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Is x = 0 ?

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by vinni.k » Tue Jan 08, 2013 6:23 am
Is x = 0 ?

(1) xy = x
(2) x + y = y

answer is B

Why answer cannot be D. Statement (1) gives x = 0 or y = 1. It is giving x = 0. Why should we concerned about y = 1 when we are already getting x = 0 as it is being already asked ?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Jan 08, 2013 6:32 am
vinni.k wrote:Is x = 0 ?

(1) xy = x
(2) x + y = y
Target question: Is x = 0 ?

Statement 1: xy = x
There are several pairs of values for x and y that meet this condition. Here are two:
Case a: x = 0 and y = 2, in which case x = 0
Case b: x = 3 and y = 1, in which case x = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x + y = y
Subtract y from both sides to get x = 0
In other words, x must equal 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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by gander123 » Tue Jan 08, 2013 6:37 am
Hey vinni,
Why should we concerned about y = 1 when we are already getting x = 0 as it is being already asked ?
You seem to rule out the possibility that x can be something different than 0. But look closely at statement (1). As you say, y = 1. But then, numerous valous for X satisfy the equation xy = x. Here are some:

(10)*(1) = 10
(9)*(1) = 9
(8)*(1) = 8

and of course (0)*(1)= 0

Hence, you cannot say with absolute certainty that x = 0. Statement (1) is INSUFFICIENT.

Statement (2) just gives you what is asked in the prompt and is thus SUFFICIENT.

brgds,

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by Brent@GMATPrepNow » Tue Jan 08, 2013 6:38 am
vinni.k wrote: Why answer cannot be D. Statement (1) gives x = 0 or y = 1. It is giving x = 0. Why should we concerned about y = 1 when we are already getting x = 0 as it is being already asked ?
Good question, Vinni.

The problem is that you've reduced the strength of the question.
Yes, for statement 1, x could equal 0, but the target question doesn't ask, "Could x = 0?" The target question asks, "Does x = 0?"
In other words, "Must it be the case that x = 0?"

With all data sufficiency questions, a statement is sufficient if we are able to answer the target question with certainty.

In statement 1, we cannot answer the target question ("Does x = 0?") with absolute certainty, so it's not sufficient.

If you're interested, we have a free set of videos that cover everything you need to know about data sufficiency questions: https://www.gmatprepnow.com/module/gmat-data-sufficiency

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Brent
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by vinni.k » Tue Jan 08, 2013 9:17 am
Brent@GMATPrepNow wrote: Statement 1: xy = x
There are several pairs of values for x and y that meet this condition. Here are two:
Case a: x = 0 and y = 2, in which case x = 0
Case b: x = 3 and y = 1, in which case x = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Thanks Brent. Actually i solved this question algebraically and didn't use different examples to verify the statement. This is where i make silly mistakes, and my questions get wrong and then i ask myself why my scores are not increasing. :(

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Vinni
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