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8^a(1/4)^b=??? Please Help

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8^a(1/4)^b=??? Please Help

by Nadia222 » Sat May 03, 2014 9:22 am
Can someone please explain the answer to this question step by step.

8^a(1/4)^b=

1. B=1.5a
2. A=2

I do understand that I can express 8 in powers of 2 so that section becomes 2^3a but how do I express 1/4 in power of 2's?
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat May 03, 2014 12:27 pm
Hi Nadia222,

When posting exponents, please use brackets to avoid any ambiguity. I believe the question should look like this...
Nadia222 wrote:
What is the value of (8^a)(1/4)^b?

1) b = 1.5a
2) a = 2
Target question: What is the value of (8^a)(1/4)^b?
Let's take (8^a)(1/4)^b and rewrite both parts with the same base of 2.
Notice that 8 = 2^3 and 1/4 = 2^(-2)
So, we can rewrite the original expression as: [(2^3)^ a][2^(-2)]^b
Simplify to get: (2^3a)(2^-2b) [power of a power law]
Combine terms to get: 2^(3a - 2b)
To determine the value of 2^(3a - 2b), we must determine the value of (3a - 2b)
So, let's rephrase the target question.
REPHRASED target question: What is the value of 3a - 2b?

Statement 1: b = 1.5a
Take 3a - 2b and replace b with 1.5a to get:
3a - 2b = 3a - 2(1.5a)
= 3a - 3a
= 0
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: a = 2
Not enough info to determine the value of 3a - 2b
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Si4S » Mon Jun 09, 2014 1:46 pm
Nadia222,

Can you site the source for this problem?

My answer is A as well.

Thanks,
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by GMATGuruNY » Mon Jun 09, 2014 3:45 pm
Nadia222 wrote:Can someone please explain the answer to this question step by step.

(8^a)(1/4)^b = ?

1. B=1.5a
2. A=2
An alternate approach is to test cases.

Statement 1: b = 1.5a
Case 1: a=2, b=3.
In this case, (8^a)(1/4)^b = (8²)(1/4)³ = (64)(1/64) = 1.
Case 2: a=4, b=6
In this case, (8^a)(1/4)^b = (8�)(1/4)� = (8²)(8²)(1/4)³(1/4)³ = (64)(64)(1/64)(1/64) = 1.
The cases above illustrate that, if b=1.5a, then (8^a)(1/4)^b = 1.
SUFFICIENT.

Statement 2: a=2
Case 1 also satisfies statement 2.
In Case 1, (8^a)(1/4)^b = 1.
Case 3: a=2, b=0
In this case, (8²)(1/4)� = (64)(1) = 64.
Since (8^a)(1/4)^b can be different values, INSUFFICIENT.

The correct answer is A.
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