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

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07 Dec 2017, 00:00
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[GMAT math practice question]

$$|x-y|=?$$

1) $$x$$ and $$y$$ are different integers
2) $$xy=4$$
[Reveal] Spoiler: OA

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

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07 Dec 2017, 00:56
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

Kudos [?]: 214 [0], given: 299

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4692

Kudos [?]: 3323 [0], given: 0

GPA: 3.82
Re: |x-y|=? 1) x and y are different integers [#permalink]

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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.

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.

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Re: |x-y|=? 1) x and y are different integers   [#permalink] 10 Dec 2017, 17:07
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