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# |√3-2|+|3-√2|+|5+√3|+|1-√2|=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8985
GMAT 1: 760 Q51 V42
GPA: 3.82

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19 Sep 2018, 01:14
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Difficulty:

15% (low)

Question Stats:

75% (01:35) correct 25% (01:56) wrong based on 162 sessions

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[Math Revolution GMAT math practice question]

$$|√3-2|+|3-√2|+|5+√3|+|1-√2|=?$$

$$A. 0$$
$$B. 2√2$$
$$C. 2√3$$
$$D. 9$$
$$E. 11$$

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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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Status: Learning stage Joined: 01 Oct 2017 Posts: 950 WE: Supply Chain Management (Energy and Utilities) |√3-2|+|3-√2|+|5+√3|+|1-√2|=? [#permalink] ### Show Tags 19 Sep 2018, 01:41 MathRevolution wrote: [Math Revolution GMAT math practice question] $$|√3-2|+|3-√2|+|5+√3|+|1-√2|=?$$ $$A. 0$$ $$B. 2√2$$ $$C. 2√3$$ $$D. 9$$ $$E. 11$$ Note: Absolute operation always yields +ve polarity. |√3-2|+|3-√2|+|5+√3|+|1-√2|=-(√3-2)+(3-√2)+(5+√3)+-(1-√2)=2-√3+3-√2+5+√3+√2-1=2+3+5-1=9 Ans. (D) _________________ Regards, PKN Rise above the storm, you will find the sunshine Math Expert Joined: 02 Aug 2009 Posts: 8584 Re: |√3-2|+|3-√2|+|5+√3|+|1-√2|=? [#permalink] ### Show Tags 19 Sep 2018, 01:43 $$|√3-2|+|3-√2|+|5+√3|+|1-√2|=2-√3+3-√2+5+√3+√2-1=2+3+5-1=10-1=9$$ D Since we know the values inside the modulus we will take the positive value.. So |√3-2| will be 2-√3... $$A. 0$$ $$B. 2√2$$ $$C. 2√3$$ $$D. 9$$ $$E. 11$$ _________________ Director Joined: 04 Aug 2010 Posts: 599 Schools: Dartmouth College |√3-2|+|3-√2|+|5+√3|+|1-√2|=? [#permalink] ### Show Tags Updated on: 13 Jun 2019, 19:27 1 MathRevolution wrote: [Math Revolution GMAT math practice question] $$|√3-2|+|3-√2|+|5+√3|+|1-√2|=?$$ $$A. 0$$ $$B. 2√2$$ $$C. 2√3$$ $$D. 9$$ $$E. 11$$ |a-b| = the distance between a and b. |a+b| = |a-(-b)| = the distance between a and -b. |√3-2| + |3-√2| + |5+√3| + |1-√2| = |5+√3| + |√3-2| + |1-√2| + |3-√2| = |√3+5| + |√3-2| + |1-√2| + |3-√2| = |√3-(-5)| + |√3-2| + |1-√2| + |3-√2| The red terms constitute the sum of the following two distances: -5<----->√3<----->2 The sum of these two distances = the distance between -5 and 2 = 7. The blue terms constitute the sum of the following two distances: 1<----->√2<----->3 The sum of these two distances = the distance between 1 and 3 = 2. Thus: Sum of all 4 terms = 7+2 = 9. _________________ GMAT and GRE Tutor New York, NY Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Originally posted by GMATGuruNY on 19 Sep 2018, 02:42. Last edited by GMATGuruNY on 13 Jun 2019, 19:27, edited 1 time in total. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8985 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: |√3-2|+|3-√2|+|5+√3|+|1-√2|=? [#permalink] ### Show Tags 21 Sep 2018, 00:24 1 => $$|A|=A$$ when $$A>0, |0|=0$$, and $$|A|=-A$$ when $$A<0$$ Since $$√3-2 < 0$$, we have $$|√3-2| = -(√3-2).$$ Since $$3-√2 > 0,$$ we have $$|3-√2| = 3-√2.$$ Since $$5+√3 > 0$$, we have $$|5+√3| = 5+√3$$ Since $$1-√2 < 0$$, we have $$|1-√2| = -(1-√2)$$ So, $$|√3-2|+|3-√2|+|5+√3|+|1-√2|= -(√3-2) +(3-√2) + (5+√3) -(1-√2) = -√3+2 + 3-√2 + 5+√3 – 1 +√2 = 9.$$ Therefore, the answer is D. Answer: D _________________ 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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Joined: 30 May 2018
Posts: 74
Concentration: General Management, Marketing
GMAT 1: 750 Q49 V45
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02 Oct 2018, 04:52
Watch out for the trap here .
|√3−2| & |1−√2| need to produce positive outcome hence you need to multiple the same with "-" so ensure the same and just solve it then.
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02 Apr 2020, 01:59
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Re: |√3-2|+|3-√2|+|5+√3|+|1-√2|=?   [#permalink] 02 Apr 2020, 01:59