shasadou wrote:
Is positive integer z greater than 275?
(1) z is a multiple of 21
(2) z is a multiple of 39
Target question: Is positive integer z greater than 275? Statement 1: z is a multiple of 21 Let's TEST some values.
There are several values of z that satisfy statement 1. Here are two:
Case a: z = 21, in which case, the answer to the target question is
NO, z is NOT greater than 275Case b: z = 2100, in which case, the answer to the target question is
YES, z IS greater than 275Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: z is a multiple of 39Let's TEST values again.
Case a: z = 39, in which case, the answer to the target question is
NO, z is NOT greater than 275Case b: z = 3900, in which case, the answer to the target question is
YES, z IS greater than 275Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that z is a multiple of 21, which means we can write
z = 21k for some integer k
Statement 2 tells us that z is a multiple of 39, which means we can write
z = 39j for some integer j
Saying that
z = 21k is the same as saying that
z = (3)(7)(k)Saying that
z = 39j is the same as saying that
z = (3)(13)(j)When we write z is these two ways, we can see that
(3)(7)(13) will be a multiple of 21 AND a multiple of 39
(3)(7)(13) = 273, so z COULD equal
273, in which case, the answer to the target question is
NO, z is NOT greater than 275Or it could be the case that z = (3)(7)(13)(2) = 546, in which case, the answer to the target question is
YES, z IS greater than 275Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
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