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If (2/3)^n = (3/2)^2, what is the value of n?

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jsphcal
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If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post   16 Jun 2012, 20:47
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If \((\frac{2}{3})^n=(\frac{3}{2})^2\), what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2
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Bunuel
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If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post   17 Jun 2012, 02:58
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jsphcal wrote:
If (2/3)^n=(3/2)^2, what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2



Since \((\frac{3}{2})^2=(\frac{2}{3})^{-2}\) then we have that \((\frac{2}{3})^n=(\frac{2}{3})^{-2}\) --> \(n=-2\).

Answer: A.

For more on number theory and exponents check: https://gmatclub.com/forum/math-number- ... 88376.html

DS questions on exponents: https://gmatclub.com/forum/search.php?s ... &tag_id=39
PS questions on exponents: https://gmatclub.com/forum/search.php?s ... &tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: https://gmatclub.com/forum/tough-and-tr ... 25967.html
Tough and tricky PS exponents and roots questions with detailed solutions: https://gmatclub.com/forum/tough-and-tr ... 25956.html

Hope it helps.
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damham17
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Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post   16 Jun 2012, 21:16
I was surprised to see this question in the 600-700 range. It's just testing the basic exponent property involving a negative sign.

(n)^-1 = (1/n)
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damstamnd
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Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post   17 Jun 2012, 10:14
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Answer: A

A negative exponent in a fraction leads to the reciprocal of the fraction. Thus the negative exponent of 2 is -2, allowing (2/3)^(-2) = (3/2)^2.
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Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post   27 Feb 2014, 20:58
(2/3)^n = (3/2)^2
= (2/3)^-2

n = -2 (Answer = A)
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Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post   12 May 2017, 13:19
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jsphcal wrote:
If (2/3)^n=(3/2)^2, what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2


(2/3)^n = (3/2)^2

Observe that 3/2 = (2/3)^-1. Then:

(2/3)^n = ((2/3)^-1)^2

(2/3)^n=(2/3)^-2

n = -2

Alternate Solution:

Let’s distribute the exponents to the numerator and the denominator:

2^n/3^n = 3^2/2^2

If we cross multiply, we have:

2^(n + 2) = 3^(n + 2)

We see that the exponents of 2 and 3 are equal. This is only possible if n + 2 = 0. Then, n = -2.

Answer: A
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Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post   15 Jul 2023, 12:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink]
15 Jul 2023, 12:15
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