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

Question

|1 - √2| + |1 - √3| - |√2 + √3| = ?

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

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?

Bunuel · 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

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

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards