)10% (b)11% (c) 21% (d)100%
Ans:
B = 11 x 11 = 121, S = 10 x 10 = 100
Profit = x 100 = 21%
100
100121

By selling 36 oranges , a vendor loses the
selling price of 4 oranges. His loss percent is
a)12% b)11 % c)10% d) none of these
Ans :
B = 36; S = 36 + 4 = 40
x 100 = x 100 = -10%
loss=10%
9
1
S
SB 
40
4036

By selling 8dozens of pencils, a shopkeeper gains
the selling price of 1 dozen pencils. His gain
percent is :
(a)12.5% (b)87.5% (c)14 % (d)none of these
Ans:
B = 8, S = 8 - 1 = 7
Profit% = x 100 = 14 %
7
2
7
1
7
2

By selling toffees at 20 for a rupee , a man loses
4%. To gain 20% , for one rupee he must sell:
(a) 16 toffees (b) 20 toffees
(c) 25 toffees (d) 24 toffees
Ans:
selling price x rate quantity = constant
i.e., 20 x 96% = ? x 120% => ? = 16

By selling 45 oranges for Rs.40 , a man loses
20%. How many should he sell for Rs.24 so
as to gain 20% in the transaction?
(a)16 (b)18 (c)20 (d)22
Ans:
= => ? = 18
40
8045X
24
120? X

A shopkeeper sells three-fourth of its articles at
a gain of 20% and the remaining at C.P His
real gain in the transaction is :
(a) 10% (b) 15% (c) 20% (d) 25%
Ans:
x 20% + x 0% = 15%
4
3
4
1

A grocer sells rice at a profit of 10% and uses
weights which are 20% less than the marked
weight. The total gain earned by him will be :
(a) 30% (b) 35%
(c)37.5% (d) none of these
Ans: B = 110 , S = 80
Profit% = x 100 = 37.5%
80
80110 

A man sells 2 horses for Rs.4000 each,
neither losing nor gaining in the deal. If he
sold one horse at a gain of 25%, the other
horse is sold at a loss of:
(a) 16 2/3% (b) 20% (c) 25% (d) 18 %
Ans:
L = i.e., L = = 16 2/3%
P
P
50
50
2550
2550

X

A person bought an article and sold it at a loss of
10%.If he had bought it for 20% less and sold it
for Rs.55 more, he would have had a profit of
40%. The C.P of the article is:
(a)Rs.200 (b)Rs.225 (c)Rs.250 (d) none of these
Ans:
140% of 80%-90% =55,
112%-90% =55
22% = 55
ie) C.P = 100% = Rs.250

A bicycle is sold at a gain of 16%. If it had
been sold for Rs.20 more 20% would have
been gained. The C.P of the bicycle is :
(a) Rs.350 (b)Rs.400
(c)Rs.500 (d)Rs.600
Ans:
120% - 116% = 4% = Rs.20
C.P = 100% = Rs.500

A dealer marks his goods 20% above the cost
price. He then allows some discount on it and
makes a profit of 8%. The rate of discount is
(a)12% (b)10% (c)6% (d)4%
Ans:
M.P =120% , S.P = 108%
Discount =
= x 100 = 10%
100
.
..
X
PM
PSPM 
120
108120

In a mixture of 60 litres, the ratio of milk and
water is 2 :1 . If the ratio of the milk and water is
to be 1:2, then the amount of water to be further
added is
(a) 20litres (b) 30litres
(c) 40litres (d) 60litres
Ans: milk is fixed.
x 60 = x 120
Quantity X Concentration of fixed one is constant.
i.e., Water to be added = 120 – 60 = 60 litres
3
2
3
1

A dishonest milk man professes to sell his
milk at C.P. but he mixes it with water and
thereby gains 25%. The percentage of water
in the mixture is
(a) 25% (b) 20%
(c) 49% (d) none of these
Ans :
x100 = 20%
25100
25


A container contains 80 Kg, of milk. From this
container , 8Kg of milk was taken out and
replaced by water. This process was further
repeated two times. How much milk is now
contained by the container?
(a) 64Kg (b) 56 Kg
(c) 58.32 Kg (d) 62.68 Kg
Ans :
Milk = 80 x ( 1 - )3 = 80 x
= 58.32 Kg
80
8
3
3
10
9

A can contains a mixture of two liquids A and B in
the proportion 7:5. When 9 litres of mixture are
drawn off and the can is filled with B, the
proportion of A and B becomes 7:9. How many
litres of liquid A was contained by the can
initially?
(a) 25 (b) 35 (c) 20 (d) 21
Ans => C = 36 litres where C is the
capacity of the can. Initially quantity of liquid A
= 36x = 21 litres
16
7
)
9
1(
12
7

c
12
7

Two vessels A and B contain milk and water mixed
in the ratio 5:2 and 8:5 respectively. Find the ratio
in which these mixtures are to be mixed to get a new
mixture containing milk and water in the ratio 9:4.
(a) 7:3 (b) 7:2 (c) 5:3 (d)2:1
Ans : Fix water. (2/7) (4/13) (5/13)
multiply by 7x13 26 28 35
35-28 : 28-26
7 : 2

A man covers a certain distance between his
house and office on scooter. Having an average
speed of 30Km/hr, he is late by 10 min. However,
with a speed of 40 Km/hr, he reaches his office 5
min earlier. Find the distance between his house
and office:
(a) 20 Km (b) 30Km (c) 40Km (d) 50 Km
Ans:
Distance = x = 30 Km
3040
3040

X
60
15

Walking 3/4th of his usual speed, a peon is
10 min too late to his office. Find the usual
time to cover the distance:
(a) 30 min (b) 40 min (c) 1 hr (d) 45 min
Ans:
Difference of Nr and Dr = 4-3 = 1 unit
1 unit = 10 min;
Usual time = Nr = 3 units = 30 min

A and B are two stations . A train goes from A to
B at 64 Km/hr and returns to A at a slower speed.
If its average speed for the whole journey is 56
Km/hr, at what speed did it return?
(a) 48 Km/hr (b) 49.77 Km/hr
(c) 52 Km/hr (d) 47.46 Km/hr
Ans:
Average speed = = a
u = 64; Average speed = 56
= 49.77 Km/hr
vu
uv

2
au
au
v


2

A is twice as fast as B and B is thrice as fast as C.
The journey covered by C in 42 min, will be
covered by A in:
(a) 14 min (b) 28 min
(c) 63 min (d) 7 min
Ans:
A is 6 times as fast as C
Time taken by A = 42/6 = 7 min.

