1) The document contains 6 questions regarding combinations, permutations, and set theory from a GRE quant section. 2) The first question asks to find the area of a rectangle and triangle given side lengths, and the perimeter of the rectangle. 3) The second question asks how many ways 6 flowers can be planted in spots for 4 flowers. 4) The third question asks how many sets of 3 books can be taken from 10 books. 5) Questions 4-6 are word problems involving sets, determining how many students take certain subjects based on overlapping data.

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
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