If (x – 1)^2 = 144, which of the following could be the value of 2x?

Question

A. –26
B. –22
C. –11
D. 12
E. 13

Manonamission · Answer

If (x-1)^2 = 144 
then (x-1) = Sq rt 144
 = 12 ( can have both positive and negative values)
If positive 
then (x-1) = 12
=> x = 13 =>  2x = 26 
If negative 
then (x-1) = -12
=> x = -12+1 = -11 =>  2x = -22 
Out of options given, we can see B has -22 value . Hence  option B

BrentGMATPrepNow · Answer

Several possible approaches!
Approach #1: 
(x – 1)² = 144
So, EITHER x - 1 = 12 OR x - 1 = -12

If x - 1 = 12, then x = 13, which means 2x = 26.
Not among the answer choices.

If x - 1 = -12, then x = -11, which means 2x = -22
Answer:  B

BrentGMATPrepNow · Answer

APPROACH #2
Given: (x – 1)² = 144
Expand to get: x² - 2x + 1 = 144
Rearrange: x² - 2x - 143 = 0
Factor: (x - 13)(x + 11) = 0
So, EITHER x = 13 OR x = -11

If x = 13, then 2x = 26.
Not among the answer choices.

If x = -11, then 2x = -22
Answer: B

BrentGMATPrepNow · Answer

APPROACH #3 -  Test the answer choices

A. -26  
If 2x = -26, then x =  -13 
Replace x with  -13  in the original equation to get: ( -13  – 1)² = 144
Simplify: (-14)² = 144
Evaluate: 196 = 144 
no good. keep going....

B. -22  
If 2x = -22, then x =  -11 
Replace x with  -11  in the original equation to get: ( -11  – 1)² = 144
Simplify: (-12)² = 144
Evaluate: 144 = 144 BINGO!!!

Answer:  B

duahsolo · Answer

You can also get to the answer by backsolving using answer choices

Starting with choice C = -11

(x – 1)^2 = 144

(-11– 1)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -11 will result in 144 in the equation so x must be -11,

Then 2x = 2 * -11 = -22

Answer: B

mayanksachdev7 · Answer

My doubt is tangential to what we did, Was there a specific case in which the square root of something had to be positive ?
I understand that -12^2 and 12^2 are both 144 but what if it's like \sqrt{12^2}
that has to be positive right but then why it isn't in our case.
Sorry for sounding really convoluted, but I had read something like that somewhere and cannot find where ?

ScottTargetTestPrep · Answer

Solution:
 
Since (x - 1)^2 = 144, we see that x - 1 could be 12 or -12.

If x - 1 = 12, then x = 13 and 2x = 26.

If x - 1 = -12, then x = -11 and 2x = -22.

Since only -22 is in the given answer choices, B is the correct answer.

Answer: B

Abhishek009 · Answer

(x - 1 ) = + 12 & - 12

Or, x = 13 , -11

SO, 2x = 26 Or, -22, Answer must be (B)

If (x – 1)^2 = 144, which of the following could be the value of 2x?

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GMAT Problem Solving (PS) Questions

If (x – 1)^2 = 144, which of the following could be the value of 2x?

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