A train leaves Meerut at 6 a.m and reaches Delhi
at 10 a.m. Another train leaves Delhi at 8a.m and
reaches Meerut at 11.30 a.m . At what time do the
two trains cross one another
(a)9.26 a.m (b) 9 a.m (c) 8.36 a.m (d) 8.56 a.m
Ans: Half of the distance is covered by first train
at 8 a.m
Meeting time = 8 hrs + hrs
= 8hrs + min
4
3
12
4
3
12

X
60
15
14
X

Two trains A and B start from stations X and Y
towards Y and X respectively.
After passing each other , they take 4 hours 48
minutes and 3 hours 20 minutes to reach Y and X
respectively. If train A is moving at 45 Km/hr,
then the train B is moving at:
(a)60 Km/hr (b)54 Km/hr (c)64.8 Km/hr
(d)37.5 Km/hr
Ans: Speed ratio of A and B is : = : =
10 : 12 = 5 : 6.
Speed of B =54 Km/hr
200 288 100 144

A train is running at the rate of 40 kmph. A man
also is going in the same direction parallel to the
train at the speed of 25 kmph. If the train crosses
the man in 48 seconds, the length of the train is
(a)50 metres (b)100 metres
(c)150 metres (d)200 metres
Ans:
Length of the train = Relative speed  time
= (40-25)   48
= 200 metres
18
5

A train speeds past a pole in 15 secs and speeds
past a platform 100 metres long in 25 secs. Its
length in metres is:
(a)200 (b)150 (c)50
(d)data inadequate
Ans:
Distance moved in 10(=25-15) secs =
Length of the platform =100 metres
Distance moved in 15 secs =
Length of the train = 150 metres.

A man rows to a place 48 km distant and back in 14
hours. He finds that he can row 4 km with the stream
in the same time as3 km against the stream. The rate
of the stream is:
(a)0.5 kmph (b)1 kmh (c)3.5 kmph (d)1.8
kmph
Ans: Speed down: speed up = 4:3
Time ratio = 3:4
7 unit time = 14 hrs
Speed down = 8 km/hr
Speed up = 6 km/hr
Speed of stream = (8-6)/2 = 1 km/hr

A man can row 6 km/hr in still water. It takes him
twice as long to row up as to row down the river.
Find the rate of stream
(a) 2 km/hr (b) 1 km/hr
(c) 2.5 km/hr (d) 1.5 km/hr
Ans: Checking the answers
Speed down = 2x speed up
6+2 = 2x(6-2)
Answer is 2 km/hr

The current of a stream runs at 1 km/hr. A
motor boat goes 35 kmph upstream and back
again to the starting point in 12 hours. The
speed of motor boat in still water is:
(a) 6 km/hr (b)7 km/hr
(c) 8 km/hr (d)8.5 km/hr
Ans: Checking the answer
= 7 + 5 = 12
Answer is 6 km/hr.
16
35
16
35




A boat covers 24 km upstream and 36 km
downstream in 6 hours, whole it covers 36 km
upstream and 24 km downstream in 6 hours. The
velocity of the current is :
(a) 1.5 km/hr (b) 1 km/hr
(c) 2 km/hr (d) 2.5 km/hr
Ans: Speed up = = 8 km/hr
Speed down = = 12 km/hr
Therefore velocity of current = 2 km/hr.
6245.636
24243636
XX
XX


5.624636
24243636
XX
XX



The difference between simple interest and compound
interest on a sum at 12.5 % rate of interest for 3 years
is Rs.600. Find the sum.
(a) Rs.12,000 (b) Rs.12,288
(c) Rs.10,500 (d) Rs.11,484
Ans:
Q = 100/12.5 = 8
P = (83x 600) / [(3 x 8) + 1] = 12,288

At certain rate of simple interest a sum amounts to
Rs.12,800 in 4 years and Rs.13,025 in 7 years. Find the
rate of interest.
(a) 0.5% (b)0.6% (c) 0.625% (d) 0.75 %
Ans :
Interest for 3 years = Rs.225
Interest for 1 year = Rs.75
Principal = 12800 – (75x4) = 12500 Rs.
 Rate of interest = 0.6%

Find the compound interest on a sum of Rs. 15,000 at 8%
rate of annual interest for 3 years, the interest being
compounded annually.
(a) Rs.3,800 (b) Rs.3,888.48
(c) Rs.3,895.68 (d) Rs.3,985.88
Ans :
3 x 1200 + 3 x 96 + 1 x 7.68 = 3895.68

S.I = PNR/100
C.I – S.I = D
For two years P= where Q=100/R
For three years P =
For four years P =
DQ2
13
3
Q
DQ
146 2
4
 QQ
DQ

The difference between simple interest and compound
interest on a sum at 10% rate of annual interest for 3 years
is rupees 620. Find the principal.
(a) Rs.32000 (b) Rs.10000 (c) Rs.20000
(d) Rs.15000

CALENDAR
1 2 3 4 5 6 7
January
October May August
February
March
November
June
September
December
April
July
LEAP
YEAR February January

 CENTURY NUMBER:
1600 – 0 ! R = 0 - Friday
1700 – 5 ! R = 1 - Saturday
1800 – 3 ! R = 2 - Sunday
1900 – 1 ! R = 3 - Monday
2000 – 0 ! R = 4 - Tuesday
2100 – 5 ! R = 5 - Wednesday
and so on . ! R = 6 - Thursday

Finding day for a date.
Example:17th June 1990
Date +month code + century number +
years + number of leap years .
17 + 5 + 1 + 90 + 22 =135
Divide by 7 . Get the remainder R = 2.
The day is Sunday.

ANGLE BETWEEN THE TWO HANDS OF A
CLOCK AT A GIVEN TIME
Time : H hours M minutes
Angle : [H-(M/5)] X 30 + (M/2) if H-(M/5) is +ve
[(M/5)-H] X 30 - (M/2) else

Finding the time when the angle between the hands is
given in an hour interval
Between H & H+1 hours,
angle b/w the hands is A0
Exact time will be 2(30H  A)/11 minutes past H

Overtaking position between H hours and H+1 hours
60H/11 minutes past H
Straight and opposite position of hands
60(H+6)/11 minutes past H

Perpendicular position of the hands
60(H-3)/11 and 60(H+3)/11 minutes past H
Hands are perpendicular - 22 times in 12 hours
Hands are straight and opposite - 11 times in 12 hours
Hand overtakes the other - 11 times in 12 hours

A clock chimes seven at 7 o’clock in
seven seconds. In how many seconds
will it chime ten at 10 o’clock?
a) 10 secs b) 10.5 secs
c) 10.75 secs d) 9 secs

Find the angle between the hands of a
clock( in degree measurement) at
8hrs 24mins.
(a) 96 (b) 102 (c) 108 (d) 88

Pointing out a lady, Rajesh said,
“ She is the daughter of the
woman who is the mother of the
husband of my mother” What is
the lady to Rajesh?
a) Daughter b) Aunt
c) Sister d) Sister-in-law

Pointing to a lady, a man said, ‘
The son of her only brother is the
brother of my wife’. How is the
lady related to the man?
a) Mother’s sister
b) Mother – in law
c) Grand mother
d) Sister of father – in - law

A and B both are children of C. If
C is the mother of A, A is the son of
C but B is not the daughter of C,
how are A and B mutually related?
a) A is the nephew of B
b) A is the cousin of B
c) A is the brother of B
d) A is the sister of B

K is brother of J ; M is sister
of K; P is brother of N; N is
daughter of J and S is the
father of M. Who is the uncle
of P?
a) N b) M C) K d) J

A man travels 12 K.M. west .
Then 3 K.M. towards south
and then 8 K.M. towards
east. How far is he from the
start?
a) 23 K.M. b) 20 K.M.
c) 15 K.M. d) 5 K.M.

