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If x=y-z, is x>y?

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If x=y-z, is x>y? [#permalink]

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New post 09 Mar 2018, 00:21
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Question Stats:

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[GMAT math practice question]

If \(x=y-z\), is \(x>y\)?

\(1) y<0\)
\(2) z<0\)

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If x=y-z, is x>y? [#permalink]

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New post 09 Mar 2018, 05:52
If \(x=y-z\), is \(x>y\)?

\(1) y<0\)
If y = -4 < 0.
Case 1: x = -5, z = -1
Case 2: x = -4, z = 0
In Case 1, x>y but in second case, x=y (Insuffiicient)

\(2) z<0\)
If z is negative, the only possibility when x = y-z
is when \(x > y\) (Sufficient - Option B)
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If x=y-z, is x>y? [#permalink]

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New post 09 Mar 2018, 10:49
MathRevolution wrote:
[GMAT math practice question]

If \(x=y-z\), is \(x>y\)?

\(1) y<0\)
\(2) z<0\)


Given, x = y - z
i.e. x - y = -z


Question : Is x > y?
Question : Is x - y > 0?
Question : Is -z > 0?


Question : Is z < 0?

Statement 1: y < 0

No Information about z hence
NOT SUFFICIENT

Statement 2: z < 0


SUFFICIENT

Answer: Option B

Key Take Away: Always rephrase the question in the simplest possible form so that we can objectively look at the information "actually needed" to solve the question
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Re: If x=y-z, is x>y? [#permalink]

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New post 11 Mar 2018, 18:30
1
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

We can modify the question as follows:
\(x>y\)
\(⇔ x-y > 0\)
\(⇔ -z > 0\) by the original condition
\(⇔ z < 0\)
This is the same as condition 2).

Condition 1)
If \(x = -1, y = -2\), and \(z = -1, x > y\), and the answer is ‘yes’.
If \(x = -2, y = -1\), and \(z = 1, x < y\), and the answer is ‘no’.
Condition 1) is not sufficient since the question does not have a unique answer.

Therefore, B is the answer.

Answer: B
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Re: If x=y-z, is x>y?   [#permalink] 11 Mar 2018, 18:30
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