Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Jul 2012
Posts: 11

If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
Updated on: 15 Sep 2013, 12:08
Question Stats:
35% (01:04) correct 65% (01:05) wrong based on 435 sessions
HideShow timer Statistics
If a^5 ≤ a, which of the following must be true? I. –1 ≤ a ≤ 0 II. a=0 III. 0 ≤ a ≤ 1 A. None of the above B. I only C. II only D. III only E. I and III only Please help me in this. TIA.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by nroy347 on 15 Sep 2013, 12:04.
Last edited by Bunuel on 15 Sep 2013, 12:08, edited 1 time in total.
Edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 48044

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
15 Sep 2013, 12:12



Intern
Joined: 10 Sep 2013
Posts: 39
Location: United States
Concentration: Strategy, Operations
GMAT Date: 12102013
GPA: 3.5
WE: Operations (Manufacturing)

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
18 Sep 2013, 07:27
can u plz elaborate y D is nt d correct answer



Math Expert
Joined: 02 Sep 2009
Posts: 48044

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
18 Sep 2013, 07:45



Intern
Joined: 07 Aug 2013
Posts: 24

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
18 Sep 2013, 07:48
fnumiamisburg wrote: can u plz elaborate y D is nt d correct answer 1<=X=<1 so none are true



Math Expert
Joined: 02 Sep 2009
Posts: 48044

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
18 Sep 2013, 07:51



Intern
Joined: 10 Sep 2013
Posts: 39
Location: United States
Concentration: Strategy, Operations
GMAT Date: 12102013
GPA: 3.5
WE: Operations (Manufacturing)

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
18 Sep 2013, 08:01
thanks Brunel... I got it now..



Intern
Joined: 28 Mar 2012
Posts: 5
Location: Yugoslavia
Concentration: Accounting, Finance
GPA: 3.75

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
18 Sep 2013, 09:52
Just put (2) as a possible "a" and do the work, it took me 30 sec to get to answer "A"



Math Expert
Joined: 02 Sep 2009
Posts: 48044

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
18 Sep 2013, 10:00
Predecessor wrote: Just put (2) as a possible "a" and do the work, it took me 30 sec to get to answer "A" That's a valid approach. "MUST BE TRUE" questions: These questions ask which of the following MUST be true, or which of the following is ALWAYS true for ALL valid sets of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular valid set of numbers, it will mean that this statement is not always true and hence not a correct answer. So, for "MUST BE TRUE" questions plugin method is good to discard an option but not 100% sure thing to prove that an option is ALWAYS true. As for "COULD BE TRUE" questions: The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer. So, for "COULD BE TRUE" questions plugin method is fine to prove that an option could be true. But here, if for some set of numbers you'll see that an option is not true, it won't mean that there does not exist some other set which will make this option true.
_________________
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



SVP
Joined: 06 Sep 2013
Posts: 1850
Concentration: Finance

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
20 Nov 2013, 07:21
Bunuel wrote: nroy347 wrote: If a^5 ≤ a, which of the following must be true?
I. –1 ≤ a ≤ 0 II. a=0 III. 0 ≤ a ≤ 1
A. None of the above B. I only C. II only D. III only E. I and III only
Please help me in this. TIA. \(a^5\leq{a}\) > \(a\leq{1}\) or \(0\leq{a}\leq{1}\). If a=2, then none of the options MUST be true. Answer: A. Hi Bunuel, I don't get it. How come do you get two ranges. It isn't just a^5<=a Then solve this inequality with key points after factorizing that gives 0<=a<=1? Where did you get the other range from? Cheers J



Math Expert
Joined: 02 Sep 2009
Posts: 48044

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
20 Nov 2013, 07:32
jlgdr wrote: Bunuel wrote: nroy347 wrote: If a^5 ≤ a, which of the following must be true?
I. –1 ≤ a ≤ 0 II. a=0 III. 0 ≤ a ≤ 1
A. None of the above B. I only C. II only D. III only E. I and III only
Please help me in this. TIA. \(a^5\leq{a}\) > \(a\leq{1}\) or \(0\leq{a}\leq{1}\). If a=2, then none of the options MUST be true. Answer: A. Hi Bunuel, I don't get it. How come do you get two ranges. It isn't just a^5<=a Then solve this inequality with key points after factorizing that gives 0<=a<=1? Where did you get the other range from? Cheers J \(a^5\leq{a}\) > \(a(a1)(a+1) (a^2+1)\leq{0}\) > reduce by a^2+1 since it's always positive: \(a(a1)(a+1)\leq{0}\). Now, solve it with key points approach.
_________________
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



SVP
Joined: 06 Sep 2013
Posts: 1850
Concentration: Finance

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
Updated on: 07 Feb 2014, 05:44
Bunuel wrote: fnumiamisburg wrote: can u plz elaborate y D is nt d correct answer The question asks: which of the following MUST be true. Now, 0 ≤ a ≤ 1 is NOT always true, because, a can be less than or equal to 1, say 2 ((2)^5<2), and in this case this option is not true. Does this make sense? Now I get it we need to factorize everything and get two ranges Therefore, none of the statement will HAVE to be true Answer is thus A Thanks all J
Originally posted by jlgdr on 01 Jan 2014, 07:43.
Last edited by jlgdr on 07 Feb 2014, 05:44, edited 1 time in total.