A man walking towards east starting from
the point P takes the following turns.
Left , right, right, right, left, left, left, left
and right.
Towards which direction will he walk
finally?
a) north b) west c) south d)east

If west is north-east, which
direction will be south?
a) north b) north-east
c) north-west d) east

A cyclist goes 30 K.M. to North
and then turning to east he goes
40K.M. Again he turns to his right
and goes 20 K.M. After this he
turns to his right and goes 40 K.M.
How far is he from his starting
point?
a) 5 K.M. b) 10 K.M.
c) 25 K.M. d) 40 K.M.

A man is facing north- west.
He turns 90 degree in the
clockwise direction and then
135 degree in the anticlockwise
direction. Which direction is
he facing now?
a) East b) West
c) North d) South

Read the following information to answer the
four questions that follow :
In a family of 6 persons A, B, C, D, E and F
i. There are two married couples
ii. D is grandmother of A but mother of B
iii. C is the wife of B and mother of F
iv. F is the granddaughter of E

What is C to A ?
a) Grandmother
b) Mother
c) Cannot be determined
d) None of these

How many male members are there in the
family ?
a) 3
b) 4
d) None of these

Which of the following is true ?
a) A is the sister of F
b) D has two grandsons
c) B has two daughters
d) None of the above

Who among the following is one of the couples ?
a) DE
b) EB
d) None of these

A, B, C, D, E, F and G are members of a family consisting
of 4 adults and 3 children, two of whom, F and G are girls,
A and D are brothers and A is a doctor. E is an engineer
married to one of the brothers and has two children. B is
married to D and G is their child. Who is C?
(a) G’s father (b) F’s father
(c) E’s daughter (d) A’s son

J, K, L, M, N and O are six family members having
different professions. There are two married couples in the
family. M is a doctor and his wife is an engineer. J is the
grand daughter of O and sister of L, who is a typist. K is
the grandfather of L and is married to a teacher. J’s
mother, who is an engineer is the daughter in law of a
lawyer.
1)What is profession of J?
2)Who is the wife of M?
3) How many male members are there in the family?

 (i) Six friends A, B, C, D, E and F are seated in a circle
facing each other.
 (ii) A is between D and B and F is between C and E.
 (iii) C is the third to the left of B.
Which of the following is the position of A in relation to F?
(a) Second to the left (b) Second to the right
(c) Fourth to the right (d) Third to the right

There are 50 students admitted to a nursery class. Some
students can speak only English and some can speak only
Hindi. Ten students can speak both English and Hindi. If
the number of students who can speak English is 21, then
how many students can speak Hindi, how many can speak
only Hindi and how many can speak only English
respectively?
(a) 39, 29 and 11 (b) 37, 27 and 13
(c) 28, 18 and 22 (d) 21, 11 and 29

A worker can claim Rs.15 for each km which he travels by
taxi and Rs.5 for each km which he drives his own car. If
in one week he claimed Rs.500 for travelling 80 km, how
many kms did he travel by taxi?
(a) 10 (b) 20 (c) 30 (d) 80

The number of boys in a class is three times the number of
girls. Which one of the following numbers cannot
represent the total number of children in the class?
(a) 48 (b) 44 (c) 42 (d) 40

Ravi has Rs.3 more than Ramu, but then Ramu wins on
the horses and trebles his money, so that he now has Rs.2
more than the original amount of money that the two boys
had between them. How much money did Ravi and Ramu
have between them before Ramu’s win?
(a) Rs.9 (b) Rs.11 (c) Rs.13 (d) Rs. 15

A man has a certain number of small boxes to pack into
parcels. If he packs 3, 4, 5 or 6 in a parcel, he is left with
one over; if he packs 7 in a parcel, none is left over. What
is the number of boxes he may have to pack?
(a) 106 (b) 301 (c) 309 (d) 400

A cube has six sides each of a different colour. The red
side is opposite black. The green side is between red and
black. The blue side is adjacent to white and the brown
side is adjacent to blue. The red side is face down. The
side opposite brown is
(a) Red (b) black (c) white (d) green

Ages are to be computed in whole numbers only and no
two persons are of the same age. Mahesh is a year older
than Vikas. Vikas is two years older than Jagan. Jagan is a
year younger than suresh. Suresh is two years younger
than Mahesh. Akmal is two years younger than Jagan.
Which of the following is the order from the oldest to the
youngest?
(a) Mahesh, Vikas, Jagan, Suresh, Akmal
(b) Mahesh, Vikas, Suresh, Akmal, Jagan
(c) Mahesh, Vikas, Suresh, Jagan, Akmal
(d) Mahesh, Jagan, Jagan, Akmal, Suresh

If the seventh day of a month is three days earlier than
Friday, what day will it be on the nineteenth day of the
month?
(a) Sunday (b) Monday
(c) Wednesday (d) Friday

Village A is 20 km to the north of village B. Village C is
18 km to the east of Village B, Village D is 12 km to the
west of Village A. If Raj Gopal starts from Village C and
goes to Village D, in which direction is he from his
starting point?
(a) North-East (b) North-West
(c) South-East (d) North

Read the following information and answer the
five questions that follow :
In a car exhibition, seven cars of seven
different companies, viz. Cadillac, Ambassador,
Fiat, Maruti, Mercedes, Bedfort and Fargo were
displayed in a row, facing east such that
i. Cadillac car was to the immediate right of
Fargo
ii. Fargo was fourth to the right of Fiat
iii. Maruti was between ambassador and
Bedfort
iv. Fiat, which was the third to the left of
Ambassador car was at one of the ends

Fiat
Bedfort
Maruti
Ambassador
Fargo
Cadillac
Mercedes

 Fiat
 Bedfort
 Maruti
 Ambassador
 Fargo
 Cadillac
 Mercedes

Which of the following was the correct position
of the Mercedes ?
a) Immediate right of Cadillac
b) Immediate right of Bedfort
c) Between Bedfort and Fargo
d) Fourth to the right of Maruti

Which of the following is definitely true ?
a) Fargo Car is between Ambassador and Fiat
b) Cadillac is to the immediate left of Mercedes
c) Fargo is to the immediate right of Cadillac
d) Mercedes is to the immediate left of Cadillac

Which cars are on the immediate either sides of
the Cadillac car ?
a) Ambassador and Maruti
b) Maruti and Fiat
c) Fiat and Mercedes
d) Mercedes and Fargo

Which of the following is definitely true ?
a) Maruti is to the immediate left of Ambassador
b) Bedfort is to the immediate left of Fiat
c) Bedfort is at one of the ends
d) Fiat is second to the right of Maruti

Which of the following groups of cars is to the
right of Ambassador car ?
a) Cadillac, Fargo and Maruti
b) Maruti, Bedfort and Fiat
c) Mercedes, Cadillac and Fargo
d) Bedfort, Cadillac and Fargo

A ball is dropped from a height of 8 ft
and every time it goes half of the
height. How much distance will it
travel before coming to rest?
a) 16 ft b) 20 ft c)24 ft d) 32 ft

John weighs twice as much as Marcia.
Marcia’s weight is 60% of Bob’s weight.
Lee weighs 90% of John’s weight. Which
of these four persons weighs the least?
a) John b) Bob c) Marciad) Lee

A square is divided into 49
smaller squares. How many
rectangles are there(including
the squares)?
a) 343 b)686 c)784 d)441

A train can travel 20% faster than a car. Both
start from a point A at the same time and reach
point B 75 Km away from A at the same time.
On the way however, the train lost about 12.5
mins while stopping at stations. Find the speed
of the car in Km/hr.
a) 50 Kmph b)55 Kmph
c) 60 Kmph d)65 Kmph

There are 10 lamps in a hall. Each
one of them can be switched
independently. The number of ways
in which the hall can be illuminated
is:
a) 1024 b)1023 c) 100 d) 10!

