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What is the value of |x|? (1) |x2 + 16| – 5 = 27

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by rommysingh » Sun Aug 02, 2015 7:21 am
What is the value of |x|?

(1) |x2 + 16| - 5 = 27

(2) x2 = 8x - 16

I solved this question as

1)x^2 + 16 = 27+5
X^2 = 32-16
X^2 = +_4

x^2 + 16 = -32
x^2 = -32-16
x^2 = -48
Since we are dealing with absolute numbers we need to test both + and _ case. but the answer is D. I don't get it. please help.
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by DavidG@VeritasPrep » Sun Aug 02, 2015 7:52 am
What is the value of |x|?

(1) |x2 + 16| - 5 = 27

(2) x2 = 8x - 16

I solved this question as

1)x^2 + 16 = 27+5
X^2 = 32-16
X^2 = +_4

x^2 + 16 = -32
x^2 = -32-16
x^2 = -48
Since we are dealing with absolute numbers we need to test both + and _ case. but the answer is D. I don't get it. please help.
For statement 1, I think you meant to write x = 4 or -4, not x^2. But in any case, we're not looking for the value of x, we're looking for the value of |x|. The absolute value of both 4 and -4 is 4, so even though we don't know the unique value of x, we do know, definitively that |x| = 4.
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by DavidG@VeritasPrep » Sun Aug 02, 2015 7:55 am
For statement 2, we have: x^2 = 8x - 16
This simplifies to x^2 - 8x +16 = 0

Factor to get (x-4)(x-4) = 0.
x = 4, so |x| = 4. Only one possible value, so this is also sufficient.
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by Brent@GMATPrepNow » Sun Aug 02, 2015 8:47 am
rommysingh wrote:What is the value of |x|?

(1) |x² + 16| - 5 = 27
(2) x² = 8x - 16
If If |x| = k, then x = k or x = -k
Note: this rule assumes that k is positive.

--------------------------------------
Target question: What is the value of |x|

Statement 1: |x² + 16| - 5 = 27
Add 5 to both sides to get: |x² + 16| = 32
So, x² + 16 = 32 or x² + 16 = -32
If x² + 16 = 32, then x² = 16, which means x = 4 or -4
If x² + 16 = -32, then x² = -48. No solutions.
So, x = 4 or x = -4
For BOTH possible values of x, |x| = 4.
In other words, |x| MUST EQUAL 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x² = 8x - 16
Rewrite as x² - 8x + 16 = 0
Factor: (x - 4)(x - 4) = 0
So, x = 4, which means |x| MUST EQUAL 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

We have a free video on solving equations with absolute values: https://www.gmatprepnow.com/module/gmat- ... ing?id=972

Cheers,
Brent
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by nikhilgmat31 » Wed Aug 05, 2015 12:45 am
both statement result in |x| = 4

Answer is D
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by rommysingh » Wed Aug 05, 2015 8:37 am
Thanks Everyone for the responce. Much help!
I had a doubt when the value was coming to be x^2 = -48
*as this is not possible hence 4 is the number.
Thanks!
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by [email protected] » Thu Aug 06, 2015 2:26 pm
Hi All,

This question was also recently discussed here:

https://www.beatthegmat.com/x-t284372.html

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