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What is the value of |x|

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by Needgmat » Sun Nov 06, 2016 6:12 am
What is the value of |x|?

(1) |x^2 + 16| - 5 = 27

(2) x^2 = 8x - 16

OA
D

How statement1 is sufficient.

In this we will have two cases and both will have different value?

case 1 = |x^2 + 16| - 5 = 27

case 2 = |x^2 + 16| - 5 = -27

Please explain.

Many thanks in advance .

Kavin
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by fiza gupta » Sun Nov 06, 2016 11:37 am
1) |x^2 + 16| - 5 = 27
|x^2 + 16| = 32
x^2 + 16 = 32 (i) or x^2 + 16 = - 32 (ii)
(ii) will not hold true in this case
because x^2(always positive or 0) + 16(always positive) so sum of both will be always positive
x^2 + 16 = 32
x = +4 or -4 => |x| = 4
SUFFICIENT

2) x^2 = 8x - 16
x^2 - 8x + 16 =0
x = 4 => |x|=4
SUFFICIENT

SO D
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by [email protected] » Sun Nov 06, 2016 12:33 pm
Hi Kavin,

You have to be careful about how you 'manipulate' equations that include an Absolute Value. In Fact 1, we're given...

| X^2 + 16 | - 5 = 27

| X^2 + 16 | = 32

On the GMAT, "X^2" can never be a negative number, so adding 16 to X^2 cannot end in a negative result either. Knowing that, this equation CANNOT result in -32, so you have to remove that option from consideration.

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by Matt@VeritasPrep » Thu Dec 08, 2016 9:43 pm
S1:

|x² + 16| = 32

So (x² + 16) = 32 or (x² + 16) = -32. The second case is impossible, since no square is negative, so our only possibility is the first one: (x² + 16) = 32, or x² = 16, or |x| = 4. SUFFICIENT!

S2:

x² - 8x + 16 = 0

(x - 4)² = 0

x = 4, so |x| = 4, SUFFICIENT!
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by Jay@ManhattanReview » Thu Dec 08, 2016 10:24 pm
Needgmat wrote:What is the value of |x|?

(1) |x^2 + 16| - 5 = 27

(2) x^2 = 8x - 16

OA
D

How statement1 is sufficient.

In this we will have two cases and both will have different value?

case 1 = |x^2 + 16| - 5 = 27

case 2 = |x^2 + 16| - 5 = -27

Please explain.

Many thanks in advance .

Kavin
Hi Kevin,

Though you got the solution for the question. I see that you have written incorrect expressions for case 1 and case 2.

When you consider two cases: one on either side, you must get rid of the modulus. So the correct way of writing would be:

First take non-modulus numbers on the RHS,

Thus, |x^2 + 16| = 27 + 5

=> |x^2 + 16| = 32

Case 1 = x^2 + 16 = 32

Case 2 = x^2 + 16 = -32

Hope this helps!

-Jay

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by Scott@TargetTestPrep » Mon Dec 12, 2016 5:07 pm
Needgmat wrote:What is the value of |x|?

(1) |x^2 + 16| - 5 = 27

(2) x^2 = 8x - 16
We need to determine the value of |x|.

Statement One Alone:

|x^2 + 16| - 5 = 27

Notice that x^2 + 16 is always positive since x^2 is always nonnegative. Therefore, |x^2 + 16| = x^2 + 16, and hence solving the equation |x^2 + 16| - 5 = 27 is equivalent to solving x^2 + 16 - 5 = 27.

x^2 + 16 - 5 = 27

x^2 + 11 = 27

x^2 = 16

Taking the square root of both sides, we get x = -4 or 4, and thus the absolute value of -4 or 4 = 4.

Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

x^2 = 8x - 16

We can simplify the given equation and determine x.

x^2 = 8x - 16

x^2 - 8x + 16 = 0

(x - 4)(x - 4) = 0

x = 4

Since x = 4, |x| = 4. Statement two alone is also sufficient to answer the question.

Answer: D

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