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Is y – z < x – z?

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Is y – z < x – z?  [#permalink]

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New post 27 Feb 2017, 03:29
2
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (01:27) correct 30% (01:38) wrong based on 74 sessions

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Re: Is y – z < x – z?  [#permalink]

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New post 27 Feb 2017, 07:33
Bunuel wrote:
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.
y may be greater or smaller than x hence
NOT SUFFICIENT

Statement 2: z < x < 0
No mention of y hence
NOT SUFFICIENT

Combining the two statements
z < x < 0 and y is between x and z

i.e. z < y < x < 0
SUFFICIENT

Answer: Option C
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Is y – z < x – z?  [#permalink]

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New post Updated on: 22 Mar 2017, 06:24
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Bunuel wrote:
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 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 GMATPrepNow on 27 Feb 2017, 08:06.
Last edited by GMATPrepNow on 22 Mar 2017, 06:24, edited 1 time in total.
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Is y – z < x – z?  [#permalink]

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New post 22 Mar 2017, 04:20
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GMATPrepNow wrote:
Bunuel wrote:
Is y – z < x – z?

(1) y lies between x and z.
(2) z < x < 0


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


Dear Brent,
While you RULES OUT the possibility that x < y < z, you then used the same ruled out possibility to reach the conclusion. You should have taken the other possibility that x < y < z and hence y<x . So, the answer you the target question should be YES.

Thanks
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Re: Is y – z < x – z?  [#permalink]

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New post 22 Mar 2017, 06:24
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Mo2men wrote:

Dear Brent,
While you RULES OUT the possibility that x < y < z, you then used the same ruled out possibility to reach the conclusion. You should have taken the other possibility that x < y < z and hence y<x . So, the answer you the target question should be YES.

Thanks


Good catch!
I've edited that portion.

Cheers and thanks,
Brent
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Re: Is y – z < x – z?  [#permalink]

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New post 23 Mar 2017, 16:02
Bunuel wrote:
Is y – z < x – z?

(1) y lies between x and z.
(2) z < x < 0


If we add z to both sides of the equation, we can simplify the given question to read:

Is y < x ?

Statement One Alone:

y lies between x and z.

Although we know that y is between x and z, we still do not have enough information to solve the question. For instance, if z = -4, y = -2, and x = -1, then y < x; however if x = -4, y = -2, and z = -1, then y > x. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

z < x < 0

Since we do not have any information regarding y, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the information from statements one and two, we can determine that z < y < x < 0, and thus, y is less than x.

Answer: C
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Re: Is y – z < x – z? &nbs [#permalink] 23 Mar 2017, 16:02
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