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

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Math Expert
Joined: 02 Sep 2009
Posts: 51160
If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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15 Oct 2014, 15:25
00:00

Difficulty:

5% (low)

Question Stats:

92% (01:04) correct 8% (01:08) wrong based on 707 sessions

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Tough and Tricky questions: Absolute Values.

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

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Intern
Joined: 12 Jul 2014
Posts: 10
Location: India
Concentration: Operations, Technology
GMAT Date: 11-06-2014
GRE 1: Q159 V144
Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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15 Oct 2014, 18:02
2
Bunuel wrote:

Tough and Tricky questions: Absolute Values.

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

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!
_________________

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Bharat Bhushan Sunkara.

"You need to sacrifice what you are TODAY, for what you want to be TOMORROW!!"

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Joined: 18 Dec 2013
Posts: 27
GPA: 2.84
WE: Project Management (Telecommunications)
Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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15 Oct 2014, 19:23
bharatS wrote:
Bunuel wrote:

Tough and Tricky questions: Absolute Values.

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

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!

Looks good, I solved it in the same exact approach as you!
+1 Kudos
Senior Manager
Joined: 23 Apr 2015
Posts: 305
Location: United States
WE: Engineering (Consulting)
Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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22 Aug 2016, 21:32
2
Bunuel wrote:

Tough and Tricky questions: Absolute Values.

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

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:

+1 for kudos
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Director
Joined: 24 Nov 2015
Posts: 521
Location: United States (LA)
Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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14 Mar 2017, 13:12
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
Intern
Joined: 12 Mar 2017
Posts: 4
Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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14 Mar 2017, 13:39
|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

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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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20 Mar 2017, 05:52
1
Bunuel wrote:

Tough and Tricky questions: Absolute Values.

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

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.

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Joined: 05 Jan 2017
Posts: 509
Location: India
Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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21 Mar 2017, 03:18
Bunuel wrote:

Tough and Tricky questions: Absolute Values.

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

|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
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Posts: 9143
Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul  [#permalink]

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01 Aug 2018, 09:44
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Re: If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the resul &nbs [#permalink] 01 Aug 2018, 09:44
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