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If x, y and z are real numbers, is y – z < x – z?

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Bunuel
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If x, y and z are real numbers, is y – z < x – z? [#permalink] New post  26 Feb 2017, 09:16
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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
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BrentGMATPrepNow
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If x, y and z are real numbers, is y – z < x – z? [#permalink] New post  Updated on: 19 Oct 2017, 16:03
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Bunuel wrote:
If x, y and z are real numbers, is y – z < x – z?

(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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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.
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Re: If x, y and z are real numbers, is y – z < x – z? [#permalink] New post  26 Feb 2017, 21:53
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Bunuel wrote:
If x, y and z are real numbers, is y – z < x – z?

(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
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BalysLTU
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Re: If x, y and z are real numbers, is y – z < x – z? [#permalink] New post  19 Oct 2017, 15:06
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Kudos
GMATPrepNow wrote:
Bunuel wrote:
If x, y and z are real numbers, is y – z < x – z?

(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 x < y < z, which means x < y
So, the answer to the REPHRASED target question is "NO. It is definitely NOT 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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Hi Brent,

Nice solution! I do think you've made a mistake in the highlighted part though. I believe you meant to say:

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"
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BrentGMATPrepNow
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Re: If x, y and z are real numbers, is y – z < x – z? [#permalink] New post  19 Oct 2017, 16:03
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Thanks BalysLTU!!

I have edited my answer accordingly.

Cheers,
Brent
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Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
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Re: If x, y and z are real numbers, is y – z < x – z? [#permalink]
19 Oct 2017, 16:03
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