Amcat 2
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The document provides a summary of topics covered in the AMCAT Quantitative Ability section of the exam, including: - Numbers: decimals, fractions, factorization, HCF, LCM - Word problems: algebra applied to rates, proportions, profit/loss, percentages, ages - Probability: permutation, combination, counting principles - Algebra: powers, logarithms, word problems involving speed, time, distance, mixtures - Several examples are provided to illustrate concepts like divisibility, proportions, averages, permutations, exponents.
Amcat 2
- 1. AMCAT 2
- 2. AMCAT QUANTITATIVE ABILITY BASIC NUMBERS • Decimals & Fractions • Factorization • HCF & LCM WORD PROBLEMS • Application of algebra to real world • Direct and Inverse Proportion • Profit/Loss Percentage Age Probability • Permutation & Combination Factorial Notation • Principles of counting P&C with repetition, restriction & counting • Probability Addition, Multiplication Law, Events Dependent, Independent, exclusive events Power Basic Algebra Divisibility Common Applications Speed–time–distance Relations Mixtures • Fractional and Negative powers Graphical, Intuitive, Understanding • Logarithm/antilog definition and properties Word Problems Mixed with Algebra
- 3. DECIMALS & FRACTIONS • 892.7 - 573.07 - 95.007 =? • i) 224.623 • Choice 1. ii) 224.777 iii) 233.523 iv)414.637
- 4. FRACTIONS
- 5. FRACTIONS
- 6. DIVISIBILITY • What least number be added to 5200 to get a number exactly divisible by 180? (1) 160 (2) 60 (3) 20 (4) 180 • 180 = 5 X 4 X 9. • 5200 – 160 = 5040 DIVISIBLE BY 9,4,5. • 5200 – 60 = 5140 NOT DIVISIBLE BY 9 • 5200 – 20 = 5080 NOT DIVISIBLE BY 9 • 5200 – 180 NOT DIVISIBLE BY 9.
- 7. DIVISIBILITY • A number when divided by 32 leaves the remainder 29. This number when divided by 8 will leave the remainder (1) 3 (2) 5 (3) 7 (4) 29 • Let the number be 32k + 29. • 32k + 29 = 32k + 24 + 5 • 8(4k+3) + 5. • The remainder is 5.
- 8. HCF & LCM
- 9. HCF & LCM • Four different electronic devices make a beep after every 30 minutes, 1 hour, 3/2 hour and 1 hour 45minutes respectively. • All the devices beeped together at 12 noon. • They will again beep together at: • i) 12 Midnight ii) 3 a.m iii) 6 a.m. iv) 9 a.m Interval after which the devices will beep together = (L.C.M. of 30, 60, 90, 105) min. = 1260 min. = 21 hrs. So, the devices will again beep together 21 hrs. after 12 noon i.e., at 9 a.m.
- 10. HCF & LCM
- 11. DIRECT & INVERSE PROPORTION
- 13. PROFIT & LOSS -5 x = - 1000 X = 200
- 14. PERCENTAGE • The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was Rs. 22. Find the amount of the bill. (1) Rs. 1100 (2) Rs. 200 (3) Rs. 2200 (4) Data inadequate • Successive 20% discount means 36% discount. • The difference between 35% and 36% is 1%. • 1% = 22 means the answer is 2200.
- 15. AGE • The average age of A and B is 20 years. If C were to replace A, the average would be 19 and if C were to replace B, the average would be 21. What are the ages of A, B and C? (1) 22, 18, 20 (2) 18, 22, 20 (3) 22, 20, 18 (4) 18, 20, 22
- 16. MIXTURES • Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1:1:2. • If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: • i) Rs. 169.50 ii) Rs. 170 iii) Rs. 175.50iv) Rs. 180
- 17. Since first and second varieties are mixed in equal proportions. So, their average price = Rs. 126 + 135 2 = Rs. 130.50 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. By the rule of alligation, we have: Cost of 1 kg of 1st kind Mean Price Cost of 1 kg of 2nd kind 130.50 153 X X–153 22.50 x - 153 22.50 =1 x - 153 = 22.50 x = 175.50
- 18. PERMUTATION & COMBINATION • In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? • A. 360 B. 480 C. 720 D. 5040 • E. None of these • The word 'LEADING' has 7 different letters. • When the vowels EAI are always together, they can be supposed to form one letter. • Then, we have to arrange the letters LNDG (EAI). • Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways. • The vowels (EAI) can be arranged among themselves in 3! = 6 ways. • Required number of ways = (120 x 6) = 720.
- 19. FACTORIAL NOTATION • What is the highest power of 5 that divides 90 x 80 x 70 x 60 x 50 x 40 x 30 x 20 x 10? • i) 10 ii) 12 iii) 14 iv) None of these • We should find out the highest power of 5 that divides 9! X 109 = 9! X 59 x 29. • The highest power of 5 which divides 9! Is 1. • Hence the answer is 10.
- 21. PERMUTATION & COMBINATION WITH RESTRICTIONS • In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? • A. 159 B. 194 C. 205 D. 209 • E. None of these • We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys). • Required number of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4) = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2) = (24 + 90 + 80 + 15) = 209.
- 22. PERMUTATIONS
- 23. • How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? • A. 5 B. 10 C. 15 D. 20 Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. Required number of numbers = (1 x 5 x 4) = 20.
- 25. NEGATIVE POWERS • What is the value of 0-10? • i) 0 • 0. ii) 1 iii) -10 iv) None of these
- 26. • • • • 2525 is divided by 24, the remainder is 1) 23 2) 22 3) 1 4) 2 2525 = (24 + 1)25 = 24K + 1. CHOICE 3.
- 27. • Consider the following statements: If a sum of money is lent at simple interest, then the • 1. Money gets doubled in 5 years if the rate of interest is 50/3 %. • 2. Money gets doubled in 5 years if the rate of interest is 20%. • 3. Money becomes four times in 10 years if it gets doubled in 5 years. • Of these Statements: • i) 1 and 3 are correct ii) 2 alone is correct iii) 3 alone is correct iv) 2 and 3 are correct • 2 alone is correct.
- 29. • The unit digit in the expression • ( 36234 x 33512 x 39180) – (5429 x 25123 x 31512) will be • (a) 2 (b) 6 (c) 8 (d) 4
- 30. ATTENTION TO DETAIL • Follow the directions given below to answer the questions that follow. Your answer for each question below would be: • A. If all the THREE items given in the question are exactly ALIKE • B. If only the FIRST and SECOND items are exactly ALIKE. • C. If only the FIRST and THIRD items are exactly ALIKE. • D. If none of the above • • 49 A0067DF667016 A0067DF667016 A0067DF667106 • (a) A (b) B (c) C (d) D • • 50 Janmasthami Janmasthhami Jamnasthami • (a) A (b) B (c) C (d) D •
- 31. • If * stands for +, + stands for -, and - stands for /, then 27/5*8+11-7=? • (a) 141.4 (b)38.4 (c) 16.4 (d)36.1 • • If * stands for -, / stands for +, + stands for / and – stands for *, then which of the following is TRUE? • A)8/12*4+20-8=18.4 B)12*8/4+20-8= -5.6 C)8*4/12+8-8= -12.2 D)8*8/4+20-8= -4 • (a) A (b) B (c) C (d) D • • Identify the correct match 345611242627 • A) 345612414627 B) 345611426227 C)345611624227 D) 345616242227 • (a) A (b) B (c) C (d) D