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

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Math Expert
Joined: 02 Sep 2009
Posts: 47110
If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink]

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30 Jan 2016, 02:57
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67% (01:30) correct 33% (01:37) wrong based on 627 sessions

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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

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Math Expert
Joined: 02 Aug 2009
Posts: 6252
Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink]

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30 Jan 2016, 07:16
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Bunuel 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

Hi,

we are given |x - y| = 12,
minimum possible value of xy would be maximum numeric value with a -ive sign..
so one of x or y will be negative and other negative..

|x-y|=12 in this case means that the numeric sum of x and y is 12..
various combinations could be -1 and 11, -2 and 10, -6 and 6, -11 and 1 and so on..

when the sum of two numbers is given, the max product is when both x and y are same numeric value...
so xy will have max numeric value when numeric value of x and y=12/2=6..
so numeric value of xy=36 but one of x and y is -ive..
so answer is -36...
D
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Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink]

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31 Jan 2016, 17:16
2
1
Hi All,

Sometimes the answer choices to a given question provide a big 'hint' as to how you can go about solving it. This prompt can also be solved without any complex math ideas - you just need to do a bit of 'brute force' math and you'll have the answer relatively quickly.

We're told that X and Y are INTEGERS and |X - Y| = 12. We're asked for the MINIMUM possible value of (X)(Y).

Since all of the answer choices are NEGATIVE, this tells us that ONE of the two variables MUST be negative (and the other must be positive), so we should restrict our work to those options.

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

From this, we can conclude the XY will start to get bigger as X continues to decrease down to 1, so there's no need to do any additional work.

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 02 Dec 2015 Posts: 12 Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink] ### Show Tags 02 Jul 2016, 09:11 I'm not sure what is going on! Why would you say maximum value when the question says minimum value of xy is to be found. And fyi the minimum value is -11 which is not even there in the answer choices chetan2u wrote: Bunuel 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 Hi, we are given |x - y| = 12, minimum possible value of xy would be maximum numeric value with a -ive sign.. so one of x or y will be negative and other negative.. |x-y|=12 in this case means that the numeric sum of x and y is 12.. various combinations could be -1 and 11, -2 and 10, -6 and 6, -11 and 1 and so on.. when the sum of two numbers is given, the max product is when both x and y are same numeric value... so xy will have max numeric value when numeric value of x and y=12/2=6.. so numeric value of xy=36 but one of x and y is -ive.. so answer is -36... D Intern Joined: 02 Dec 2015 Posts: 12 If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink] ### Show Tags 02 Jul 2016, 09:14 Hey Bunuel Is the question wrong? It says find the minimum and the two answers above find the maximum. Besides the minimum value (-11) isnt even there in the answer choice. Am I missing something here? Regards Parth Bunuel 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 Math Expert Joined: 02 Sep 2009 Posts: 47110 Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink] ### Show Tags 02 Jul 2016, 10:22 ppb1487 wrote: Hey Bunuel Is the question wrong? It says find the minimum and the two answers above find the maximum. Besides the minimum value (-11) isnt even there in the answer choice. Am I missing something here? Regards Parth Bunuel 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 The minimum value is -36, which is less tha -11. _________________ VP Status: It's near - I can see. Joined: 13 Apr 2013 Posts: 1138 Location: India Concentration: International Business, Operations GMAT 1: 480 Q38 V22 GPA: 3.01 WE: Engineering (Consulting) If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink] ### Show Tags 02 Jul 2016, 10:34 ppb1487 wrote: Hey Bunuel Is the question wrong? It says find the minimum and the two answers above find the maximum. Besides the minimum value (-11) isnt even there in the answer choice. Am I missing something here? Regards Parth Bunuel 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 $${-11}>{-36}$$ on the number line. Thus, D is the correct answer. _________________ "Do not watch clock; Do what it does. KEEP GOING." Intern Joined: 02 Dec 2015 Posts: 12 Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink] ### Show Tags 03 Jul 2016, 02:52 Oh yea I'm sorry for this. Was doing the question at 2am in the morning so maybe all the numbers scrambled up! But thanks for the clarification. Regards Bunuel wrote: ppb1487 wrote: Hey Bunuel Is the question wrong? It says find the minimum and the two answers above find the maximum. Besides the minimum value (-11) isnt even there in the answer choice. Am I missing something here? Regards Parth Bunuel 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 The minimum value is -36, which is less tha -11. Intern Joined: 15 Jul 2016 Posts: 7 Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink] ### Show Tags 08 Aug 2016, 15:54 hello Bunuel not sure but |24-12|=12 and then xy =24(-12) =-288 I might not be getting the question can you help Thanks Utkarsh EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11989 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink] ### Show Tags 08 Aug 2016, 22:16 1 Hi Utkarsh, In your example, X = +24 and Y = +12, so the product is (24)(12) = +288. From the answer choices, we know that the minimal product is NEGATIVE, so +24 and +12 cannot be the combination of numbers that you're looking for. If you read through my explanation (a few posts up the page), then you'll see how to quickly get to the correct answer. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink]

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08 Aug 2016, 22:45
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This question is a twist on the concept: Given a particular sum of two positive integers, product is maximum when the integers are equal.

You have |x - y| = 12
To get the minimum possible value of xy, you need a negative sign with the maximum possible absolute value of the product. So exactly one of x and y should be negative. Let's assume y is negative (either way doesn't matter since we will take its absolute value).

If y is negative, x - y becomes the sum of two positive integers which is given to be 12. We need the maximum absolute value of xy. This will happen when x and y have the same absolute value. So both should have absolute value of 6.
So minimum product is 6*(-6) = -36

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Re: If x and y are integers and |x - y| = 12, what is the minimum possible [#permalink]

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10 May 2018, 10:44
Bunuel 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.)

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Re: If x and y are integers and |x - y| = 12, what is the minimum possible   [#permalink] 10 May 2018, 10:44
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