Author 
Message 
TAGS:

Hide Tags

EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11074
Location: United States (CA)
GRE 1: 340 Q170 V170

Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
04 Nov 2015, 18:17
1
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
Question Stats:
64% (01:57) correct 36% (01:57) wrong based on 153 sessions
HideShow timer Statistics
QUANT 4PACK SERIES Problem Solving Pack 3 Question 2 What is the positive difference...If \(x^{2}\) + xy  32 = 0, and x and y are integers, then y could equal each of the following except…? A) 31 B) 14 C) 2 D) 4 E) 14 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4Pack seriesScroll Down For Official Explanation
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
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!***********************





Math Expert
Joined: 02 Aug 2009
Posts: 5662

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
04 Nov 2015, 19:43
EMPOWERgmatRichC wrote: QUANT 4PACK SERIES Problem Solving Pack 3 Question 2 What is the positive difference...If \(x^{2}\)  xy  32 = 0, and x and y are integers, then xy could equal each of the following except…? A) 31 B) 14 C) 2 D) 4 E) 14 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4Pack seriesScroll Down For Official Explanation hi rich, there can be three answers for this Q. You may have to change the options... straight method would be to substitute the value of xy in the equation and find if x^2 is an integer, as x itself is an integer.. eqn..\(x^{2}\)  xy  32 = 0 or \(x^{2}\) = xy + 32 A) 31... x^2=1.. ok B) 14... x^2=18, x will not be an integer..not possible C) 2... x^2=34, x will not be an integer..not possible D) 4... x^2=36.. ok E) 14... x^2=46, x will not be an integer..not possible so B,C and E all are contenders for the possible answer...
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
BANGALORE/



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4908
GPA: 3.82

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
05 Nov 2015, 01:17
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. If x2  xy  32 = 0, and x and y are integers, then xy could equal each of the following except…? A) 31 B) 14 C) 2 D) 4 E) 14 Hi rich, all the choices except (A) are impossible. So you should change the question as "xy could be...." Here is my methods. Since 32 = x^2 – xy= x *(xy) and x and y are integers. x and xy should be the factors of 32. So (x, xy) has following possibilities (1, 32), (2, 16), (4, 8), (8, 4), (16, 2), (32, 1), (1, 32), (2, 16), (4, 8), (8, 4), (16, 2), (32, 1) After tedious calculations we have (x, y)=(1, 31), (2, 14), (4, 4), (8, 4), (16, 14), (32, 31), (1, 31), (2, 14), (4, 4), (8, 4), (16, 14), (32, 31). So xy can be –31, 28, 16, 32, 224, 992. So only (A) is possible. And To Chetan2u D) 4... x^2=36.. ok.> By your explanation we have x= 6 or –6. But we cannot find integer y satisfying xy=4. So (D) is also impossible.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons  try it yourself See our Youtube demo



Math Expert
Joined: 02 Aug 2009
Posts: 5662

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
05 Nov 2015, 02:29
MathRevolution wrote: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
If x2  xy  32 = 0, and x and y are integers, then xy could equal each of the following except…?
A) 31 B) 14 C) 2 D) 4 E) 14
Hi rich, all the choices except (A) are impossible. So you should change the question as "xy could be...."
Here is my methods. Since 32 = x^2 – xy= x *(xy) and x and y are integers. x and xy should be the factors of 32. So (x, xy) has following possibilities (1, 32), (2, 16), (4, 8), (8, 4), (16, 2), (32, 1), (1, 32), (2, 16), (4, 8), (8, 4), (16, 2), (32, 1)
After tedious calculations we have (x, y)=(1, 31), (2, 14), (4, 4), (8, 4), (16, 14), (32, 31), (1, 31), (2, 14), (4, 4), (8, 4), (16, 14), (32, 31).
So xy can be –31, 28, 16, 32, 224, 992.
So only (A) is possible.
And To Chetan2u
D) 4... x^2=36.. ok.> By your explanation we have x= 6 or –6. But we cannot find integer y satisfying xy=4. So (D) is also impossible. hi buddy, thanks, in the hurry, i forgot to test the integer value of y.... and ofcourse we dont have to get into the tedious calculations but substitue xy and look for integer values for both x and y..
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
BANGALORE/



Manager
Joined: 02 Jun 2015
Posts: 91
Location: Brazil
Concentration: Entrepreneurship, General Management
GPA: 3.3

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
05 Nov 2015, 08:13
1
This post received KUDOS
MathRevolution wrote: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
If x2  xy  32 = 0, and x and y are integers, then xy could equal each of the following except…?
A) 31 B) 14 C) 2 D) 4 E) 14
Hi rich, all the choices except (A) are impossible. So you should change the question as "xy could be...."
Here is my methods. Since 32 = x^2 – xy= x *(xy) and x and y are integers. x and xy should be the factors of 32. So (x, xy) has following possibilities (1, 32), (2, 16), (4, 8), (8, 4), (16, 2), (32, 1), (1, 32), (2, 16), (4, 8), (8, 4), (16, 2), (32, 1)
After tedious calculations we have (x, y)=(1, 31), (2, 14), (4, 4), (8, 4), (16, 14), (32, 31), (1, 31), (2, 14), (4, 4), (8, 4), (16, 14), (32, 31).
So xy can be –31, 28, 16, 32, 224, 992.
So only (A) is possible.
And To Chetan2u
D) 4... x^2=36.. ok.> By your explanation we have x= 6 or –6. But we cannot find integer y satisfying xy=4. So (D) is also impossible. I think exactly like you I only got the letter A corrected. xˆ2  xy  32 = 0 xˆ2 = xy + 32 (picking the numbers) xˆ2 = 31 + 32 x = +/ 1 if I choose +1 or 1, in both of this choices i can get an integer value for Y. Therefore, only (A) is correct.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11074
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
05 Nov 2015, 11:47
Hi All, Thanks for pointing out the inconsistency in the prompt. It had 2 small typos that have since been fixed. Sorry for the inconvenience. 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
CoFounder & GMAT Assassin
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!***********************



