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If x and y are two different integers, is |x|=|y|?

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by VJesus12 » Thu May 03, 2018 10:44 am

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If x and y are two different integers, is |x|=|y|?

(1) x and y are positive numbers.
(2) x=y+2

The OA is the option A.

Could someone help me here? Please. I don't understand why the second statement is not sufficient. May someone give me an example here?
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu May 03, 2018 12:20 pm
VJesus12 wrote:If x and y are two different integers, is |x|=|y|?

(2) x=y+2

I don't understand why the second statement is not sufficient. May someone give me an example here?
Case 1: y=0, with the result that x = y+2 = 0+2 = 2
In this case, |x|=2 and |y|=0, so the answer to the question stem is NO.
Case 2: y=-1, with the result that x = y+2 = -1+2 = 1
In this case, |x|=1 and |y|=1, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, Statement 2 is INSUFFICIENT.
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by Vincen » Thu May 03, 2018 12:27 pm
Hello Vjesus12.

We have to respond if |x|=|y|? Let's take a look.

(1) x and y are positive numbers.

Since both numbers are positive and they are different, then $$\left|x\right|\ne\left|y\right|\ always.$$ Here, the answer is YES. SUFFICIENT.

(2) x=y+2

Here we have two see the following cases:

- if y=0 then x=2, therefore $$\left|x\right|=\left|2\right|=2\ne0=\left|0\right|=\left|y\right|.\ The\ answer\ is\ YES.$$ - if y=-1 then x=-1, therefore $$\left|x\right|=\left|1\right|=1\ne1=\left|-1\right|=\left|y\right|.\ The\ answer\ is\ NO.$$ Since we've got two different answers, this statement is NOT SUFFICIENT.

In conclusion, the correct answer is the option A.
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