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# |1 - √2| + |1 - √3| - |√2 + √3| = ?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9014
GMAT 1: 760 Q51 V42
GPA: 3.82
|1 - √2| + |1 - √3| - |√2 + √3| = ?  [#permalink]

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Updated on: 13 Sep 2018, 19:44
1
8
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:16) correct 42% (01:30) wrong based on 240 sessions

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[GMAT math practice question]

|1 - √2| + |1 - √3| - |√2 + √3| = ?

A. -2
B. -1
C. 0
D. 1
E. 2

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 05 Oct 2017, 02:18. Last edited by Bunuel on 13 Sep 2018, 19:44, edited 4 times in total. Renamed the topic and edited the question. Retired Moderator Joined: 25 Feb 2013 Posts: 1124 Location: India GPA: 3.82 Re: |1 - √2| + |1 - √3| - |√2 + √3| = ? [#permalink] ### Show Tags 05 Oct 2017, 05:36 MathRevolution wrote: [GMAT math practice question] When | 1 - √2 |+| 1 - √3 |+| √2 + √3 | = ? A. -2 B. -1 C. 0 D. 1 E. 2 Hi Bunuel Can you clarify how can the sum of mod function be negative? Can you confirm whether the question is framed correctly or I am missing something Math Expert Joined: 02 Sep 2009 Posts: 64117 Re: |1 - √2| + |1 - √3| - |√2 + √3| = ? [#permalink] ### Show Tags 05 Oct 2017, 05:40 niks18 wrote: MathRevolution wrote: [GMAT math practice question] When | 1 - √2 |+| 1 - √3 |+| √2 + √3 | = ? A. -2 B. -1 C. 0 D. 1 E. 2 Hi Bunuel Can you clarify how can the sum of mod function be negative? Can you confirm whether the question is framed correctly or I am missing something No. An absolute value is 0 or positive, so the sum of any number of absolute values is also 0 or positive. _________________ Retired Moderator Joined: 25 Feb 2013 Posts: 1124 Location: India GPA: 3.82 Re: |1 - √2| + |1 - √3| - |√2 + √3| = ? [#permalink] ### Show Tags 05 Oct 2017, 05:48 Bunuel wrote: niks18 wrote: MathRevolution wrote: [GMAT math practice question] When | 1 - √2 |+| 1 - √3 |+| √2 + √3 | = ? A. -2 B. -1 C. 0 D. 1 E. 2 Hi Bunuel Can you clarify how can the sum of mod function be negative? Can you confirm whether the question is framed correctly or I am missing something No. An absolute value is 0 or positive, so the sum of any number of absolute values is also 0 or positive. Thanks Bunuel for the confirmation, then in that case, the question seems incorrect. Can you provide the explanation/solution? Math Expert Joined: 02 Sep 2009 Posts: 64117 Re: |1 - √2| + |1 - √3| - |√2 + √3| = ? [#permalink] ### Show Tags 05 Oct 2017, 06:50 niks18 wrote: Bunuel wrote: niks18 wrote: When | 1 - √2 |+| 1 - √3 |+| √2 + √3 | = ? A. -2 B. -1 C. 0 D. 1 E. 2 Hi Bunuel Can you clarify how can the sum of mod function be negative? Can you confirm whether the question is framed correctly or I am missing something No. An absolute value is 0 or positive, so the sum of any number of absolute values is also 0 or positive. Thanks Bunuel for the confirmation, then in that case, the question seems incorrect. Can you provide the explanation/solution? For the correct answer to be A. -2, the question should read: |1 - √2| + |1 - √3| - |√2 + √3| = ? Both √2 and √3 are greater than 1, so |1 - √2| = -(1 - √2) and |1 - √3| = -(1 - √3), thus $$|1 - √2| + |1 - √3| - |√2 + √3| = -(1 - √2) - (1 - √3)- (√2 + √3) = -2$$. Answer: A. Edited the question. _________________ Retired Moderator Joined: 25 Feb 2013 Posts: 1124 Location: India GPA: 3.82 Re: |1 - √2| + |1 - √3| - |√2 + √3| = ? [#permalink] ### Show Tags 05 Oct 2017, 07:06 1 Quote: For the correct answer to be A. -2, the question should read: |1 - √2| + |1 - √3| - |√2 + √3| = ? Both √2 and √3 are greater than 1, so |1 - √2| = -(1 - √2) and |1 - √3| = -(1 - √3), thus $$|1 - √2| + |1 - √3| - |√2 + √3| = -(1 - √2) - (1 - √3)- (√2 + √3) = -2$$. Answer: A. Edited the question Yes completely agree. This is the way i had solved but was stunned by the OA Below is another question from MathRevolution which according to me is ambiguous and yet MathRevolution team has not clarified. https://gmatclub.com/forum/if-the-opera ... l#p1937876 RSM Erasmus Moderator Joined: 26 Mar 2013 Posts: 2441 Concentration: Operations, Strategy Schools: Erasmus Re: |1 - √2| + |1 - √3| - |√2 + √3| = ? [#permalink] ### Show Tags 05 Oct 2017, 22:51 MathRevolution wrote: [GMAT math practice question] |1 - √2| + |1 - √3| - |√2 + √3| = ? A. -2 B. -1 C. 0 D. 1 E. 2 Knowing √2 & √3 will help to estimate perfectly. $$√2\approx{1.4}$$ $$√3\approx{1.7}$$ |1 - √2| + |1 - √3| - |√2 + √3| = |1 - 1.4| + |1 - 1.7| - |1.4 + 1.7| = |-0.4| + |-0.7| - |1.4 + 1.7| = 0.4 + 0.7 - 3.1 = 1.1 - 3.1 = -2 Answer: A Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9014 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: |1 - √2| + |1 - √3| - |√2 + √3| = ? [#permalink] ### Show Tags 08 Oct 2017, 17:03 => | 1 - √2 |+| 1 - √3 |+| √2 + √3 | = -( 1 - √2 ) – ( 1 - √3 ) + ( √2 + √3 ) = -1 + √2 – 1 + √3 + √2 + √3 = -2 Answer: A _________________ 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$79 for 1 month Online Course"
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Retired Moderator
Joined: 25 Feb 2013
Posts: 1124
Location: India
GPA: 3.82
Re: |1 - √2| + |1 - √3| - |√2 + √3| = ?  [#permalink]

