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# |x-y|=? 1) x and y are different integers

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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|x-y|=? 1) x and y are different integers  [#permalink]

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07 Dec 2017, 00:00
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Difficulty:

25% (medium)

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67% (01:03) correct 33% (00:51) wrong based on 130 sessions

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[GMAT math practice question]

$$|x-y|=?$$

1) $$x$$ and $$y$$ are different integers
2) $$xy=4$$

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" DS Forum Moderator Joined: 21 Aug 2013 Posts: 1375 Location: India Re: |x-y|=? 1) x and y are different integers [#permalink] ### Show Tags 07 Dec 2017, 00:56 2 MathRevolution wrote: [GMAT math practice question] $$|x-y|=?$$ 1) $$x$$ and $$y$$ are different integers 2) $$xy=4$$ (1) x and y are different integers. This just tells us that since they are not same, |x-y| cannot be 0. But there are so many possibilities. Insufficient. (2) xy =4. So many possibilities. Eg, x=y=2, then |x-y| = 0, But if x=4, y=1 then |x-y| = 3. Insufficient. Combining the two statements, x & y are different integers and their product =4. Lets look at the possibilities. x=4, y=1 x=1, y=4 x=-4, y=-1 x=-1, y=-4 For each of the above cases, |x-y| = 3. So Sufficient. Hence C answer Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6535 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: |x-y|=? 1) x and y are different integers [#permalink] ### Show Tags 10 Dec 2017, 17:07 => 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. Since we have 2 variables ($$x$$ and $$y$$) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. Condition 1) & 2) Since x and y are different integers, $$xy = 4$$ has the following four solutions: $$x = 1, y = 4$$ $$x = 4, y = 1$$ $$x = -1, y = -4$$ $$x = -4, y = -1$$ In all cases, $$|x-y| = 3$$. Thus, both conditions 1) and 2) together are sufficient. Therefore, C is the answer. In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: |x-y|=? 1) x and y are different integers  [#permalink]

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13 Mar 2018, 02:53
Are -2, and 2 not "different integers"?
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Re: |x-y|=? 1) x and y are different integers  [#permalink]

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13 Mar 2018, 02:57
msurls wrote:
Are -2, and 2 not "different integers"?

Yes, they are. One is known as positive integer and the other positive integer.
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Re: |x-y|=? 1) x and y are different integers  [#permalink]

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13 Mar 2018, 03:53
msurls wrote:
Are -2, and 2 not "different integers"?

Hello

Yes they are But their product is Not 4. As per second statement product should be 4
Re: |x-y|=? 1) x and y are different integers &nbs [#permalink] 13 Mar 2018, 03:53
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# |x-y|=? 1) x and y are different integers

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