CAT 1991 — QA Question 44
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.
If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values of x is
Answer & solution
- A
2
- B
5
6
- D
12
If (2x + 12) is perfectly divisible by x, then (2x + 12)/x has to be an integer.
Now if we divide, the expression simplifies to (2 + 12/x).
The only way in which this expression would be an integer is when 12/x is an integer or if 12 is perfectly divisible by x. [i.e., x is a factor of 12]
This is possible if x takes either of these values : 1, 2, 3, 4, 6, 12. Hence the answer is 6 values.
Hence, option (c).