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09 Oct 2017, 06:51
1
MathRevolution wrote:
=>
| 1 - √2 |+| 1 - √3 |+| √2 + √3 |
= -( 1 - √2 ) – ( 1 - √3 ) + ( √2 + √3 )
= -1 + √2 – 1 + √3 + √2 + √3
= -2

Hi MathRevolution

I understand this must be a typo error but while posting solution also who have not rectified the typo error. initially you had posted a wrong question and now a wrong solution. Refer above post by Bunuel, how he corrected it and provided the correct solution.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: |1 - √2| + |1 - √3| - |√2 + √3| = ?  [#permalink]

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12 Oct 2017, 16:57
3
1
MathRevolution wrote:
[GMAT math practice question]

|1 - √2| + |1 - √3| - |√2 + √3| = ?

A. -2
B. -1
C. 0
D. 1
E. 2

Recall that |x| = x if x ≥ 0, and |x| = -x if x < 0.

Since 1 - √2 < 0, |1 - √2| = -(1 - √2).

Similarly, since 1 - √3 < 0, |1 - √3| = -(1 - √3).

However, √2 + √3 > 0, so |√2 + √3| = √2 + √3. Therefore:

|1 - √2| + |1 - √3| - |√2 + √3|

-(1 - √2) - (1 - √3) - (√2 + √3)

-1 + √2 - 1 + √3 - √2 - √3

= -2

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Re: |1 - √2| + |1 - √3| - |√2 + √3| = ?  [#permalink]

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02 Apr 2020, 02:16
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Re: |1 - √2| + |1 - √3| - |√2 + √3| = ?   [#permalink] 02 Apr 2020, 02:16