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|1 - √2| + |1 - √3| - |√2 + √3| = ?

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

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New post 05 Oct 2017, 02:18
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[GMAT math practice question]

|1 - √2| + |1 - √3| + |√2 + √3| = ?

A. -2
B. -1
C. 0
D. 1
E. 2
[Reveal] Spoiler: OA

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Last edited by MathRevolution on 28 Oct 2017, 11:41, edited 3 times in total.

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

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New post 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

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

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

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New post 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?

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

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

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New post 05 Oct 2017, 07:06
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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 :grin:

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

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

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New post 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

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

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

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

Answer: A


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.

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

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New post 12 Oct 2017, 16:57
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

Answer: A
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Re: |1 - √2| + |1 - √3| - |√2 + √3| = ?   [#permalink] 12 Oct 2017, 16:57
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