Two men undertake to do a piece of work
for Rs.200. One alone can do it in 6 days,
the other in 8 days. With the help of a boy
they finish it in 3 days. How much is the
share of the boy?
a)Rs.45 b) Rs.40 c)Rs.30 d) Rs.35

A man walks up a stalled escalator in 90
seconds. When the escalator is moving it
takes him 30 secs to walk up. If he were
to stand in escalator it would take him in :
a) 60 secs b)30 secs
c) 45 secs d) 75 secs

Ten persons are arranged in a row the
number of ways of choosing 4
persons so that no two persons sitting
next to each other are selected is:
a) 35 b) 40 c)42 d) 48

There are 30 socks in a drawer. 60% of
the socks are red and the rest are blue.
What is the minimum number of socks
that must be taken from the drawer
without looking, in order to be certain that
atleast 2 blue socks have been chosen?
a) 15 b) 18 c) 20 d)12

Given 80 coins out of each 79 are of equal
weight and one with more weight. Using a
balance with two pans and without
standard weights, in how many
measurements can the odd one can be
taken out?
a) 3 b) 4 c) 6 d) 7

On an item a company gave 25%
discount and gained 25%. If it
allows only 10% discount then
what will be its profit?
a) 30% b) 40%
c) 50% d) 62.5%

A college schedules lectures of 9
professors, 3 professors every day, till
all combination are exhausted. No
combination of professors is ever
repeated in any day. How many days
will each professor has to come?
a) 28 b) 30 c)84 d) 72

A cylindrical hole 6cm long has been
drilled through the centre of a solid
sphere. What is the volume of the
remaining sphere?
a) 36π cm3 b) 6π cm3
c) 216π cm3 d) data insufficient

Jack and Jill are playing cards for a
stake of Rs.10 a game. At the end of
the evening Jack has won 3 games
and Jill has won Rs.30. How many
games did they play?
a) 6 b) 9 c) 12 d) 15

In an octagon, how many triangles using the
vertices of the octagon can be formed such that
only one side of the triangle is the same as one
side of the octagon?
a) 48 b) 28 c) 32 d) 36

If 11 cuts are made along the edges of a
cube find the number of ways in which
the cuts can be made.
a) 29 b) 22
c) 16 d) 13

The difference between the ages of two of
my three children is 3. My eldest child is 3 times older
than my youngest child and my eldest child’s age is 2
years more than the ages of my two youngest children
added together. How old is my eldest child ?
A) 12 B) 13 C) 10 D) 15

X is 6 years younger to Y. After 5 years,
the ratio of ages of X and Y will be 1:2. Now, X’s
father is 20 years older to Y and Y’s father is 30 years
more than X. What is the age of X and Y together ?
A) 6 B) 8 C) 12 D) 18

The ratio between the ages of two suspects
is 6:5 and the sum of their ages is 66 years. After how
many years will the ratio be 8:7 ?
A) 11 B) 12 C) 6 D) 7

Peter is twice as old as Paul was when
Peter was as old as Paul is now. The combined age of
Peter and Paul is 42 years. How old is Peter now ?
A) 18 B) 21 C) 24 D) 26

6 persons standing in the queue for a movie
are wearing different coloured shirts. All of them
belong to different age groups. After two years their
average age will be 43. A seventh person joined with
them, hence the current average age has become 45.
Find the age of seventh person.
A) 67 B) 69 C) 72 D) 74

The citizens of planet nigiet are 8 fingered
and have thus developed their decimal system in base
8. A certain street in nigiet contains 1000 (in base 8)
buildings numbered 1 to 1000. How many 3s are used
in numbering these buildings ?
A) 192 B) 102 C) 64 D) 54

After the typist writes 12 letters and
addresses 12 envelopes, she inserts the letters
randomly into the envelopes (1 letter per envelope).
What is the probability that exactly one letter is
inserted in an improper envelope ?
(a) (b) (c) (d) 0
12
1
12
5
12
11

A circular dart board of radius 1 foot is at a
distance of 20 feet from you. You throw a dart at it
and it hits the dart board at some point Q in the circle.
What is the probability that Q is closer to the centre of
the circle than the periphery ?
A) ¼ B) ½ C) ¾ D) ⅓

A sheet of paper has statements numbered
from 1 to 40. For each value of n from 1 to 40, statement n
says “Exactly n of the statements on this sheet are false.”
Which statements are true and which are false ?
A) All statements are false
B) The odd numbered statements are true and the
even numbered statements are false
C) Second last statement is true and the remaining
statements are false
D) The even numbered statements are true and the
odd numbered statements are false

Given 3 lines in the plane such that the
points of intersection form a triangle with sides of
length 20, 20 and 30. The number of points
equidistant from all the three lines is
A) 0 B) 1 C) 2 D) 4

Anoop managed to draw 6 circles of equal
radii with their centres on the diagonal of a square
such that the two extreme circles touch two sides of
the square and each middle circle touches two circles
on either side. Find the ratio of the side of the square
to the radius of the circle ? ( = 1.4)
A) 9:1 B) 6.2:1 C) 10.4:1 D) 7.6:1
2

10 suspects are rounded by the police and
questioned about a bank robbery. Only one of them is
guilty. The suspects are made to stand in a line and
each person declares that the person next to him on his
right is guilty. The rightmost person is not questioned.
Which of the following possibilities are true ?
(1) All suspects are lying
(2) The leftmost suspect is guilty
(3) The rightmost suspect is guilty
A) 1 only B) 3 only C) 1 and 2 D) 1 and 3

24 programmers take 24 minutes to write
24 lines of code in total. How many programmers will
write 72 lines of code in 72 minutes ?
A) 72 B) 24 C) 48 D) 216

There is a pie to be divided among 20
people. A man eats 3 pieces, a woman eats 2 pieces
and a child eats half a piece of pie. Find the number of
men, women and children so that they are 20 people
in total and every one gets some pie. There are 20
pieces of pie in all.
A) 1 m 5 w 14 c B) 2 m 4 w 14 c
C) 1 m 3 w 16 c D) 3 m 5 w 12 c

There are 30 cans out of them one is
poisoned. If a person tastes very little of this, he will
die within 14 hours. So they decided to test it with
mice. Given that a mouse dies in 24 hours and you
have 24 hours in all to find out a poisoned can, how
many mice are required to find the poisoned can ?
A) 5 B) 6 C) 15 D) 29

5 digit numbers are formed using the digits
1, 2, 3, 4 and 5 without repetition. The probability that
a number so formed is divisible by 6 is
A) 0.2 B) 0.4 C) 0.6 D) 0.8

A bag contains 20 yellow balls, 23 green balls,
27 white balls. What is the minimum number of balls one
should pick out so that to make sure that he gets at least
two balls of all colours ?
A) 48 B) 52 C) 60 D) 68

