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• ### $450 Tuition Credit & Official CAT Packs FREE February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT practice February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST Instead of wasting 3 months solving 5,000+ random GMAT questions, focus on just the 1,500 you need. # What is the value of |x|?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 52905 What is the value of |x|? [#permalink] ### Show Tags 10 Nov 2014, 06:38 1 10 00:00 Difficulty: 45% (medium) Question Stats: 65% (01:44) correct 35% (01:50) wrong based on 433 sessions ### HideShow timer Statistics Tough and Tricky questions: Absolute Values. What is the value of |x|? (1) |x^2 + 16| - 5 = 27 (2) x^2 = 8x - 16 Kudos for a correct solution. _________________ Intern Joined: 01 Nov 2014 Posts: 2 Re: What is the value of |x|? [#permalink] ### Show Tags 10 Nov 2014, 07:04 The answer should be option (2) - statement 2 alone is sufficient but statement (1) alone is not sufficient. Here's the solution: (1) Using Statement 1 alone, |x^2 + 16| - 5 = 27 It means that either (x^2 + 16) - 5 = 27 or (x^2 + 16) - 5 = - 27 Solving the first of these, x^2 + 16 = 32 => x^2 = 16 => x = -4 or 4 Solving the second, x^2 + 16 = -22 => x^2 = -6 => x = \sqrt{6}, -\sqrt{6} Using statement 1 alone, we don't get a unique answer. Using Statement 2 alone, x^2 = 8x - 16 => x^2 - 8x + 16 = 0 => x^2 - 4x - 4x + 16 = 0 => (x-4) (x-4) = 0 This gives x = 4 and |x| = 4. So, statement 2 alone is sufficient but statement 2 alone is not sufficient Manager Joined: 10 Sep 2014 Posts: 96 Re: What is the value of |x|? [#permalink] ### Show Tags 10 Nov 2014, 10:21 2 This was my rationale for picking choice D statement 1: sufficient After adding 5 to each side you can set x^2 + 16= -32 and x^2 + 16 = 32 since it has absolute value brackets around it. Thus, x = 4 or x = -4, and the absolute value of each of those values is 4. statement 2: sufficient - I subtracted 8x-16 from x^2 to get x^2 - 8x + 16 = 0 - Factored to get (x-4)(x-4) - x =4 which has absolute value of 4 Manager Joined: 27 May 2014 Posts: 81 Re: What is the value of |x|? [#permalink] ### Show Tags 10 Nov 2014, 11:25 2 D is correct, the absolute value portion of the equation will never be negative as X^2 is always positive Manager Joined: 22 Sep 2012 Posts: 129 Concentration: Strategy, Technology WE: Information Technology (Computer Software) Re: What is the value of |x|? [#permalink] ### Show Tags 10 Nov 2014, 18:12 3 Statement 1: |x^2 + 16| - 5 = 27 |X^2+16| = 32 Since X^2 will always be positive x^2 = 16 therefore |x| = 4. Sufficient Statement 2: x^2 = 8x - 16 (x-4)^2=0 x = 4 , therefore |x|=4. Sufficient D) should be the answer Senior Manager Joined: 12 Aug 2015 Posts: 283 Concentration: General Management, Operations GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27 GPA: 3.3 WE: Management Consulting (Consulting) Re: What is the value of |x|? [#permalink] ### Show Tags 23 Aug 2015, 01:01 1 OA: Note that the question is asking for the absolute value of x rather than just the value of x. Keep this in mind when you analyze each statement. (1) SUFFICIENT: Since the value of x2 must be non-negative, the value of (x2 + 16) is always positive, therefore |x2 + 16| can be written x2 +16. Using this information, we can solve for x: |x2 + 16| – 5 = 27 x2 + 16 – 5 = 27 x2 + 11 = 27 x2 = 16 x = 4 or x = -4 Since |-4| = |4| = 4, we know that |x| = 4; this statement is sufficient. (2) SUFFICIENT: x2 = 8x – 16 x2 – 8x + 16 = 0 (x – 4)2 = 0 (x – 4)(x – 4) = 0 x = 4 Therefore, |x| = 4; this statement is sufficient. The correct answer is D. _________________ KUDO me plenty Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6949 GMAT 1: 760 Q51 V42 GPA: 3.82 What is the value of |x|? [#permalink] ### Show Tags 30 Dec 2015, 22:27 Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. What is the value of |x|? (1) |x^2 + 16| – 5 = 27 (2) x^2 = 8x – 16 There is 1 variable (x) in the original condition. In order to match the number of variables and the number of equations, we need 1 equation. Since the condition 1) and 2) both has 1 equation, there is high chance D is going to be the answer. In the case of the condition 1), we can obtain, |x^2+16|=5+27=32. Then, |x^2+16|=-32 or 32. However, since x^2+16=-32 is only possible when x^2=-48, this is not possible. In case of x^2+16=32, x=-4 or 4. However, since |x|=|-4|=|4|=4, the answer is unique and the condition becomes sufficient. In the case of the condition 2), we can obtain x^2-8x+16=0. Then, (x-4)^2=0. So, x=4. Since, |x| can be 4, the answer is unique, and the condition is sufficient. Therefore, the correct answer is D. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: What is the value of |x|?  [#permalink]

### Show Tags

29 Mar 2016, 17:32
Bunuel wrote:

Tough and Tricky questions: Absolute Values.

What is the value of |x|?

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

(2) x^2 = 8x - 16

Kudos for a correct solution.

since we are asked for the absolute value of x, we need to find the value of either x or -x.

1. |x^2+16|=32
ok 2 options:
x^2 +16=32 => x^2 = 16 -> |x|=4
x^2 +16 = -32 -> x^2 = -48 - this is not possible
only one option: |x|=4. sufficient.

2. x^2 -8x+16 = 0
(x-4)(x-4)=0
x=4
|x|=4. sufficient.

D
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Re: What is the value of |x|?  [#permalink]

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25 Mar 2018, 04:23
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Re: What is the value of |x|?   [#permalink] 25 Mar 2018, 04:23
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