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Intern  Joined: 11 Jul 2015
Posts: 2
x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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1 00:00

Difficulty:   55% (hard)

Question Stats: 34% (01:35) correct 66% (01:04) wrong based on 101 sessions

### HideShow timer Statistics x = ?

(1) $$a^{(2x)}=b^{(x+6)}$$

(2) ab = 1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..

Originally posted by allenh on 06 Sep 2015, 06:07.
Last edited by Bunuel on 25 Dec 2018, 17:28, edited 3 times in total.
Renamed the topic and edited the question.
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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allenh wrote:
x = ?

(1) $$a^{(2x)}=b^{(x+6)}$$

(2) ab = 1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..

Statement 1: $$a^{(2x)}=b^{(x+6)}$$

@a=4 and b=2, $$4^{(2x)}=2^{(x+6)}$$, i.e. x can be 1
But the statement will also be balanced if a = 1/b and x = -2 hence
NOT SUFFICIENT

Statement 2: ab = 1

No relation of a and b with x is given so nothing can be concluded about x, hence
NOT SUFFICIENT

Combining the two statements
ab = 1 and $$a^{(2x)}=b^{(x+6)}$$

Substituting b = 1/a

$$a^{(2x)}=b^{(x+6)}$$ => $$a^{(2x)}=(1/a)^{(x+6)}$$

i.e. $$a^{(2x)}=b^{(x+6)}$$ => $$a^{(2x)}=(a)^{-(x+6)}$$

i.e. 2x = -(x+6)
i.e. 3x = -6
i.e. x = -2

SUFFICIENT

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Manager  Joined: 29 Jul 2015
Posts: 157
Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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allenh wrote:
x = ?

(1) $$a^{(2x)}=b^{(x+6)}$$

(2) ab = 1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..

Statement 1:
It does not provide enough information about a,b and x to get concrete values. Even on simplification, the expression will be in terms of a,b and x.
INSUFFICIENT

Statement2:
ab=1
or a=1/b
this statement provides relation between a and b but no information about x.
INSUFFICIENT

Combining 1 and 2

$$(\frac{1}{b})^{(2x)}=b^{(x+6)}$$

or $$1= b^{2x}(b^{x+6})$$
or $$1= b^{3x+6}$$
or $$b^0= b^{3x+6}$$
or 0 = 3x+6
or x=-2

SUFFICIENT

This questions is a value based data sufficiency question. You need single value of x.
here you cannot take different values of a and b because for each value of a and b you will get different values of x.
So, you should not consider a=b=1 but rather use given statements to get single distinct value of x.
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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kunal555 wrote:

This questions is a value based data sufficiency question. You need single value of x.
here you cannot take different values of a and b because for each value of a and b you will get different values of x.
So, you should not consider a=b=1 but rather use given statements to get single distinct value of x.

Not really. When statement 2 mentions that ab=1, then all combinations satisfying ab=1 , MUST give you consistent values. Thus, using a=b=1 is absolutely fine.

You can not have C as the correct answer if you got different values of x for different combinations of ab=1. If you did get different values of x, then E would have been the correct answer.
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Posts: 157
Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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1
Engr2012 wrote:
kunal555 wrote:

This questions is a value based data sufficiency question. You need single value of x.
here you cannot take different values of a and b because for each value of a and b you will get different values of x.
So, you should not consider a=b=1 but rather use given statements to get single distinct value of x.

Not really. When statement 2 mentions that ab=1, then all combinations satisfying ab=1 , MUST give you consistent values. Thus, using a=b=1 is absolutely fine.

You can not have C as the correct answer if you got different values of x for different combinations of ab=1. If you did get different values of x, then E would have been the correct answer.

My bad, did the question in a hurry and missed out on this detail. For all the values of a and b where ab=1, x will be -2, except for a=b=1 or a=b=-1 where x will be 6.
OA should be E then i guess, not C
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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X=?

1.a^(2x)=b^(x+6)

2.ab=1

In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and equations ensures a solution.

vatiables'number:3 --> needs 3 equations --> E

1) & 2)

if a=b=1, it is possble that 2x is not equal to x+1, therefore the answer is E
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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allenh wrote:
x = ?

(1) $$a^{(2x)}=b^{(x+6)}$$

(2) ab = 1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..

Dear Moderator,
Looks like the OA for this one is incorrect.

Statement 1: a=1 and b=1 then x can be anything . Hence Insufficient
Statement 2 : No info about X , Hence Insufficient

1+2

a=1 and b=1 x= 2
a=1 and b=1 x= 3
Insufficient . ( In fact if a=1 and b=1 then x can be anything )

Also please check this post my MathRevolution:
https://gmatclub.com/forum/x-1-a-2x-b-x ... l#p1570471

Hope you will look into this. Thank you.
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Posts: 56306
Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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stne wrote:
allenh wrote:
x = ?

(1) $$a^{(2x)}=b^{(x+6)}$$

(2) ab = 1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..

Dear Moderator,
Looks like the OA for this one is incorrect.

Statement 1: a=1 and b=1 then x can be anything . Hence Insufficient
Statement 2 : No info about X , Hence Insufficient

1+2

a=1 and b=1 x= 2
a=1 and b=1 x= 3
Insufficient . ( In fact if a=1 and b=1 then x can be anything )

Also please check this post my MathRevolution:
https://gmatclub.com/forum/x-1-a-2x-b-x ... l#p1570471

Hope you will look into this. Thank you.

The correct answer is E. Edited. Thank you.
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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allenh wrote:
x = ?

(1) $$a^{(2x)}=b^{(x+6)}$$

(2) ab = 1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..

Statement 1) a can be 1 or -1 or 0. Similarly, b can 1 or -1 or 0. In each case. We can't find the value of x.

Statement 2) Nothing has been given about x. Also, a or b can 1 or -1.

(1)+(2),

Same as statement 1, if a=b=1/-1, we can't find the value of x.

So, Option E seems correct.
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Re: x = ? (1) a^(2x) = b^(x+6) (2) ab = 1  [#permalink]

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allenh wrote:
x = ?

(1) $$a^{(2x)}=b^{(x+6)}$$

(2) ab = 1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..

If a = b = 1. Then X can take any value.

Hence, E.
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