If Arun buys only pens costing Rs. 13 each
or only pencils costing Rs. 5 each, he is left with Rs.
2 in each case. Which of the following cannot be the
amount available with him ?
A) 457 B) 782 C) 577 D) 1042

A father with 8 children takes 3 at a time to
the botanical garden as often as he can without taking
the same three children together more than once. How
often will he go and how often will each child go ?
A) 56, 35 B) 56, 21 C) 56, 42 D) 112, 42

John buys a cycle for 31 dollars and gives a
cheque for 35 dollars. The shopkeeper exchanges the
cheque with his neighbour and gives the change to
John. After 2 days the cheque bounces and the
shopkeeper is forced to pay the cheque amount to his
neighbour. The cost price of the cycle is 19 dollars.
What is the loss incurred by the shopkeeper ?
A) 23 B) 35 C) 19 D) 31

Dwarf lies on Mondays, Tuesdays and
Wednesdays, and tells the truth on the other days of
the week. Byte, on the other hand, lies on Thursdays,
Fridays and Saturdays, but tells the truth on the other
days of the week. Now they make the following
statements :
Dwarf : Yesterday was one of those days when I lie
Byte : Yesterday was one of those days when I lie
What days is it ?
A) Sunday B) Monday C) ThursdayD) Saturday

How many 3 digit numbers have even
number of factors ?
A)21 B) 22 C) 878 D) 879

On the planet Ozone, there are 36 hours in
a day and each hour has 90 minutes, while each
minute has 60 seconds. As on Earth, the hour hand
covers the dial twice every day. Find the approximate
angle between the hands of clock on Ozone, when the
time is 12:40.
A) 79 B) 89 C) 111 D) 251

If 29th February 2004 was a Sunday, which
month starts with a Sunday in that year ?
A) August B) September C) October D) November

A hollow cube of size 5 cm is taken with a
thickness of 1 cm. It is made up of smaller of cubes of
size 1 cm. If the four faces of the outer surface of the
cube are painted, totally how many faces of the small
cubes remain unpainted ?
A) 575 B) 538 C) 488 D) 500

There are two water tanks A and B, A is
much smaller than B. While water fills at the rate of
one litre every hour in A, it gets filled up like 10, 20,
40, 80 and so on… litres in tank B.(at the end of first
hour B has 10 litres, second hour it has 20 and so
on…). If tank B is 1/32 filled after 12 hours, what is
the total duration required to fill it completely ?
A) 16 B) 17 C) 20 D) 21

How many 9 digit numbers can be formed
using the digits 1, 2, 3, 4, 5 (but with repetition) that
are divisible by 4 ?
A) 390625 B) 198562 C) 156025 D) 300625

24 people meet and shake hands in a
circular fashion. The size of the smallest set of people
such that the rest have shaken hands with at least one
person in the set is :
A) 7 B) 8 C) 12 D) 11

The diameter of spherical coins should be
at least 128 mm and not exceed 512 mm. Given a
coin, the diameter of the next larger coin is at least
50% greater. The diameter of the coin must always be
an integer. You are asked to design a set of coins of
different diametres with these requirements and your
goal is to design as many coins as possible. How
many coins can you design ?
A) 3 B) 4 C) 5 D) 6

The pace length P is the distance between
the rear of two consecutive foot prints. For men, the
formula N/P = 150 gives an approximate relationship
between N and P where N = number of steps per
minute and P = pace length in metres. Bernard knows
his pace length is 152 cm. The formula applies to
Bernard’s walking. Calculate Bernard’s walking speed
in kmph.
A) 207.936 B) 27.72 C) 228 D) 20.794

Amir and Babu play the following coins-on-a-stack game. 50
coins are stacked one above the other. One of them is a special(gold)
coin and the rest are ordinary coins. The goal is to bring the gold
coin to the top by repeatedly moving the topmost coin to another
position in the stack. Amir starts and the players take turns. A turn
consist of moving the coin on the top to a position i below the top
coin(0 ≤ i ≤ 50). We will call this an i-move. The proviso is that an i-
move cannot be repeated. If the gold coin happens to be on top when
it’s a player’s turn, then the player wins the game. Initially, the gold
coin is the third coin from the top. Then
A) In order to win, Amir’s first move should be a 0-move
B) In order to win, Amir’s first move should be a 1-move
C) In order to win, Amir’s first move can be a 0-move or1-move
D) Amir has no winning strategy

Given a collection of points P in the plane,
a 1-set is a point in P that can be separated from the
rest by a line; i.e., the point lies on one side of the line
while the others lie on the other side. The number of
1-sets of P is denoted by n1(P). The minimum and
maximum values of n1(P) over all configurations P of
30 points in the plane are :
A) 2, 30 B) 3, 30 C) 1, 29 D) 2, 29

There are two boxes, one containing 11 red
balls and the other containing 15 green balls. You are
allowed to move the balls between the boxes, so that
when you choose a box at random and a ball at
random from the chosen box, the probability of
getting a red is maximized. This maximum probability
is :
A) 0.70 B) 0.30 C) 0.25 D) 0.50

It is rumoured that in a match between two
teams A and B, Paul fix A with the same probability as
A’s chances of winning. Let’s assume such rumours to
be true and that in a match between India and
Pakistan, India the stronger team has a probability of
5/9 of winning the game. What is the probability that
Paul will correctly pick the winner of the India-
Pakistan match.
A) 0.46 B) 0.49 C) 0.51 D) 0.52

If there are 10 rounds played in a knock-out
tournament, how many matches were played ?
A) 1000 B) 1024 C) 1025 D) 1023

A school yard contains only bicycles and
four wheeled wagons. On Tuesday, the total number
of wheels in the school yard was 166. What could be
the possible number of bicycles ?
A) 14 B) 12 C) 10 D) 11

Alok and Banu play the following min-max game. Given
the expression N = 12 + X * (Y – Z), where X, Y and Z are
variables representing single digits (0 to 9). Alok could like to
maximize N, while Banu would like to minimize it. Towards
this end, Alok chooses a single digit number and Banu
substitutes this for a variable of her choice(X, Y or Z). Alok
then chooses the next value and Banu, the variable to substitute
the value. Finally Alok proposes the value for the remaining
variable. Assuming both play to their optimal strategies, the
value of N at the end of the game would be :
A) 30 B) 12 C) 20 D) 23

A hare and a tortoise race along a circle of
100 yards diameter. The tortoise goes in one direction
and the hare in the other. The hare starts after tortoise
has covered 1/5 of its distance and that too leisurely.
The hare and tortoise meet when the hare has covered
only 1/8 of the distance. By what factor should the
hare increase its speed so as to tie the race ?
A) 5 B) 8 C) 37.8 D) 40

A person drives with constant speed and
after sometime he sees a milestone with two digits.
Then travels for one hour and sees the same two digits
in reverse order. One hour later he sees that the
milestone has the same two digits with a 0 between
them. What is the speed of the car ?
A) 27 B) 36 C) 45 D) 54

There are five pentagonal pyramid shaped bottles
whose volumes are in geometric progression and there are 5
materials to make a perfume inside the bottle viz. Lilac,
Balsalmic, Lemon, Woody and Mimosaic. Also all the faces of
the pyramids are painted in different colours. To make a
perfume that is in demand, the following conditions are to be
followed : Lemon and Balsalmic go together. Woody and
Mimosaic go together. Woody and Balsalmic never go together.
Lilac can be added with any material. All of the following
combinations are possible to make a perfume EXCEPT :
A) Balsalmic and Lemon
B) Woody and Lilac
C) Mimosaic and Woody
D) Mimosaic and Lemon

