If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul

Question

If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the result of a + b?

A. -1
B. -1/3
C. 1/3
D. 2/3
E. 1

bharatS · Accepted Answer

Hello There,
|a| = 1/3
Absolute value of 'a' can have two values = 1/3 and -(1/3)
|b| = 2/3
Absolute value of 'b' can have two values = 2/3 and -(2/3)

Now different combinations of a + b are as follows:
a + b = (1/3) + (2/3) = 1
- a - b = -(1/3) - (2/3) = -1
a - b = (1/3) - (2/3) = -(1/3)
-a + b = -(1/3) + (2/3) = 1/3

Cross verifying with the given options, left over option is D.
Please correct my approach if any. 
Thanks!

Senthil1981 · Answer

Since  a  can be  \frac{1}{3}  or  \frac{-1}{3}  and similarly  b  can be  \frac{2}{3}  or  \frac{-2}{3}  . To get all values of a + b and hence eliminate:

D is the answer.

+1 for kudos

dmmk · Answer

Looks good, I solved it in the same exact approach as you! +1 Kudos :ninja

rhine29388 · Answer

basically we have to check the combinations of various values of a and b 
|a| = 1/3 means a can be equal to 1/3 or - 1/3
|b| = 2/3 means b can be equal to 2/3 or - 2/3
after adding them in various possible ways the answer are 1 , -1 , 1/3 , -1/3
the total can never be 2/3
Correct answer - D

avinash07 · Answer

|a|=-1/3 and 1/3
Similarly |b|= -2/3 and 2/3
So after doing addition one value of a with one value of b ,we will get four value -1,+1,-1/3,+1/3.
So option D is correct.

Thanks

Sent from my HTC Desire 728 dual sim using  GMAT Club Forum mobile app

JeffTargetTestPrep · Answer

We see that a = 1/3 or -1/3 and that b = 2/3 or -2/3.

Thus, the possible combinations of a + b are follows:

1/3 + 2/3 = 1 or

1/3 + (-2/3) = -1/3 or

(-1/3) + 2/3 = 1/3 or

(-1/3) + (-2/3) = -1

Thus, 2/3 cannot be the sum of a and b.

Answer: D

KrishnakumarKA1 · Answer

|a| = 1/3, a = 1/3 or -1/3
|b| = 2/3. b = 2/3 or -2/3

therefore a+b could be 1/3+2/3 = 1, 1/3-2/3 = -1/3, -1/3+2/3 = 1/3, -1/3-2/3 = -1

hence option D

ManishaPrepMinds · Answer

Solution:
Given: |a| = 1/3 and |b| = 2/3, meaning a and b can each be positive or negative.

Table of Possible Cases

Case 1: a = 1/3, b = 2/3, a + b = 1
Case 2: a = -1/3, b = 2/3, a + b = 1/3
Case 3: a = 1/3, b = -2/3, a + b = -1/3
Case 4: a = -1/3, b = -2/3, a + b = -1

Possible Results for a + b:
The results for a + b are -1, -1/3, 1/3, and 1.

Checking Answer Choices:
The only option that cannot be the result of a + b is 2/3.

Final Answer:
(D) 2/3

ManifestDreamMBA · Answer

Since the question mentions CANNOT be the result of a+b, lets evaluate option D, 2/3 which is one of the numbers being considered. If we take b = 2/3, then adding or removing anything from 2/3 won't result in 2/3. If we take b = -2/3, then adding or removing 1/3 will not make it positive, i.e. result in 2/3. Hence D is the answer

Bunuel

If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the result of a + b?

A. -1
B. -1/3
C. 1/3
D. 2/3
E. 1

If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul

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

If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul

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