wunstepcloser wrote:
Is v − w < 0?
(1) v − 2w < 0
(2) 5w − v < 0
Target question: Is v − w < 0?This is a good candidate for
rephrasing the target question.
Take:
v − w < 0Add w to both sides to get:
v < wREPHRASED target question: Is v < w? Statement 1: v − 2w < 0 Let's TEST some values.
There are several values of v and w that satisfy statement 1. Here are two:
Case a: v = 0 and w = 1. In this case, the answer to the REPHRASED target question is
YES, it is true that v < wCase b: v = 3 and w = 2. In this case, the answer to the REPHRASED target question is
NO, it is NOT true that v < wSince we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 5w − v < 0 Let's TEST some values.
There are several values of v and w that satisfy statement 2. Here are two:
Case a: v = -2 and w = -1. In this case, the answer to the REPHRASED target question is
YES, it is true that v < wCase b: v = 1 and w = 0. In this case, the answer to the REPHRASED target question is
NO, it is NOT true that v < wSince we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that v − 2w < 0
Statement 2 tells us that 5w − v < 0
If we ADD the two inequalities, we get: 3w < 0, which means
w is NEGATIVEAlso, if we can take v − 2w < 0 and add 2w to both sides, we get
v < 2wAnd, if we can take 5w − v < 0 and add v to both sides, we get
5w < vSo, we can combine the inequalities to get:
5w < v < 2wSince, we already know that
w is NEGATIVE, we know that 2w < w
So, we can add this to our existing inequality to get:
5w < v < 2w < wAt this point, we can see that within our inequality, it is certain that
v < wIn other words, the answer to the REPHRASED target question is
YES, it is true that v < wSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
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