Five men and five women meet and the
men dance with the women. Which of the following
are always true ?
(1) There are two men who have danced with the
same number of women
(2) There are two women who have danced with
same number of men
A) Both 1 and 2 B) 1 only
C) 2 only D) Neither 1 nor 2

There are ten reading spots in a reading
room. Each reading spot consists of a round table with
four chairs placed around it. There are some readers
such that in each occupied reading spot there are
different numbers of readers. If in all, there are 10
readers, how many reading spots are empty ?
A) None B) 6 C) 5 D) 4

A taxi driver commenced his journey from
a point and drove 10 km towards north, and turned to
his left and drove another 20 km. After waiting to
meet a friend, here he turned to his right and
continued to drive another 50 km. In which direction
is he now ?
A) North B) South C) East D) West

Three boys John, Tom and Oliver and two
girls Rachel and Kim are to be seated in a row. Rachel
always sits to the left of John. No girl sits at the
extreme positions and at the middle position. Tom
always sits at the extreme positions. Who sits to the
right of Kim ?
A) Oliver B) Tom C) John D) Tom or Oliver

The teams participating in a world cup tournament
have been divided into two groups of nine teams each.
Each team in a group plays the other teams in the group.
The top two teams from each group enter the semi finals;
after which the winner is decided by knock-out. The
probability that India wins a match is 2 out of 3. In order
to qualify for the semi finals, it is sufficient for India to
win 7 of its group matches. What is the probability that
India will win the world cup ?
A) (2/3)10 B) (2/3)9 x (8/3)
C) (2/3)9 x (1 + (8/3)) D) (2/3)10 + (2/3)9 x (8/3)

1) If 102101=210212 then
112112=?
2) If 102101=200111 then
112112=?
3) If 102101=101201 then
112112=?

4)A four digit number when
multiplied by 4 gets reversed . Find
that number .
ANS: 2178
5)A five digit number when
multiplied by 4 gets reversed . Find
that number.
ANS: 21978

6(a) A four digit number when
multiplied by 9 gets reversed.
Find that number.
Ans:1089
6(b) How many four digit
numbers are there which when
multiplied by 7 will get the
digits reversed?
Ans: Nil

7) 3 , 6 , 13 , 26 , 33 , 66 , ____
a)73 b)43 c)63 d)86
Ans: 73

8) 4 , 9 , 25 , 49 , ______
a)64 b)121 c)81 d)145
Ans: 121

9)In a two dimensional array , X(9,7)
with each element occupying 4
bytes of memory , with the address
of the first element X(1,1) is 3000
,find the address of X(8,5).
a)3040 b)3216 c)3212 d)3124
Ans: 3212

10) There are 150 weights . Some are
1 Kg weights and some are 2 Kg
weights . The sum of the weights is
260 Kg . What is the number of 1 Kg
weights?
a)40 b)60 c)48 d)80
Ans: 40

11)5 men or 8 women do equal
amount of work in a day . A job
requires 3 men and 5 women to
finish the job in 10 days. How
many women are required to
finish the job in 14 days?
(c) 6 days (d) 8 days
Ans: 7 days

12)In an objective test , for a
correct answer 4 marks are
added and for a wrong answer
2 marks are subtracted. A
student scores 480 marks
from 150 questions . How
many answers are correct?
Ans: 130

13)What number should be
added to or subtracted from
each term of the ratio 17:24 so
that it becomes 1:2?
Ans: 10

14) The average age of 10
members of a committee is the
same as it was 4 years ago ,
because an old member has
been replaced by a young
member . Find how much
younger is the new member
than the old member?
Ans: 40

15)A farmer has a square plot
which he wants to fence . This
plot requires 29 poles for each
side . Then what is the total
number of poles used for the
entire plot?
Ans: 112

16)Three containers A , B and C
have volumes a , b and c
respectively; and container A is full
of water while the other two are
empty. If from container A water is
poured into container B which
becomes 1/3 full , and into
container C which becomes 1/2 full
, how much water is left in the
containerA?
Ans: a-b/3-c/2

17)I ate 100 apples in the last 5
days . Each day I ate 5 more
than the day before . How many
did I eat 2 days ago?
Ans: 25

18)A and B can finish a piece of
work in 20 days . B and C in 30
days and C and A in 40 days . In
how many days will A alone can
finish the work?
Ans: 48

19)The difference of a number
and its square is 1260 . What is
that number?
Ans: 36

20)If the letters of the word
“rachit” are arranged in all
possible ways and these words are
written out as in a dictionary,
what is the rank of the word
“rachit”?
Ans: 481

21)How long will a train 100
metre long , travelling at
72Kmph take to overtake
another train 200 metre
travelling at 54Kmph?
Ans: 1 minute

2 @ @ ! 7 does not
3 @ @ !occur in this multiplic-
----------------- !ation . Complete the
5 @ @ !multiplication
@ 6 @ !
@ @ 3 !
-------------------------- !
@ @ @ @ @ !
----------------------------------- !
Ans: 281x 322

23)A beggar collects cigarette
stubs and makes one full
cigarette with every 7 stubs.
Once he gets 49 stubs. How
many cigarettes can he smoke
totally ?
Ans: 8

24)The seven digits in this subtraction problem are 0 , 1 ,
2 , 3 , 4 , 5 and 6. Each letter represents the same digit
whenever it occurs.
D A D C B
E B E G
--------------------------
B F E G
---------------------------
What digit does each letter represent?
Ans: 12106-5653=6453.

25)One monkey climbs a pole at
the rate of 6metre/minute and
slips down 3metre in the
alternate minute . Length of the
pole is 60 metre . How much
time it will take to reach the
top?
Ans: 37 minutes.

26)A person is travelling from A to B
and his friend is travelling from B to
A. The person started at noon from A
to B and his friend started at 2.00 p.m
from B to A. They both met at five
minutes past 4.00 p.m. They both
reach the destination at the same time
. At what time will they reach the
destination?
Ans: 7.00 p.m.

27)A train after running for one
hour blasted something and runs
with 3/5th of its original speed and
reaches the destination two hour
late . If the blast had occurred 50
miles ahead it would have reached
the destination 40 minute sooner .
Determine the total distance
travelled.
Ans: 200 miles.

28)The diameter of the driving
wheel of a bus is 1.40 metres .
How many revolutions per
minute must the wheel make in
order to keep a speed of 66
Kmph?
Ans:250.

29)What is the number of ending
zero’s in the product of numbers
from 1 to 100?
Ans:24.

30)The length of a rectangle is
reduced by 4 meter and the
breadth is increased by 3 meter.
Then the resultant square’s area
is equal to the area of the
rectangle . Find the perimeter of
the rectangle.
Ans:2x(16+9)=50 metre.

31)A person tells a secret to two
other persons in 5 minutes .
How long will it take to tell the
secret to 728 people?
Ans:30 minutes.

32)Mr. A meets Mrs. B .Mr. B has
a daughter and a son . Son is
Moti and is married and has a
son . Mrs. Moti is Mr. A’s
mother . How is Mr. A related to
Mr. B?
Ans:Grand son.

