Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45458

2
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
Question Stats:
64% (02:33) correct 36% (02:14) wrong based on 56 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 45458

Re M2637 [#permalink]
Show Tags
16 Sep 2014, 01:26
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Official Solution: (1) \(2^{xy}=\sqrt[(x+y)]{16}\) \(2^{xy}=16^{\frac{1}{x+y}}=2^{\frac{4}{x+y}}\); Equate the powers: \(xy=\frac{4}{x+y}\); \((xy)(x+y)=4\). Now, since both \(x\) and \(y\) are integers (and \(x+y \gt 0\)) then \(xy=2\) and \(x+y=2\) so, \(x=2\) and \(y=0\). Therefore, \((x+y)^{xy}=2^0=1=odd\), so the answer to the question is No. Sufficient. (Note that \(xy=1\) and \(x+y=4\) is not a valid scenario (solution), since in this case we would have that \(x=2.5\) and \(y=1.5\), which is not possible as given that both unknowns must be integers) (2) \(2^x+3^y=\sqrt[(x+y)]{25}\). Obviously \(\sqrt[(x+y)]{25}\) must be an integer (since \(2^x+3^y=integer\)) and as \(x+y=integer\) then the only solution is \(\sqrt[(x+y)]{25}=\sqrt[2]{25}=5\) giving \(x+y=2\). So, \(2^x+3^y=5\). From that, two scenarios are possible: A. \(x=2\) and \(y=0\) (notice that \(x+y=2\) holds true): \(2^x+3^y=2^2+3^0=5\), and in this case: \((x+y)^{xy}=2^0=1=odd\); B. \(x=1\) and \(y=1\) (notice that \(x+y=2\) holds true): \(2^x+3^y=2^1+3^1=5\), and in this case: \((x+y)^{xy}=2^1=2=even\). Two different answers. Not sufficient. Answer: A
_________________
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



Intern
Joined: 17 Mar 2015
Posts: 16

Re M2637 [#permalink]
Show Tags
26 Jun 2016, 06:43
I think this is a poorquality question and I agree with explanation. I think it's quite a stretch to expect this question to be solved in 2 minutes.



Senior Manager
Joined: 31 Mar 2016
Posts: 402
Location: India
Concentration: Operations, Finance
GPA: 3.8
WE: Operations (Commercial Banking)

Re M2637 [#permalink]
Show Tags
07 Aug 2016, 02:52
I think this is a highquality question and I agree with explanation. Fantabulous question!



Manager
Joined: 29 Feb 2016
Posts: 106
Location: India
GPA: 3

Re: M2637 [#permalink]
Show Tags
31 Oct 2016, 21:39
Is there any simple method to know whether a large number is prime or not ?
_________________
Find what you love and let it kill you. — Charles Bukowski



Intern
Joined: 26 Jul 2016
Posts: 3

Re: M2637 [#permalink]
Show Tags
15 Dec 2016, 23:33
Hi Bunuel... not able to understand how you got xy=2 and x+y=2 in statement 1.



Math Expert
Joined: 02 Sep 2009
Posts: 45458

Re: M2637 [#permalink]
Show Tags
16 Dec 2016, 06:12



Director
Joined: 18 Aug 2016
Posts: 632
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38

Re: M2637 [#permalink]
Show Tags
21 Jun 2017, 05:58
Bunuel wrote: If \(x\) and \(y\) are nonnegative integers and \(x+y \gt 0\) is \((x+y)^{xy}\) an even integer?
(1) \(2^{xy}=\sqrt[(x+y)]{16}\)
(2) \(2^x+3^y=\sqrt[(x+y)]{25}\) BunuelCan you suggest any other approach for the (2)?? Basically to reject that the second equation is sufficient Thanks
_________________
We must try to achieve the best within us
Thanks Luckisnoexcuse



Math Expert
Joined: 02 Sep 2009
Posts: 45458

Re: M2637 [#permalink]
Show Tags
21 Jun 2017, 07:05



Director
Joined: 18 Aug 2016
Posts: 632
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38

Bunuel wrote: mynamegoeson wrote: Bunuel wrote: If \(x\) and \(y\) are nonnegative integers and \(x+y \gt 0\) is \((x+y)^{xy}\) an even integer?
(1) \(2^{xy}=\sqrt[(x+y)]{16}\)
(2) \(2^x+3^y=\sqrt[(x+y)]{25}\) BunuelCan you suggest any other approach for the (2)?? Basically to reject that the second equation is sufficient Thanks I think identifying that RHS and LSH must be integers, is pretty much it. Thank you,,i think now i understand the difference between Q40s and Q50s
_________________
We must try to achieve the best within us
Thanks Luckisnoexcuse



Manager
Joined: 22 Apr 2017
Posts: 113
Location: India
GMAT 1: 620 Q46 V30 GMAT 2: 620 Q47 V29 GMAT 3: 630 Q49 V26 GMAT 4: 690 Q48 V35
GPA: 3.7

Re: M2637 [#permalink]
Show Tags
21 Jul 2017, 04:01
Hi Bunuel, Can we conclude from the below mentioned eqn, (xy)(x+y)=4 that either (xy) or (x+y) has to be even? & if (xy) is even the (x+y) is bound to be even.
Hence (x+y)^xy will be even. But if any of x,y is 0, the result is odd. Kindly help.



Math Expert
Joined: 02 Sep 2009
Posts: 45458

Re: M2637 [#permalink]
Show Tags
21 Jul 2017, 04:10
ManishKM1 wrote: Hi Bunuel, Can we conclude from the below mentioned eqn, (xy)(x+y)=4 that either (xy) or (x+y) has to be even? & if (xy) is even the (x+y) is bound to be even.
Hence (x+y)^xy will be even. But if any of x,y is 0, the result is odd. Kindly help. Yes, since both x and y are integers then for (x  y)(x + y) = even to be true at least one of the multiples must be even. Next, it turns out that if x + y is even, then x  y is even too and viseversa. After this I lost you. What is your question?
_________________
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: 22 Apr 2017
Posts: 113
Location: India
GMAT 1: 620 Q46 V30 GMAT 2: 620 Q47 V29 GMAT 3: 630 Q49 V26 GMAT 4: 690 Q48 V35
GPA: 3.7

Re: M2637 [#permalink]
Show Tags
21 Jul 2017, 07:09
I mean to say is Since x+y is even, (x+y)^xy will be even, but if any of x,y is 0, the result is 1. So not sufficient???
Thanks!!



Math Expert
Joined: 02 Sep 2009
Posts: 45458

Re: M2637 [#permalink]
Show Tags
21 Jul 2017, 07:15



Manager
Joined: 22 Apr 2017
Posts: 113
Location: India
GMAT 1: 620 Q46 V30 GMAT 2: 620 Q47 V29 GMAT 3: 630 Q49 V26 GMAT 4: 690 Q48 V35
GPA: 3.7

Re: M2637 [#permalink]
Show Tags
21 Jul 2017, 07:19
Its clear now. Thanks for your prompt reply.



Intern
Joined: 24 Jul 2017
Posts: 18
Location: Germany
WE: Research (Energy and Utilities)

Re: M2637 [#permalink]
Show Tags
09 Sep 2017, 10:46
How does y=0 satisfy the "nonnegative integer" part? Zero is neither positive nor negative.



Math Expert
Joined: 02 Sep 2009
Posts: 45458

Re: M2637 [#permalink]
Show Tags
09 Sep 2017, 10:48



Intern
Joined: 13 Jun 2015
Posts: 5

Re: M2637 [#permalink]
Show Tags
23 Apr 2018, 11:39
Hi! Can anyone please explain the second statement graphically?










