If x and y are integers and |x-y|=12, what is the minimum

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AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Wed May 09, 2018 7:15 am

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If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?

A. -12
B. -18
C. -24
D. -36
E. -48

The OA is D.

Is there a strategic approach to solve this PS question? Can anyone help?

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Source: Beat The GMAT — Problem Solving | Wed May 09, 2018 7:15 am

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by [email protected] » Wed May 09, 2018 7:22 pm

Hi AAPL,

We're told that X and Y are integers and |X - Y| = 12. We're asked for the MINIMUM possible value of (X)(Y). You will likely find that a bit of 'brute force' Arithmetic is the easiest way to get to the correct answer.

To start, ALL of the answers are NEGATIVE, which means that one of the variables will be POSITIVE and the other will be NEGATIVE.

IF....
X = 11 and Y = -1, then the product is -11
X = 10 and Y = -2, then the product is -20
X = 9 and Y = -3, then the product is -27
X = 8 and Y = -4, then the product is -32
X = 7 and Y = -5, then the product is -35
X = 6 and Y = -6, then the product is -36
X = 5 and Y = -7, then the product is -35

From here, the products will follow the above pattern, but in reverse. Thus, the minimum possible product is -36.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Thu May 10, 2018 4:56 pm

AAPL wrote:If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?

A. -12
B. -18
C. -24
D. -36
E. -48

We see that all the answer choices are negative; thus, one of the values of x and y must be negative and the other positive. We can let x be negative, and y be positive.

If x = -1, then y = 11 and xy = -11.
If x = -2, then y = 10 and xy = -20.
If x = -3, then y = 9 and xy = -27.
If x = -4, then y = 8 and xy = -32.
If x = -5, then y = 7 and xy = -35.
If x = -6, then y = 6 and xy = -36.
If x = -7, then y = 5 and xy = -35.

We can stop here since we see that we have the minimum product of -36 when x = -6 and y = 6. (Note: Had we continued, the product will be increasing rather than decreasing since the product will be a mirror image of what we have. That is, after the last product -35, the subsequent ones will be -32, -27, -20 and -11.)

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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