DS

[aditya67]

If x is an integer, is 72/x an integer?



(1) 18 < x < 54

(2) x is a multiple of 18

[Brent@GMATPrepNow]

If x is an integer, is 72/x an integer?



(1) 18 < x < 54

(2) x is a multiple of 18

Target question: Is 72/x an integer?
Important: 72/x will be an integer IF x is a divisor of 72.
In other words, 72/x will be an integer IF x equals one of the following values: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, or 72

Statement 1: 18 < x < 54
Since 24 and 36 are among the possible x-values between 18 and 54, it is possible that 72/x IS an integer.
However, x could also equal a number like 20, in which case 72/x is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is a multiple of 18
There are several values of x satisfy statement 2. Here are two:
Case a: x = 18, in which case 72/x = 72/18 = 4. So, in this case, 72/x IS an integer
Case b: x = 90, in which case 72/x = 72/90. So, in this case, 72/x is NOT an integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 18 < x < 54
Statement 2 tells us that x is a multiple of 18 (18, 36, 54, 72, 90, ...)
Since 36 is the ONLY multiple of 18 that's BETWEEN 18 and 54, we can be certain that x = 36
So, 72/x = 72/36 = 2
So, 72/x IS an integer
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent