January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 99
Concentration: Finance, General Management

If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
02 Jan 2011, 15:33
Question Stats:
71% (00:58) correct 29% (01:10) wrong based on 878 sessions
HideShow timer Statistics
If xy = 1, what is the value of \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}\) ? A. 2 B. 4 C. 8 D. 16 E. 32
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 52284

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
02 Jan 2011, 15:41




Retired Moderator
Joined: 20 Dec 2010
Posts: 1809

Re: if xy=1, what is the value of (2^(x+y)^2)/(2^(x+y)^2)?
[#permalink]
Show Tags
18 Jun 2011, 06:44
WishMasterUA wrote: if xy=1, what is the value of (2^((x+y)^2))/(2^((xy)^2))? 1) 2 2) 4 3) 8 4) 16 5) 32 \(\frac{2^{(x+y)^2}}{2^{(x+y)^2}}\) \(=\frac{2^{(x^2+y^2+2xy)}}{2^{(x^2+y^22xy)}}\) [:Note: \((x+y)^2=x^2+y^2+2xy \hspace{3} & \hspace{3} (xy)^2=x^2+y^22xy\) ]\(=2^{(x^2+y^2+2xy(x^2+y^22xy))}\) [:Note: \(\frac{x^m}{x^n}= x^{(mn)}\) ]\(=2^{(x^2+y^2+2xyx^2y^2+2xy)}\) \(=2^{(4xy)}\) \(=2^{(4xy)}=2^4=16\) [:Note: xy=1]Ans: "D"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings




Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 99
Concentration: Finance, General Management

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
02 Jan 2011, 16:12
Bunuel wrote: tonebeeze wrote: If xy = 1, what is the value of \(\frac {2^{(x + y)^2}} {2^{(x  y)^2}\) ?
a. 2
b. 4
c. 8
d. 16
e. 32 \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}=2^{(x+y)^2(xy)^2}=2^{(x+y+xy)(x+yx+y)}=2^{(2x)(2y)}=2^{4xy}=2^4=16\). Answer: D. Hey Bunuel, Thanks for the response. I totally understand the key logic of this problem. My method: \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}=2^{(x+y)^2(xy)^2}=2^{(x^2+2xy+y^2)  (x^22xy + y^2)} =2^{(x^2+2xy+y^2  x^2+ 2xy  y^2)}=2^{(4xy)}=2^4=16\) Your method looks more simple and I would like to understand it. I just got a little lost during your factoringout transition from \(2^{(x+y)^2(xy)^2}=2^{(x+y+xy)(x+yx+y)}\) . Can u please explain. Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 52284

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
02 Jan 2011, 16:20
tonebeeze wrote: Bunuel wrote: tonebeeze wrote: If xy = 1, what is the value of \(\frac {2^{(x + y)^2}} {2^{(x  y)^2}\) ?
a. 2
b. 4
c. 8
d. 16
e. 32 \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}=2^{(x+y)^2(xy)^2}=2^{(x+y+xy)(x+yx+y)}=2^{(2x)(2y)}=2^{4xy}=2^4=16\). Answer: D. Hey Bunuel, Thanks for the response. I totally understand the key logic of this problem. My method: \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}=2^{(x+y)^2(xy)^2}=2^{(x^2+2xy+y^2)  (x^22xy + y^2)} =2^{(x^2+2xy+y^2  x^2+ 2xy  y^2)}=2^{(4xy)}=2^4=16\) Your method looks more simple and I would like to understand it. I just got a little lost during your factoringout transition from \(2^{(x+y)^2(xy)^2}=2^{(x+y+xy)(x+yx+y)}\) . Can u please explain. Thanks! \(a^2b^2=(a+b)*(ab)\), so \((x+y)^2(xy)^2=((x+y)+(xy))*((x+y)(xy))=2x*2y=4xy\). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 26 Feb 2015
Posts: 115

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
04 Mar 2015, 08:36
\(2^{(x+y)^2}/2^{(xy)^2}=2^{(x+y)^2(xy)^2}\)
This part is very unclear to me. I do understand the basics of negative square is just "one over", but I dont understand this. The math compendium barely touches on this either. Can someone explain this please?



Math Expert
Joined: 02 Sep 2009
Posts: 52284

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
04 Mar 2015, 08:50



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13341
Location: United States (CA)

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
07 Mar 2015, 16:44
Hi All, Most Quant questions can be approached in a variety of ways, so it's useful to practice more than one method during your studies. In this question, it appears that all of the posters took the same Algebraic approach (which is fine), but was that approach really the fastest and easiest way to get to the solution.....? Watch what happens when we TEST VALUES.... We're told that XY = 1. Since the answer choices are all numbers, one of them MUST be the solution to the equation, so I should be able to use ANY combination of X and Y that I choose (as long as the product of those values = 1). Let's try... X = 1 Y = 1 The question then becomes...what is the value of (2^4)/(2^0)? (2^4)/(2^0) = 16/1 = 16 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!*****



Intern
Joined: 26 Apr 2017
Posts: 5
Location: Spain
WE: Consulting (Consulting)

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
26 Jul 2017, 06:21
Bunuel wrote: tonebeeze wrote: If xy = 1, what is the value of \(\frac {2^{(x + y)^2}} {2^{(x  y)^2}\) ?
A. 2 B. 4 C. 8 D. 16 E. 32 \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}=2^{(x+y)^2(xy)^2}=2^{(x+y+xy)(x+yx+y)}=2^{(2x)(2y)}=2^{4xy}=2^4=16\). Answer: D. Hi Bunuel, Could you help me with the following question? There is a rule for exponents that: \((n^a)^b= n^{a*b}\) So If we have: \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}\) Why woudn't it be the following? \(\frac{2^{2(x+y)}}{2^{2(xy)}}=\frac{2^{2x+2y}}{2^{2x2y}}=2^{2x2x+2y+2y}=2^{4y}\) I'm confused because if we have \(2^{x^2}\) the value when \(x=3\), is the value \(2^{3·2}=2^6\) or \(2^{2^3}=2^8\)? Thank you in advance!



Math Expert
Joined: 02 Sep 2009
Posts: 52284

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
26 Jul 2017, 06:31
guillemgc wrote: Bunuel wrote: tonebeeze wrote: If xy = 1, what is the value of \(\frac {2^{(x + y)^2}} {2^{(x  y)^2}\) ?
A. 2 B. 4 C. 8 D. 16 E. 32 \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}=2^{(x+y)^2(xy)^2}=2^{(x+y+xy)(x+yx+y)}=2^{(2x)(2y)}=2^{4xy}=2^4=16\). Answer: D. Hi Bunuel, Could you help me with the following question? There is a rule for exponents that: \((n^a)^b= n^{a*b}\) So If we have: \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}\) Why woudn't it be the following? \(\frac{2^{2(x+y)}}{2^{2(xy)}}=\frac{2^{2x+2y}}{2^{2x2y}}=2^{2x2x+2y+2y}=2^{4y}\) I'm confused because if we have \(2^{x^2}\) the value when \(x=3\), is the value \(2^{3·2}=2^6\) or \(2^{2^3}=2^8\)? Thank you in advance! Because it's \(2^{(x+y)^2}\) and not \((2^{(x+y)})^2\) \((a^m)^n=a^{mn}\) \(a^m^n=a^{(m^n)}\) and not \((a^m)^n\) (if exponentiation is indicated by stacked symbols, the rule is to work from the top down).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
09 Aug 2017, 12:27
tonebeeze wrote: If xy = 1, what is the value of \(\frac {2^{(x + y)^2}} {2^{(x  y)^2}\) ?
A. 2 B. 4 C. 8 D. 16 E. 32 We can simplify the given expression: [2^(x+y)^2]/[2^(xy)^2] Expanding the exponents in both the numerator and the denominator, we have: [2^(x^2+y^2+2xy)]/[2^(x^2+y^22xy] We subtract the denominator’s exponent from the numerator’s exponent: 2^(x^2 + y^2 + 2xy  x^2  y^2 + 2xy) 2^(2xy + 2xy) = 2^(4xy) Since xy = 1, 2^4xy = 2^4 = 16. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 10 Oct 2018
Posts: 6

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
05 Nov 2018, 23:58
HI!
I got the right answer but with different approach...
I assumed that xy=1 if x=1 and y=1;
So if we substitute x as 1 or 1 and y as 1 or 1 both lead to 16.
Can this be a correct solution?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13341
Location: United States (CA)

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
06 Nov 2018, 12:00
Hi aaliyahkhalifa, YES  your approach (TESTing VALUES) works perfectly on this question; compared with some of the longer 'mathheavy' approaches, it's considerably easier and faster. That's something to keep in mind as you continue to study for the GMAT. Most questions can be approached in more than one way  and it's possible that "your way" of dealing with a question might not actually be the most efficient option. Learning multiple approaches/Tactics can make the overall GMAT a lot easier to deal with and is essential to maximizing your performance on Test Day. 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!*****



Manager
Joined: 22 Sep 2014
Posts: 109

If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
14 Nov 2018, 21:24
what the xxxx
my lord
i just took prep1 ...spent like 8 min on this question ..eventually i had to give up ,,
It was the very first question !! can you believe it ???? 8 min wasted on this one .......
what i saw is different from this lol
2(x+y)^2 / 2(x−y)^2
no wonder i couldnt get an answer ....my lord ..very disgusting
my fault ????? geeeeeeeeeeeeeeeeeee



Director
Joined: 13 Mar 2017
Posts: 697
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
14 Nov 2018, 22:12
tonebeeze wrote: If xy = 1, what is the value of \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}\) ?
A. 2 B. 4 C. 8 D. 16 E. 32 \(\frac{2^{(x+y)^2}}{2^{(xy)^2}}\) \(= 2^{(x+y)^2  (xy)^2}\) \(= 2^{(4xy)}\) \(= 2^{(4xy)}\) \(= 2^4\) \(= 16\)
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Intern
Joined: 11 Jun 2018
Posts: 7

Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2?
[#permalink]
Show Tags
21 Nov 2018, 06:15
newyork2012 wrote: what the xxxx
my lord
i just took prep1 ...spent like 8 min on this question ..eventually i had to give up ,,
It was the very first question !! can you believe it ???? 8 min wasted on this one .......
what i saw is different from this lol
2(x+y)^2 / 2(x−y)^2
no wonder i couldnt get an answer ....my lord ..very disgusting
my fault ????? geeeeeeeeeeeeeeeeeee I did the exact same thing, I don't think that it is presented as clearly as it should be. Rather frustrating.




Re: If xy = 1, what is the value of 2^(x + y)^2/2^(xy)^2? &nbs
[#permalink]
21 Nov 2018, 06:15






