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26 Feb 2017, 09:16
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70% (01:32) correct
30%
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If x, y and z are real numbers, is y – z < x – z?
(1) y lies between x and z.
(2) z < x < 0
(1) y lies between x and z.
(2) z < x < 0
Updated on: 19 Oct 2017, 16:03
Originally posted by BrentGMATPrepNow on 26 Feb 2017, 10:45.
Last edited by BrentGMATPrepNow on 19 Oct 2017, 16:03, edited 1 time in total.
Last edited by BrentGMATPrepNow on 19 Oct 2017, 16:03, edited 1 time in total.
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Bunuel
If x, y and z are real numbers, is y – z < x – z?
(1) y lies between x and z.
(2) z < x < 0
(1) y lies between x and z.
(2) z < x < 0
Target question: Is y – z < x – z?
This is a good candidate for rephrasing the target question.
Take y – z < x – z and add z to both sides to get: y < x.
So,......
REPHRASED target question: Is y < x?
Statement 1: y lies between x and z.
BE CAREFUL, we cannot conclude that x < y < z, because it could also be the case that z < y < x
In both cases, y lies between x and z on the number line. These two possible scenarios yield different answers to the REPHRASED target question.
Case a: if x < y < z, then we can see that x < y.
Case b: if z < y < x, then we can see that y < x.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: z < x < 0
There's no information about y.
So, there's no way to determine whether or not y < x
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that EITHER x < y < z OR z < y < x
Statement 2 tells us that z < x, which RULES OUT the possibility that x < y < z
So, it MUST be the case that z < y < x, which means y < x
So, the answer to the REPHRASED target question is "YES. It is definitely the case that y < x"
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer: C
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26 Feb 2017, 21:53
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Bunuel
If x, y and z are real numbers, is y – z < x – z?
(1) y lies between x and z.
(2) z < x < 0
(1) y lies between x and z.
(2) z < x < 0
Question: Is y – z < x – z?
Question: Is y < x ?
Statement 1: y lies between x and z.
But y may be greater than or smaller than x
NOT SUFFICIENT
Statement 2: z < x < 0
No mention of y hence
NOT SUFFICIENT
Combining the two statements
z < x < 0 and
y lies between x and z
i.e. y must be smaller than x hence
SUFFICIENT
Answer: option C
