Target question: Is (100 - n)/n an integer?VJesus12 wrote:If n is an integer, is $$\frac{100-n}{n}$$ an integer?
(1) n > 4
(2) n² = 25
Statement 1: n > 4
Let's TEST some values
There are infinitely many values of n that satisfy statement 1. Here are two:
Case a: n = 5. In this case, (100 - n)/n = (100 - 5)/5 = 95/5 = 19. So, the answer to the target question is YES, (100 - n)/n IS an integer
Case b: n = 7. In this case, (100 - n)/n = (100 - 7)/7 = 93/7 = 13 2/7. So, the answer to the target question is NO, (100 - n)/n is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n² = 25
So, EITHER n = 5 OR n = -5
Case a: If n = 5, then (100 - n)/n = (100 - 5)/5 = 95/5 = 19. So, the answer to the target question is YES, (100 - n)/n IS an integer
Case b: If n = -5, then (100 - n)/n = (100 - -5)/-5 = 105/-5 = -21. So, the answer to the target question is YES, (100 - n)/n IS an integer
In both possible cases, the answer to the target question is the SAME: YES, (100 - n)/n IS an integer
So, (100 - n)/n MUST BE an integer
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
