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What the value of w^-2?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Jul 27, 2017 12:22 pm

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jjjinapinch wrote:What the value of w^-2?

(1) w^-1 = 1/2
(2) w^3 = 8

Official Guide question
Answer: D
Target question: What is the value of w^-2?

Statement 1: w^(-1) = 1/2
w^(-1) = 1/w
So, statement 1 is telling us that 1/w = 1/2, which means w = 2, which means w^(-2) = 2^(-2) = 1/4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: w^3 = 8
Only one value of w satisfies this equation: w = 2, which means w^(-2) = 2^(-2) = 1/4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

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by [email protected] » Sun May 20, 2018 3:16 pm

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Hi All,

We're asked for the value of w^(-2). This is a great example of a 'concept question' - meaning that you don't actually have to do any math to get the answer as long as you understand the concept(s) involved.

The concepts tested here are all about exponents of numbers. The two FACTS both deal with ODD exponents. When an exponent is an ODD number, there is just one solution and the 'sign' will match whatever the 'sign' of the number is. For example:

A^1 = 2 has just one solution: +2
X^3 = -27 has just one solution: -3
Y^(-1) = 1/4 has just one solution: +4
Z^(-3) = 1/125 has just one solution: +5
Etc.

1) W^-1 = 1/2

The equation in Fact 1 has an ODD exponent, so there is just one solution. Since W has just one value, there would be just one value of W^(-2).
Fact 1 is SUFFICIENT.

2) W^3 = 8

The equation in Fact 2 has an ODD exponent, so there is just one solution. Since W has just one value, there would be just one value of W^(-2).
Fact 2 is SUFFICIENT.

Final Answer: D

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Re: What the value of w^-2?

by AdityaBir » Fri Jan 24, 2020 5:02 am

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w^-2 = ?
1) w^-1 =1/2
1/w = 1/2 => w=2.
w^-2 = 1/4.
statement 1) alone is sufficient.
2) w^3 = 8
w=2
w^-2 = 1/4.
statement 2) alone is also sufficient.
Both statements independently are suffcient.
Hence option D is correct.
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