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What is the value of x ?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Dec 18, 2019 5:38 am

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BTGmoderatorDC wrote:What is the value of x ?

(1) \(4^{x + 1} + 4^x = 320\)
(2) \(x^2 = 9\)

OA A

Source: Official Guide
Let's take each statement one by one.

(1) \(4^{x + 1} + 4^x = 320\)

\(4^x*(4 + 1) = 320\)

\(4^x*5 = 320\)

\(4^x = 64\)

\(x=3\). Sufficient

(2) \(x^2 = 9\)

\(x = ±3\). No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Wed Dec 18, 2019 6:06 am

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Your Answer

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C

D

E

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BTGmoderatorDC wrote:What is the value of x ?

(1) \(4^{x + 1} + 4^x = 320\)
(2) \(x^2 = 9\)
Target question: What is the value of x ?

Statement 1: \(4^{x + 1} + 4^x = 320\)
Factor the left side to get: \(4^x(4^1 + 1) = 320\)
Simplify to get: \(4^x(5) = 320\)
Divide both sides by 5 to get: \(4^x = 64\)
Solve: x = 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: \(x^2 = 9\)
This equation has two possible solutions: x = 3 and x = -3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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