Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46167

If a ≠ 0, does xa = a ? [#permalink]
Show Tags
24 Aug 2015, 23:51
Question Stats:
60% (00:58) correct 40% (00:59) wrong based on 182 sessions
HideShow timer Statistics



Senior Manager
Joined: 21 Jan 2015
Posts: 283
Location: India
Concentration: Strategy, Marketing
WE: Sales (Consumer Products)

Re: If a ≠ 0, does xa = a ? [#permalink]
Show Tags
25 Aug 2015, 00:38
Bunuel wrote: If a ≠ 0, does xa = a ?
(1) x is a single digit prime integer
(2) 0 < a < 10[/i] Ans: A Solution: because a ≠ 0 : we can say xaa=0 a(x1)= 0 so x=1 we need to see that is x=1 or not? 1) x is a prime number means x can not be 1 so it gives us the ans [Sufficient] 2) this statement talks about the values of a but nothing about x so [Not sufficient]
_________________
 The Mind is Everything, What we Think we Become. Kudos will encourage many others, like me. Please Give Kudos !! Thanks



Manager
Joined: 26 Dec 2012
Posts: 146
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)

Re: If a ≠ 0, does xa = a ? [#permalink]
Show Tags
25 Aug 2015, 10:42
Reframe the question; xa=a when x=1 or a=1, otherwise xa is not = a. 1. x = 2,3,5,7; hence xa will never = a; sufficient 2. a = 1,2,3,4...9 so xa may = a or xa may not =a, Not sufficient.
Hence A.
Thanks



Intern
Joined: 13 Nov 2014
Posts: 48
GMAT 1: 590 Q42 V29 GMAT 2: 630 Q47 V29

If a ≠ 0, does xa = a ? [#permalink]
Show Tags
25 Aug 2015, 19:11
A should be the answer, Because to prove xa = a, x must be 1, per 1st statement, x is a prime number and hence x cannot be 1 [Remember that 1 is not a prime number], so enough. per 2nd statement, x may be or may not be 1, hence out.
_________________
 Consider Cudos if you like this post. 



Manager
Joined: 14 Mar 2014
Posts: 148

Re: If a ≠ 0, does xa = a ? [#permalink]
Show Tags
25 Aug 2015, 22:58
Bunuel wrote: If a ≠ 0, does xa = a ?
(1) x is a single digit prime integer
(2) 0 < a < 10
Kudos for a correct solution. IMO: AIf a ≠ 0, does xa = a ? xaa = 0 a(x1) = 0 since a ≠ 0, the question is asking if x =1 ? St 1: x is a single digit prime integerThus x = {2,3,5,7} Thus x ≠ 1. Suff St 2: 0 < a < 10Gives nothing whether x = 1 or not Not Suff
_________________
I'm happy, if I make math for you slightly clearer And yes, I like kudos ¯\_(ツ)_/¯



Director
Joined: 21 May 2013
Posts: 646

Re: If a ≠ 0, does xa = a ? [#permalink]
Show Tags
26 Aug 2015, 00:17
Bunuel wrote: If a ≠ 0, does xa = a ?
(1) x is a single digit prime integer
(2) 0 < a < 10
Kudos for a correct solution. Statement 1: x is a single digit prime number i.e x=2,3,5 or 7 Now, is xa=a? This can only be possible if a=0. But a is not equal to 0(given) Therefore, xa will never be equal to a. Sufficient Statement 2: 0<a<10 If a=1,x=1, then xa=a But if x=0, a=1, then , above equation does not hold true. Insufficient Answer A



Math Expert
Joined: 02 Sep 2009
Posts: 46167

Re: If a ≠ 0, does xa = a ? [#permalink]
Show Tags
30 Aug 2015, 09:17
Bunuel wrote: If a ≠ 0, does xa = a ?
(1) x is a single digit prime integer
(2) 0 < a < 10
Kudos for a correct solution. PRINCETON REVIEW OFFICIAL SOLUTION:The question is equivalent to asking “Does x = 1?” For the first statement, x could be 2, 3, 5 or 7. In each case, given that a ≠ 0, the answer to the question “Does xa = a ?” is ‘no’ so the statement is sufficient. Statement (2) on the other hand is no help – x could be 1 for any number chosen for a or x could be some other number. So, the correct answer to this question is (A). However, anybody who forget that 1 is not prime, would probably think that the first statement could lead to either a ‘yes’ or a ‘no’ answer to the question. That person would most likely pick (E) as their answer. The moral to the story is that the GMAT test writers employ very precise language when they write questions. In order to avoid the traps, you need to know the precise definitions of the terms employed and you need to take the time to explore all the possibilities implied by those terms.
_________________
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



NonHuman User
Joined: 09 Sep 2013
Posts: 7004

Re: If a ≠ 0, does xa = a ? [#permalink]
Show Tags
16 Mar 2017, 19:34
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




Re: If a ≠ 0, does xa = a ?
[#permalink]
16 Mar 2017, 19:34






