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|√3-2|+|3-√2|+|5+√3|+|1-√2|=?

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|√3-2|+|3-√2|+|5+√3|+|1-√2|=?  [#permalink]

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New post 19 Sep 2018, 02:14
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A
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D
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Question Stats:

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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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|√3-2|+|3-√2|+|5+√3|+|1-√2|=?  [#permalink]

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New post 19 Sep 2018, 02:41
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)
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Re: |√3-2|+|3-√2|+|5+√3|+|1-√2|=?  [#permalink]

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New post 19 Sep 2018, 02:43
\(|√3-2|+|3-√2|+|5+√3|+|1-√2|=2-√3+3-√2+5+√3+√2-1=2+3+5-1=10-1=9\)

D

Since we know the values inside the modulus we will take the positive value..
So |√3-2| will be 2-√3...

\(A. 0\)
\(B. 2√2\)
\(C. 2√3\)
\(D. 9\)
\(E. 11\)
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|√3-2|+|3-√2|+|5+√3|+|1-√2|=?  [#permalink]

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New post Updated on: 13 Jun 2019, 20:27
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.


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Originally posted by GMATGuruNY on 19 Sep 2018, 03:42.
Last edited by GMATGuruNY on 13 Jun 2019, 20:27, edited 1 time in total.
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Re: |√3-2|+|3-√2|+|5+√3|+|1-√2|=?  [#permalink]

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New post 21 Sep 2018, 01:24
=>

\(|A|=A\) 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
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Re: |√3-2|+|3-√2|+|5+√3|+|1-√2|=?  [#permalink]

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New post 02 Oct 2018, 05:52
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.
Answer will be option D
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Re: |√3-2|+|3-√2|+|5+√3|+|1-√2|=?   [#permalink] 02 Oct 2018, 05:52
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