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Math Revolution GMAT Instructor V
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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1
3 00:00

Difficulty:   45% (medium)

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

### HideShow timer Statistics 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.

_________________

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.
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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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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]

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I think you are correct Vyshak. I have also got the same ans.
Math Expert V
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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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]

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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. $$2^4 = 16$$

Please let me know if the method I used is incorrect or if you have any improvements on the method used.
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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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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 V
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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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.
_________________

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 V
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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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 V
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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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 V
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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Sorry for the confusion.

I have modified the question and the solution.

Thank you.
_________________
Math Expert V
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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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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Posts: 11720
Re: When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=?  [#permalink]

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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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