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# When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42
GPA: 3.82
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?  [#permalink]

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Updated on: 08 Feb 2016, 21:27
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:52) correct 35% (02:37) wrong based on 78 sessions

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When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?

A. 2
B. 4
C. 8
D. 16
E. 32

* A solution will be posted in two days.

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 04 Feb 2016, 18:22. Last edited by MathRevolution on 08 Feb 2016, 21:27, edited 1 time in total. Retired Moderator Joined: 13 Apr 2015 Posts: 1676 Location: India Concentration: Strategy, General Management GMAT 1: 200 Q1 V1 GPA: 4 WE: Analyst (Retail) Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? [#permalink] ### Show Tags 04 Feb 2016, 20:03 2 2^a = (2^x)*(2^(1/x)) 2^b = (2^x)/(2^(1/x)) (2^a)^2 = 2^2a = (2^2x)*(2^2/x) (2^b)^2 = 2^2b = (2^2x)/(2^2/x) ((2^a)^2)/(2^b)^2) = (2^2/x) * (2^2/x) = 2^4/x If x = 1 then Answer = 16 If x = 2 then Answer = 4 If x = 4 then Answer = 1 If x = 4/3 then Answer = 8 If x = 4/5 then Answer = 32 Thus we can have multiple answers for this question since value of x is not specified. Please correct the question or let me know if I have made a mistake. Intern Joined: 04 May 2015 Posts: 11 Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? [#permalink] ### Show Tags 04 Feb 2016, 20:30 I think you are correct Vyshak. I have also got the same ans. Math Expert Joined: 02 Aug 2009 Posts: 7764 Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? [#permalink] ### Show Tags 04 Feb 2016, 21:13 Vyshak wrote: 2^a = (2^x)*(2^(1/x)) 2^b = (2^x)/(2^(1/x)) (2^a)^2 = 2^2a = (2^2x)*(2^2/x) (2^b)^2 = 2^2b = (2^2x)/(2^2/x) ((2^a)^2)/(2^b)^2) = (2^2/x) * (2^2/x) = 2^4/x If x = 1 then Answer = 16 If x = 2 then Answer = 4 If x = 4 then Answer = 1 If x = 4/3 then Answer = 8 If x = 4/5 then Answer = 32 Thus we can have multiple answers for this question since value of x is not specified. Please correct the question or let me know if I have made a mistake. hi, you are absolutely correct in your observation.. looking at the equation and the OA, the equation could have been:- (2^a)^(a+b)/(2^b)^(a+b).. try out this Q .. just a point, in these Q to save time, take the power to the numerator and then substitute for a and b.. example 2^a/2^b= 2^(a-b)= 2^(x + 1/x - x - (1/x)) = 2^(2/x)... you should do this when you see a and b have common terms with change of sign.. Ofcourse, the way you have done is also absolutely correct.. _________________ Intern Joined: 14 Jul 2015 Posts: 22 GMAT 1: 680 Q44 V40 GMAT 2: 710 Q49 V37 Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? [#permalink] ### Show Tags 04 Feb 2016, 22:09 I have an itching feeling that my method is grasping at too many straws, but it gave me the correct answer. Can anyone give me some feedback on my method for solving the question? Solve for a to get a = 2: 1. Given: $$a = x + \frac{1}{x}$$ 2. $$ax = x^2 + \frac{x}{x}$$ -> $$ax = x^2 + 1$$ 3. $$0 = x^2 - ax + 1$$ 4. $$x^2 - ax + 1 = (x-1)^2$$. To complete the expression, a = 2 Solve for b to get b = 0: 1. Given: $$b = x - \frac{1}{x}$$ 2. $$bx = x^2 - \frac{x}{x}$$ -> $$bx = x^2 - 1$$ 3. $$0 = x^2 - bx - 1$$ 4. $$x^2 - bx - 1 = (x - 1)(x + 1)$$. To complete the expression, b = 0 We plug in a = 2 and b = 0 into $$\frac{(2^a)^2}{(2^b)^2}=?$$: 1. $$\frac{(2^a)^2}{(2^b)^2}=?$$ 2. $$\frac{{2^{2a}}}{{2^{2b}}}=?$$ 3. $$2^{2a} * 2^{-2b}$$ 4. $$2^{2(a - b)}$$ 5. $$2^{2(2 - 0)}$$ 6. $$2^4 = 16$$ My answer is D, 16. Please let me know if the method I used is incorrect or if you have any improvements on the method used. Retired Moderator Joined: 13 Apr 2015 Posts: 1676 Location: India Concentration: Strategy, General Management GMAT 1: 200 Q1 V1 GPA: 4 WE: Analyst (Retail) Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? [#permalink] ### Show Tags 04 Feb 2016, 22:31 1 Hi @Beixi88, Your solution focuses only on one of the solutions for 'a'. But a can also vary with the value of x. According to your solution, we have one of the equations as x^2 - ax + 1 = 0. Here we have two unknowns x and a.. X and a can be plugged in many ways to solve the equation. If x = 2, 5 - 2a = 0 --> a = 5/2. Thus we can have many values of a depending on the value of x. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7612 GMAT 1: 760 Q51 V42 GPA: 3.82 When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? [#permalink] ### Show Tags Updated on: 08 Feb 2016, 21:30 When a=x+(1/x) and b=x-(1/x), (2^a)^2/(2^b)^2=? A. 2 B. 4 C. 8 D. 16 E. 32 --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=2/x and a+b=2x, 2^(a-b)(a+b)=2^(2/x)(2x)=2^4=16. Therefore, the answer is D. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Originally posted by MathRevolution on 08 Feb 2016, 00:16.
Last edited by MathRevolution on 08 Feb 2016, 21:30, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?  [#permalink]