33) 50 coins are placed on a table.
All show head. Flipping exactly
4 coins is one operation. In how
many operations will all show
tail?
Ans:13.

34)A beats B by 20 meter, while C
beats B by 40 meter in a 100
meter race . By how much can C
beat A?
Ans:25 metre.

35)A cube is of size 5*5*5 . Every
face has been coloured . It is
divided into 125 equal parts .
a)what is the number of parts
having only one face coloured?
b)what is the number of parts
having two faces coloured?
c)what is the number of parts
having no face coloured?
Ans:6x9=54; 12x3=36; 27.

36)If you start your journey 30
minutes late you have to
increase your speed by 250
Kmph to cover up 1500 Kms in
the same time . What is your
usual speed?
Ans:750 km/hr.

37) The length and the breadth of
a rectangle are increased by
20% and 25% respectively. Its
area will increase by how much
percentage?
Ans:20+25+20x25/100=50%

38)A man sells a product at 10%
discount and still earns a profit
of 10% . If the marked price of
the product is Rs.330/- what is
his buying price?
Ans:110:90=330:?. ?=270.

39) Given an accurate two pan
balance and twelve coins of identical
appearance. Of these one is
defective, but it is not known how its
weight compares with that of a
normal coin: it could be heavier or
lighter. What is the least number of
weighings needed to identify the
defective coin and also the nature of
its defect?

40)A cyclist got his tyre punctured
when he had covered two third of
the distance to be covered .
Finishing on foot , he takes twice
the time taken before to reach the
destination . How fast does he ride
than walking?
Ans:4 times as fast as walking.

41)The quarter of the time from
midnight to present time added
to the half of the time from the
present to midnight gives the
present time . What is the
present time?
Ans:9.36 a.m.

42)There is a number when
divided by 5 gives a remainder 3
and when divided by 7 gives a
remainder 5 . Find the least
such number .
Ans:33.

43)Find the number in the series
1 , 2 , 3 , 8 , __, 224.
Ans:27.

44)A bag contains 20 yellow balls,
10 green balls, 5 white balls, 8
black balls and 1 red ball. What
is the minimum number of balls
one should take, to make sure
that he gets at least two balls of
the same colour ?
Ans:6.

45)Two trains each 1/6 mile in
length run in opposite directions
to each other with equal speed
of 60 miles/hour . What is the
time taken to completely cross
over the two trains?
Ans:10 seconds.

46)If A, B, C, D, E, F, G, H, I represent the
digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 in some order
and if A+B+C= 13, C+D+E= 13,
E+F+G = 13 and G+H+I = 13, find the value
of E?
Ans: E = 4

47)How many squares with sides
1/2 inch long are needed to
cover a rectangle that is 4 ft long
and 6 ft wide?
Ans:13824.

48)Two boats start from opposite banks
of river perpendicular to the shore. One
is faster than the other. They meet at
720 yards from one of the ends. After
reaching opposite ends they rest for 10
minutes each. After that they start
back. This time on the return journey
they meet at 400 yards from the other
end of the river. Calculate the width of
the river.
Ans:1760 yards.

49)There are 12 consecutive flags
at an equal interval of distance .
A man passes the 8th flag in 8
seconds . How many more
seconds he will take to pass the
remaining 4 flags?
Ans: 7
4
4

50)A man covered 28 steps in 30
seconds . Next time he decided
to move fast and covered 34
steps in 18 seconds . How many
steps are there on the escalator
when it is stationary?
Ans: 43

51) “How old are your three daughters?” Fred asked a
friend one day.
“The product of their ages is 36”, replied his friend.
“You are not giving me enough information” protested
Fred.
“The sum of their ages is the age of your oldest son”
“I still need more information”
“All right, then, I can tell you that the eldest daughter,
who is atleast a year older than the other two, is a very
fine pianist”.
“Ah! Now I know how old your daughters are”.
What are the ages of Fred’s friend’s daughters?
Ans: 9, 2, 2.

52) Four athletes Ann, Bea, Carol and Dorothy went out one
morning and ran a race.
At the end of the race, the following statements were made:
Ann : “I didn’t come in first or last”.
Bea : “I didn’t come in last”.
Carol : “I was first”.
Dorothy : “I was last”.
It is known that one, and one only, of the four athletes is
lying. Who won the race?
Ans: Bea

53) Four brother’s go to a dance.
As they leave, each one of the brothers accidentally takes a
hat belonging to another brother and a coat belonging to
another different brother.
Maurice takes the coat belonging to the brother whose hat
got taken by Phil, while Phil’s coat got taken by the brother
who took Maurice’s hat.
Serge took John’s hat. Whose coats and hats were taken by
Maurice and Phil?
Ans: S, P and J, S

54) An international school has 250
students, each of whom speaks
several languages. For any pair of
students, say A and B, there is one
language that A speaks that B
doesn’t and another language that B
speaks but A doesn’t. What is the
minimum number of different
languages spoken in the school?

55) Eleven theatre groups took part in a
festival. Everyday some of the groups
put on their plays while the others
watched. When the festival was over it
was possible to affirm that each one of
the groups had been able to attend,
atleast once, the performance of each of
the other groups. What is the minimum
number of days that the festival lasted?

56) Three sisters Marcia, Jan and Cindy
went into a shop.
Marcia bought four pastries, a
chocolate bar and ten mints all for
$1.69.
Jan bought three pastries, a chocolate
bar and seven mints and paid $1.26.
How much did Cindy pay in total for
one pastry, one chocolate bar and one
mint?

57) A barrel is full of water. All the water
in a barrel is put in equal quantities
into three buckets of different sizes.
When the operation has been completed
it is noted that the first bucket is half-
full, the second is two-thirds full, while
the third is three-quarters full. If the
capacity in gallons of the barrel and
each of the buckets is a whole number,
what is the minimum capacity of the
barrel?

58(a) How to express 64 using
only two fours and any
combination of arithmetical
signs?
58(b) How to express 20 using
only two threes and any
combination of arithmetical
signs?

59) In a school there are 158
students. Although there are
more girls than boys, only 1/11 of
the girls wear glasses, while 1/7
of the boys wear them. How
many boys and how many girls
are there in the school?

60) Solve the following cryptarithms
JUNE + JULY = APRIL
THREE + THREE + FOUR = ELEVEN
CROSS + ROADS = DANGER
FLY + FOR + YOUR= LIFE
ACID + BASE = SALT + H20
SEND + MORE = MONEY
TWO TIMES TWO EQUALS THREE

61) I have twelve envelopes
numbered 1 through 12 and
twelve cards numbered 110
through 121. Can I place one
card inside each envelope so
that the number in the envelope
divides the number on the card
inside it?

62) Take any positive whole number not
greater than 50. If the number is even,
divide by 2. If the number is odd multiply
it by 3 and add 1 to the result. Apply the
same method to the resulting number, and
continue in this way forming a chain of
numbers until you finally arrive at the
number 1. Of the numbers not greater
than 50, which takes the longest to reach
the number 1?

63) A certain whole number
whose last digit is 7, has the
curious property that in order
to multiply it by 7, all that
needed is to take the 7 from its
right end and place it at the
beginning. What is the number?

