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# If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?

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Intern
Joined: 10 Sep 2015
Posts: 26
If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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Updated on: 10 Sep 2015, 08:33
1
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:56) correct 11% (02:20) wrong based on 64 sessions

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If $$x^a = 2$$, $$x^b = 3$$ and$$x^c = 6$$ then $$x^{(3a+b-2c)} =$$ ?

A) 1/9
B) 1/6
C) 1/2
D) 2/3
E) 3/4

It's meant to read x^(3a+b-2c) = ?
Is this a valid question? I had no idea where to start?

Originally posted by skylimit on 10 Sep 2015, 08:27.
Last edited by Bunuel on 10 Sep 2015, 08:33, edited 2 times in total.
Renamed the topic and edited the question.
Manager
Joined: 13 Apr 2015
Posts: 74
Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
GPA: 3.25
WE: Project Management (Energy and Utilities)
If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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Updated on: 10 Sep 2015, 09:00
Question Stem can be re - written as

[X^(3a) * X^(b)] / [ X^(2c)]

Now Substitute the respective values fron the stem i.e (X^a) = 2, (X^b) = 3 & (X^ c) = 6.

[2^3 * 3] / 6^2 = 2 / 3.

Therefore Ans is D.

Originally posted by goldfinchmonster on 10 Sep 2015, 08:47.
Last edited by goldfinchmonster on 10 Sep 2015, 09:00, edited 1 time in total.
Intern
Joined: 10 Sep 2015
Posts: 26
Re: If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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10 Sep 2015, 08:54
goldfinchmonster wrote:
Question Stem can be re - written as

[X^(3a) * X^(b)] / [ X^(2c)]

Now Substitute the respective values fron the stem i.e (X^a) = 2, (X^b) = 3 & (X^ c) = 6.

[2^3 * 3] / 6^2 = 2 / 3.

Therefore Ans is D.

I understood the answer that was with the question, but is it a valid question? Would I ever see such a question on the real test?
Manager
Joined: 13 Apr 2015
Posts: 74
Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
GPA: 3.25
WE: Project Management (Energy and Utilities)
If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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10 Sep 2015, 09:05
Hi

Though i am not the right person to answer your query, but according to me this question can very well be a part of GMAT. It just tests basic exponent rules.

It would be nice if bunuel could put some light on this query.
CEO
Joined: 20 Mar 2014
Posts: 2631
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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10 Sep 2015, 09:34
goldfinchmonster wrote:
Hi

Though i am not the right person to answer your query, but according to me this question can very well be a part of GMAT. It just tests basic exponent rules.

It would be nice if bunuel could put some light on this query.

This is a pretty regular question for GMAT standards as it tests addition and subtration of exponents with same bases.
Senior Manager
Joined: 04 Jun 2018
Posts: 361
Location: Germany
Concentration: General Management, Finance
GPA: 3.6
WE: Analyst (Transportation)
Re: If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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01 Aug 2018, 08:03
I dont really understand this question, could someone elaborate?
_________________

A couple of things that helped me in verbal:
https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

Gmat Prep CAT #1: V42, Q34, 630
Gmat Prep CAT #2: V46, Q35, 660
Gmat Prep CAT #3: V41, Q42, 680

On the mission to improve my quant score, all help is appreciated!

MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1536
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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01 Aug 2018, 08:15
1
Arro44

Using the formula $$x^{a+b+c} = x^a * x^b * x^c$$

GIven equation $$x^{3a+b-2c}$$ can be rewritten as $$x^{3a}*x^b*x^{-2c}$$

It involves 3 terms $$x^{3a}$$ and $$x^b$$ and $$x^{-2c}$$

If we can find the values of above 3 independent terms, we can find the value of the total term

Using the formula $$(x^a)^b = x^{ab}$$

We need to find $$x^{3a}$$ => $$(x^a)^3$$ = $$2^3 = 8$$

We already have $$x^b = 3$$

$$x^{-2c}$$ = $$(x^c)^{-2}$$ = $$6^{-2}$$ = $$\frac{1}{36}$$

The product of all the terms = $$\frac{8*3}{36} = \frac{2}{3}$$

Hence option D
_________________
Senior Manager
Joined: 04 Jun 2018
Posts: 361
Location: Germany
Concentration: General Management, Finance
GPA: 3.6
WE: Analyst (Transportation)
If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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01 Aug 2018, 08:20
1
workout wrote:
Arro44

Using the formula $$(x^a)^b = x^{ab}$$

We need to find $$x^{3a}$$ => $$(x^a)^3$$ = $$2^3 = 8$$

We already have $$x^b = 3$$

Hence option D

This is where I got lost...

How come we now take some to the power of something else and then get 2?

EDIT: Its cause it was mentioned in the question stem, now I get it

Thank you!
_________________

A couple of things that helped me in verbal:
https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

Gmat Prep CAT #1: V42, Q34, 630
Gmat Prep CAT #2: V46, Q35, 660
Gmat Prep CAT #3: V41, Q42, 680

On the mission to improve my quant score, all help is appreciated!

MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1536
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

### Show Tags

01 Aug 2018, 08:22
Arro44 wrote:
workout wrote:
Arro44

Using the formula $$(x^a)^b = x^{ab}$$

We need to find $$x^{3a}$$ => $$(x^a)^3$$ = $$2^3 = 8$$

We already have $$x^b = 3$$

Hence option D

This is where I got lost...

How come we now take some to the power of something else and then get 2?

This information is provided in the question stem $$x^a = 2$$ and $$x^b = 3$$ and $$x^c = 6$$
_________________
If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ? &nbs [#permalink] 01 Aug 2018, 08:22
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# If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?

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