CAT 1991 — QA Question 36
Answer the following questions based on the information given below:
There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.
Let k be a positive integer such that k + 4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k + 2n is divisible by 7 equals
Answer & solution
9
- B
7
- C
5
- D
3
a = k + 4 is divisible by 7
b = k + 2n is divisible by 7
⇒ b – a = 2n – 4 is divisible by 7
⇒ 2n – 4 = 0 or 7 or 14 ...
For minimum integral value of n, greater than 2
2n – 4 = 14
⇒ n = 9
Hence, option (a).