GRE QUANT- SET THEORY,PERMUTATIONS AND COMBINATIONS
- 1. GRE QUANT SIMILARITY, PERMUTATIONS AND COMBINATIONS, SET THEORY
- 2. D A B C D E F AF=7cm, FD=3 cm AB=5 cm 7 3 5 Find i) A(rectangle ABCD) ii) A(triangle AEF) iii) Length of BD iv) Perimeter of rectangle ABCD Question 1
- 3. 𝑖) 𝐴 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 𝐴𝐵𝐶𝐷 = 𝑙 × 𝑏 = 10 × 5 = 50 𝑠𝑞𝑢𝑎𝑟𝑒 𝑐𝑚 ii) A(∆ 𝐴𝐸𝐹) = 1 2 𝐴𝐹 × ℎ = 1 2 7 × 5 = 17.5 𝑠𝑞𝑢𝑎𝑟𝑒 𝑐𝑚 Height of triangle AEF = width of rectangle ABCD iii) Using Pythagoras theorem, 𝐵𝐷2 = 102 + 52 = 125 BD= 5 5𝑐𝑚 iv) Perimeter = 2( 10 +5) = 30 cm
- 4. Question 2 A row has place for 4 flowers. In how many ways can 6 different flowers be planted The first flower can be planted in 6 ways Second in 5 ways Third in 4 ways Fourth in 3 ways Answer = 6 × 5 × 4 × 3 = 360
- 5. Question 3 If I have 10 books that I haven’t read and I want to take 3 of them, how many possible sets of books can I take This is a selection problem, so we use Combinations We are choosing 3 out of 10 books This can be done in 10𝐶3= 10×9×8 1×2×3 = 120 𝑤𝑎𝑦𝑠
- 6. Question 4 In a class of 15000 students, 1700 take English and Ethics,2200 take Ethics, 9500 take neither. How many are taking English Let A= number of students taking English B = number of students taking Ethics 𝑛 𝐴 ∩ 𝐵 = 1700 n(B)=2200 n(𝐴 𝐶 ∩ 𝐵 𝐶 ) = 9500 𝑛(𝐴 ∪ 𝐵) 𝐶 = 9500
- 7. 𝑛 𝐴 ∪ 𝐵 = 15000 − 9500 = 5500 n(A∪ 𝐵) = 𝑛(𝐴) + 𝑛(𝐵) − 𝑛(𝐴 ∩ 𝐵) 5500=n (A) +2200 – 1700 n(A ) = 5000
- 8. Question 5 In a class of 400 students, 50 take German, 150 take French, 230 do not take any language How many take at least one language We need to remember that at least one is 𝐴 ∪ 𝐵 Let A = number of students who take German B = number of students taking French 𝑛 𝐴 = 50, 𝑛 𝐵 = 150, 𝑛 𝐴 𝐶 ∩ 𝐵 𝐶 = 230 n(𝐴 ∪ 𝐵) 𝐶 = 230 n(A∪ 𝐵) = 400 − 230 = 170
- 9. Question 6 A school offers subjects B,C and D. In a class of 120 students, 70 students take B, 73 take C, 45 take D, 37 take B and C, 20 take B and D, 8 take all 3. 25 take only C, nothing else. How many take only D 25 2 C B C 8 25 37 take B and C and 8 take all 3 12 D 29 73 take C 73-29-8-25= 11 11 45 take D No of students who take only D = 45 -11-8-12=14 20 take B and D *****************************