64) The number of digits used to
number the pages of a book is
exactly a multiple of the number
of pages in the book. The book
contains over 1000 pages but
fewer than 10,000. Exactly how
many pages does it contain?

65) There are 100 marbles in five bags.
If the first and second bag contains
between them 52 marbles, the second
and third together contains 43, the
third and fourth contain 34, and the
fourth and fifth contain 30 marbles,
how many marbles are there in each
bag?

66) I had some Coconuts in a basket for
sale. A customer came and asked half
of the coconuts plus half a coconut with
the condition that no coconut should be
broken or cut. I gave him. The second
customer came and he also bought
coconuts in the same manner.
Altogether six customers came and they
bought coconuts in the same
manner. Two coconuts were left in
the basket. How many coconuts did I
have for sale?

67) A group of boys and girls are
playing. 15 boys leave. There
remain two girls for each boy.
Then 45 girls leave. There
remain five boys for each girl.
How many boys were there in
the original group?

68) Zita, her brother, her daughter and her
son are tennis players. As a game of
doubles is about to begin:
Zita’s brother is directly across the net
from her daughter.
Her son is diagonally across the net from
the worst player’s sibling.
The best player and the worst player are
on the same side of the net.
Who is the best player?

69) A father had three sons. He brought some apples.
He ate one apple and divided the remaining into three
equal parts and placed it on the dining table . The first
son took one share and kept it in his room. Further he
took one apple from the two shares and ate it. He then
divided the remaining into three equal parts. The second
son came, took one share for him, ate one apple from the
two shares and divided the remaining apples into three
equal parts. The third son also acted like the first two
sons. Again the father came. He took one share. He ate
an apple from the remaining two shares. But he could
not divide the remaining into three equal parts. Find the
minimum number of fruits that the father first brought
to home.

70) Four men- Aaron, Barry, Colin and David and four women-
Marie, Norma, Olive and Pearl attended a wedding. One of
the four men married one of the four women.
If Aaron did not get married and if Marie did not get
married, then Olive got married.
If Aaron did not get married and if Norma did not get
married, then Barry got married.
If Barry did not get married and if Olive did not get married,
then Colin got married.
If Colin did not get married and if Norma did not get
married, then Marie got married.
Who got married?

71) The owner of the mansion has been murdered.
The visitors to the mansion were Allen, Bixby and Crain.
The murderer, who was one of the three visitors, arrived
at the mansion later than atleast one of the other two
visitors.
A detective, who was one of the three visitors, arrived at
the mansion earlier than atleast one of the other two
visitors.
The detective arrived at the mansion at midnight.
Neither Allen nor Bixby arrived at the mansion after
midnight.
The earlier arriver of Bixby and Crain was not the
detective.
The later arriver of Allen and Crain was not the
murderer.
Who was the murderer?

72) A says to B, on the occasion of
their common birthday:
“When I reach your age you will be
three times as old as I was, when
you were my age now. But don’t
feel too bad about it; we really are
the youngest we could be under the
circumstances.”
How old are A and B?

73) A says to B, “If I were your
age, I would be three times as
old as I am”. B replies, “Yes,
and if I were as old as you are, I
would have to wait 15 years to
be half as old as I am now”
How old are they?

74) The combined ages of reena
and seena are 64 years and
reena is twice as old as seena
was when reena was half as old
as seena will be when seena is
three times as old as reena was
when reena was three times as
old as seena.
How old is reena?

75) The hour hand and the
minute hand of a clock are
exactly on minute divisions of
the clock face and the minute
hand is exactly 13 minute
divisions ahead of the hour
hand.
What is the exact time?

76) Write down a ten digit number
satisfying the following:
The digit in the highest place
value is equal to the number of
zeros in the whole number. The
next digit is equal to the number of
ones in the number. Continue in
this manner until you have filled in
the complete ten digit number.

77) A magician has one hundred cards numbered 1
to 100. He puts them into three boxes a red one, a
white one and a blue one, so that each box
contains atleast one card. A member of the
audience selects two of the three boxes, chooses
one card from each and announces the sum of the
numbers on the chosen cards. Given this sum, the
magician identifies the box from which no card
has been chosen.
How many ways are there to put all the cards into
the boxes so that this trick always work?

78) A says, “ The horse is not
black”
B says, “ The horse is either
brown or grey”.
C says, “ The horse is
brown”.
Atleast one is telling truth
and atleast one is lying. Tell the
colour of the horse.

79) There are some fruits in a
basket. The first customer buys
half of the fruits. The second
customer buys one-third of the
remaining, the third customer buys
one fourth of the remaining and so
on and the nineth customer buys
one-tenth of the remaining. There
are 252 fruits remaining in the
basket. How many fruits are there
in the beginning?

80) Four persons A,B,C,D are sitting
around a round table. Each has some
money. They play a three round game. A
starts the game. He gives to B,C, and D,
the same amount that each has. Then B
gives to A,C and D, the same amount that
each has now. Then C gives to A,B and D,
the same amount that each has now. At
the end of this game each member has
Rs.32. How much money does each have
at the beginning?

81) A pilgrim wants to offer 5
coconuts to the main deity of a
large temple. To reach the main
deity at the sanctum sanatorium,
the pilgrim has to pass through 10
gates. At each gate he has to offer
one coconut for each bag he carries.
Each bag can hold only ten
coconuts. How many coconuts
should he carry from the main
gate?

82) A test has 50 questions. A
student scores 1 mark for a
correct answer, -1/3 for a wrong
answer and –1/6 for not
attempting a question. If the
net score of a student is 32, the
number of questions answered
wrongly, by that student cannot
be less than______

83) My house has a number. If my
house number is a multiple of 3,
then it is a number from 50
through 59. If my house number is
not a multiple of 4, then it is a
number from 60 through 69. If my
house number is not a multiple of 6,
then it is a number from 70
through 79. What is my house
number?

84) I live in a long street. Numbered
on the side of my house are the
houses one, two, three and so on.
All the numbers on one side of my
house add up to exactly the same as
all the numbers on the other side of
my house. There are more than 50
houses on that side of the street but
not so many as 500.
find my house number.

85) There are 100 ballot boxes in a
room and there are 100 men. All
the boxes are closed. The first man
opens all the boxes. The second
man closes every second box. The
third man changes the state of
every third box and so on. Finally
the 100th man changes the state of
the 100th box. How many ballot
boxes are opened?

86) You are given 100 coins of which
one is having less weight and all
others are of equal weight.You are
given a balance without standard
weight. In how many weighing can
the false coin be taken out?

87)Find the least number of standard
weights necessary to weigh any
integral weight from 1 to 121 kg,
a)When the weights are put in one
pan only
and
b)When the weights can be placed
in either pan.

88) There is a false balance. When a
standard weight of 1 kg is placed in the
left pan, we have to place 12 apples in
the right pan to balance it. When the
standard weight of 1 kg is placed in the
right pan, we have to place 8 apples in
the left pan to balance it. If each apple
is of the same weight, what is the weight
of each apple?

89) Sam and Mala have a
conversation. Sam says, “I am
certainly not over 40”. Mala says,
“I am 38 and you are atleast 5 years
older than me”. Now Sam says,
“You are atleast 39”. All the
statements by the two are false.
How old are they really?

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