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08 Feb 2016, 00:32
MathRevolution wrote:
When a=x+(1/x) and b=x-(1/x), (2^a)^2/(2^b)^2=?

A. 2
B. 4
C. 8
D. 16
E. 32

--> (2^a)^2/(2^b)^2 ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=2/x and a+b=2x, 2^(a-b)(a+b)=2^(2/x)(2x)=2^4=16.

HI,

I am sorry, your solution is wrong,...
(2^a)^2/(2^b)^2 = 2^(2a-2b) and not {(2)^(a^2-b^2)}

(2^a)^2=(2^a)*(2^a)=2^(a+a)= 2^2a..
REQUEST rectify the Question or the answer accordingly
_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7764
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?  [#permalink]

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08 Feb 2016, 20:55
chetan2u wrote:
MathRevolution wrote:
When a=x+(1/x) and b=x-(1/x), (2^a)^2/(2^b)^2=?

A. 2
B. 4
C. 8
D. 16
E. 32

--> (2^a)^2/(2^b)^2 ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=2/x and a+b=2x, 2^(a-b)(a+b)=2^(2/x)(2x)=2^4=16.

HI,

I am sorry, your solution is wrong,...
(2^a)^2/(2^b)^2 = 2^(2a-2b) and not {(2)^(a^2-b^2)}

(2^a)^2=(2^a)*(2^a)=2^(a+a)= 2^2a..
REQUEST rectify the Question or the answer accordingly

Hi Bunuel,
since you are the math expert here..
May I request you to inform MathRevolution to be slightly careful in the wordings of his Q.
Inspite of observations raised by members, he just moves on to the next question without correcting the previous ones.

But this time he has gone beyond that.
He has changed the power rule of exponent... (a^m)^n= a^mn
..

I have nothing against the institute, but this attitude may harm the institute itself.
that's ofcourse is their outlook but NOW we are teaching wrong things to students..
As, There will be many who will take his answer as correct since he is the source..
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?  [#permalink]

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08 Feb 2016, 21:28
Sorry for the confusion.

I have modified the question and the solution.

Thank you.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?  [#permalink]

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08 Feb 2016, 21:37
MathRevolution wrote:
Sorry for the confusion.

I have modified the question and the solution.

Thank you.

Hi,
thanks a lot...
pl dont mistake me. I did think there were some typo error..
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Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?  [#permalink]

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29 Dec 2018, 12:14
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Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?   [#permalink] 29 Dec 2018, 12:14
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