Manager
Status: Student
Joined: 26 Aug 2013
Posts: 218
Location: France
Concentration: Finance, General Management
GPA: 3.44

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
01 Jan 2014, 10:28
jlgdr wrote: Bunuel wrote: fnumiamisburg wrote: can u plz elaborate y D is nt d correct answer The question asks: which of the following MUST be true. Now, 0 ≤ a ≤ 1 is NOT always true, because, a can be less than or equal to 1, say 2 ((2)^5<2), and in this case this option is not true. Does this make sense? I don't quite get it Bunuel. I mean it looks fine that when you pick 2 it satisfies the inequality on question stem and is not good for any of the statements BUT, when one tries to find the range for a^5<=a, one ends up with 0<=a<=1, which is the exact same as option III I'm pretty sure I'm getting the reasoning incorrectly Please advice Cheers! J The trick here is more on the answer choices. Look at I II and III. all are right (pick out some numbers). Therefore I was totally confused because non of the answers had the right answer (I II and III) I finally chose D, but hesitate between A and D quite a long time... This is a tricky tricky question, since it takes into consideration that the answers are correct but they do not cover all the POSSIBLE answers. Therefore it is A. Confusing...
_________________
Think outside the box



Senior Manager
Joined: 21 Oct 2013
Posts: 433

If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
06 Jun 2014, 08:26
If a^5 ≤ a, which of the following must be true?
I –1 ≤ a ≤ 0 II a=0 III 0 ≤ a ≤ 1
A) None of the above B) I only C) II only D) III only E) I and III only



Math Expert
Joined: 02 Sep 2009
Posts: 48044

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
06 Jun 2014, 08:29



Senior Manager
Joined: 21 Oct 2013
Posts: 433

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
07 Jun 2014, 04:48
Hi, What is the difference between these 2 equations? I am trying to apply this inequality trick. http://gmatclub.com/forum/inequalitiestrick91482.htmlhttp://gmatclub.com/forum/whichofthefollowingrepresentsthecompleterangeofx108884.html\(x^34x^5<0\) > \(x^3(14x^2)<0\) > \((1+2x)(x^3)(12x)<0\) > roots are 1/2, 0, and 1/2 > \(\frac{1}{2}<x<0\) or \(x>\frac{1}{2}\). \(a^5\leq{a} > a(a1)(a+1) (a^2+1)\leq{0}\) > reduce by \((a^2+1)\) since it's always positive: \(a(a1)(a+1)\leq{0}\) > \(a^5\leq{a}\) > \(a\leq{1}\) or \(0\leq{a}\leq{1}\).



Math Expert
Joined: 02 Sep 2009
Posts: 48044

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
08 Jun 2014, 04:55



Intern
Joined: 22 Feb 2014
Posts: 27

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
15 Jul 2014, 09:45
Bunuel wrote: nroy347 wrote: If a^5 ≤ a, which of the following must be true?
I. –1 ≤ a ≤ 0 II. a=0 III. 0 ≤ a ≤ 1
A. None of the above B. I only C. II only D. III only E. I and III only
Please help me in this. TIA. \(a^5\leq{a}\) > \(a\leq{1}\) or \(0\leq{a}\leq{1}\). If a=2, then none of the options MUST be true. Answer: A. Hi How can 2 comes in the range?? 0<=a<=1.. I dont understand.. Can you pls explain.... I checked all threads in the discussion still did not get it. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 48044

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
15 Jul 2014, 10:12



Intern
Joined: 26 Jan 2017
Posts: 10

Re: If a^5 ≤ a, which of the following must be true?
[#permalink]
Show Tags
21 Feb 2017, 22:09
Hi, I have understood the whole solution except for the part where a^5 reduces to a(a1)(a+1)(a^2 1).can anyone guide me if I am doing it correctly?. a^5 <a a^5 a <0 a (a^4 1)<0 a(a^21)(a^2+1)<0 a(a+1)(a1)(a^2+1)<0 a<0 a<1 a<1




Re: If a^5 ≤ a, which of the following must be true? &nbs
[#permalink]
21 Feb 2017, 22:09



Go to page
1 2
Next
[ 21 posts ]