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11074
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
07 Nov 2015, 14:47
EMPOWERgmatRichC wrote: QUANT 4PACK SERIES Problem Solving Pack 3 Question 2 What is the positive difference...If \(x^{2}\) + xy  32 = 0, and x and y are integers, then y could equal each of the following except…? A) 31 B) 14 C) 2 D) 4 E) 14 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4Pack seriesScroll Down For Official Explanation Hi All, This question is based on a common Algebra pattern  Quadratics. Since x and y are INTEGERS, we have to determine the limited number of possible values for x and y and determine which of the 5 answer choices is NOT a possible value for y. To start, we're given the Quadratic: \(x^{2}\) + xy  32 = 0 Using the "32", we can determine the various 'pairs' of values for x and y... 32 and +1 32 and 1 16 and +2 16 and 2 8 and +4 8 and 4 Given the above 'pairs', we can quickly determine the possible values of y (and you don't technically have to do the entire FOIL calculation)... IF the quadratic is (x  32)(x + 1), then the FOILed term is \(x^{2}\) 31x  32 = 0 so y COULD be 31. IF the quadratic is (x  16)(x + 2), then the FOILed term is \(x^{2}\) 14x  32 = 0 so y COULD be 14. IF the quadratic is (x +8)(x  4), then the FOILed term is \(x^{2}\) +4x  32 = 0 so y COULD be +4. IF the quadratic is (x + 16)(x  2), then the FOILed term is \(x^{2}\) +14x  32 = 0 so y COULD be +14. The only answer that is NOT possible under these conditions is 2. Final 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
CoFounder & GMAT Assassin
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!***********************



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
08 Nov 2015, 02:03
1
This post was BOOKMARKED
EMPOWERgmatRichC wrote: QUANT 4PACK SERIES Problem Solving Pack 3 Question 2 What is the positive difference...
If \(x^{2}\) + xy  32 = 0, and x and y are integers, then y could equal each of the following except…?
\(x^{2} + xy  32 = 0\) Or, \(x^{2} + xy = 32\) Now check the options  A) 31 \(x^{2} 31x  32 =0\) x = 1 and 32 This quadratic equation can be solved.B) 14 \(x^{2} 14x  32 =0\) x = 2 and 16 This quadratic equation can be solved.C) 2 \(x^{2} +2x  32 =0\) This quadratic equation can not be solved, we can stop here and mark this as our answer.D) 4 \(x^{2} +4x  32 =0\) x = 4 and 8 This quadratic equation can be solved.E) 14 \(x^{2} +14x  32 =0\) x = 2 and 16 This quadratic equation can be solved.Hence our answer is (C)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Intern
Joined: 27 Dec 2015
Posts: 9
Concentration: Accounting, Economics
GPA: 3.02
WE: Analyst (Accounting)

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
22 Jan 2016, 12:27
QUANT 4PACK SERIES Problem Solving Pack 3 Question 2 What is the positive difference...
If x2  xy  32 = 0, and x and y are integers, then xy could equal each of the following except…?
Hi rich, all the choices except (A) are impossible. So you should change the question as "xy could be...."
X2xy32=0 (x16) (x+2)=0 X=16v X=2
X31xy32=0 X=31
IF the quadratic is (x  32)(x + 1), then the FOILed term is x2 31x  32 = 0 so y COULD be 31.
IF the quadratic is (x  16)(x + 2), then the FOILed term is x2 14x  32 = 0 so y COULD be 14.
IF the quadratic is (x +8)(x  4), then the FOILed term is x2 +4x  32 = 0 so y COULD be +4.
IF the quadratic is (x + 16)(x  2), then the FOILed term is x2 +14x  32 = 0 so y COULD be +14.
The only answer that is NOT possible under these conditions is 2



NonHuman User
Joined: 09 Sep 2013
Posts: 13759

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
26 Mar 2017, 02:03
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



SVP
Joined: 12 Dec 2016
Posts: 1922
Location: United States
GPA: 3.64

Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0.... [#permalink]
Show Tags
16 Apr 2017, 17:34
there is an easy approach to this problem, remember to put kudos for me :D
x^2 +xy  32 = 0 => 4x^2 +4xy +y^2 = 128 + y^2 => (2x + y)^2 = 128 + y^2 Then, try each options, starting at the smallest => C is the answer
Pls dont forget to feed me kudos :D




Re: Problem Solving Pack 3, Question 2 If x^2  xy  32 = 0....
[#permalink]
16 Apr 2017, 17:34






