|1 - 2| + |1 - 3| - |2 + 3| = ?

Question

|1 - √2| + |1 - √3| - |√2 + √3| = ?

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

Bunuel · Accepted Answer

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.

niks18 · Answer

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

Bunuel · Answer

No. An absolute value is 0 or positive, so the sum of any number of absolute values is also 0 or positive.

niks18 · Answer

Thanks  Bunuel  for the confirmation, then in that case, the question seems incorrect. Can you provide the explanation/solution?

niks18 · Answer

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

Mo2men · Answer

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

MathRevolution · Answer

=>
| 1 - √2 |+| 1 - √3 |+| √2 + √3 |
= -( 1 - √2 ) – ( 1 - √3 ) + ( √2 + √3 )
= -1 + √2 – 1 + √3 + √2 + √3
= -2

Answer: A

niks18 · Answer

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.

JeffTargetTestPrep · Answer

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

Carolweszxdrcftvb · Answer

|1 - √2| + |1 - √3| - |√2 + √3| = ?
convert in to approx nos.

= | 1-1.41| + | 1 -1.73 | - | 1.41+1.73|
= |-0.41| + |-0.73| -|3.14|
= 0.41 + 0.73 -3.14
=-2

bumpbot · Answer

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|1 - 2| + |1 - 3| - |2 + 3| = ?

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