cdrectenwald wrote:
If d and e are positive integers, is d a multiple of 9?
(1) 5e - 7 is a multiple of 9.
(2) d - 2 = 5e
Target question: Is d a multiple of 9? Statement 1: 5e - 7 is a multiple of 9This statement provides no information about d
Statement 1 is NOT SUFFICIENT
Statement 2: d - 2 = 5eIt's easier to analyze the statement if we rewrite the equation as:
d = 5e + 2There are several values of d and e that satisfy this equation. Here are two:
Case a: d = 7 and e = 1. Since 7 is not a multiple of 9, the answer to the target question is
NO, d is not a multiple of 9Case b: d = 27 and e = 5. Since 27 is a multiple of 9, the answer to the target question is
YES, d is a multiple of 9Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that 5e - 7 is a multiple of 9.
This means we can write: 5e - 7 =
9k (for some integer value of k)
Statement 2 tells us that d - 2 = 5e, which we can rewrite as: d = 5e + 2
KEY STEP: Take d = 5e + 2 and rewrite it as:
d = 5e - 7 + 9 Aside: I did this because we have some very specific information about 5e - 7 (it equals
9k, for some integer value of k)
So, we have:
d = 5e - 7 + 9Which is the same as:
d = (5e - 7) + 9Now substitute to get: d =
9k + 9
Now factor out the 9 to get: d =
9(
k + 1)
At this point, it's clear that d is a multiple of
9The answer to the target question is
YES, d is a multiple of 9Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
_________________