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

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Math Revolution GMAT Instructor
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|x-y|=? 1) x and y are different integers  [#permalink]

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New post 07 Dec 2017, 01:00
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (00:44) correct 38% (00:33) wrong based on 125 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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Re: |x-y|=? 1) x and y are different integers  [#permalink]

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New post 07 Dec 2017, 01:56
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
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Re: |x-y|=? 1) x and y are different integers  [#permalink]

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New post 10 Dec 2017, 18:07
=>

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
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Re: |x-y|=? 1) x and y are different integers  [#permalink]

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New post 13 Mar 2018, 03:53
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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New post 13 Mar 2018, 03:57
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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New post 13 Mar 2018, 04:53
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, 04:53
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