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

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

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New post Updated on: 10 Sep 2015, 08:33
1
00:00
A
B
C
D
E

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

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New post 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.
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Re: If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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New post 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?
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If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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New post 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.
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Re: If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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New post 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.
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Re: If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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New post 01 Aug 2018, 08:03
I dont really understand this question, could someone elaborate?
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If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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New post 01 Aug 2018, 08:15
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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
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If x^a = 2, x^b = 3 and x^c = 6 then x^(3a + b - 2c) = ?  [#permalink]

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New post 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!
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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! :)

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

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New post 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 \(x^c = 6\)
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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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