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# What is the value of ab?

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Manager
Joined: 01 Feb 2012
Posts: 86
What is the value of ab?  [#permalink]

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30 Apr 2013, 05:26
2
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Difficulty:

65% (hard)

Question Stats:

55% (01:27) correct 45% (01:28) wrong based on 233 sessions

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What is the value of ab?

(1) |a| + b = a
(2) a + |b| = b

I cant combine the two statements and reach anywhere -
1. |a| + b = a
we wil have two cases once a positive and once a negative -
when a positive
a+b = a
implies b =0
when a -ve
-a+b=a
b=2a

so by statement -
either ab = 0 (when b is zero)
or ab= 2a² (when b=2a) (we dont know the value of a)

so we dont have one unique value of b

Statement II
a + |b| = b
either a = 0
or a= 2b
again we dont get a clear value for ab.

can someone please tell me if my approach so far is ok and how do I combine the two statements now....thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 47983
Re: What is the value of ab?  [#permalink]

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30 Apr 2013, 05:36
5
4
What is the value of ab?

(1) |a| + b = a. Just plug numbers to see that this statement is NOT sufficient: if a=b=0, then ab=0 but if a=-1 and b=-2, then ab=2. Not sufficient.

(2) a + |b| = b. The same here. Not sufficient.

(1)+(2) Sum (1) and (2): |a| + b + a + |b|= a + b --> |a| + |b| = 0. The sum of two non-negative values (|a| and |b|) to be 0, each must be 0, thus a=b=0 --> ab=0. Sufficient.

Hope it's clear.
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Math Expert
Joined: 02 Sep 2009
Posts: 47983
Re: What is the value of ab?  [#permalink]

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30 Apr 2013, 05:38
tirbah wrote:
What is the value of ab?

(1) |a| + b = a
(2) a + |b| = b

I cant combine the two statements and reach anywhere -
1. |a| + b = a
we wil have two cases once a positive and once a negative -
when a positive
a+b = a
implies b =0
when a -ve
-a+b=a
b=2a

so by statement -
either ab = 0 (when b is zero)
or ab= 2a² (when b=2a) (we dont know the value of a)

so we dont have one unique value of b

Statement II
a + |b| = b
either a = 0
or a= 2b
again we dont get a clear value for ab.

can someone please tell me if my approach so far is ok and how do I combine the two statements now....thanks.

Similar question to practice: is-xy-132217.html

Hope it helps.
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Manager
Joined: 01 Feb 2012
Posts: 86
Re: What is the value of ab?  [#permalink]

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30 Apr 2013, 10:55
1
Bunuel wrote:
What is the value of ab?

(1) |a| + b = a. Just plug numbers to see that this statement is NOT sufficient: if a=b=0, then ab=0 but if a=-1 and b=-2, then ab=2. Not sufficient.

(2) a + |b| = b. The same here. Not sufficient.

(1)+(2) Sum (1) and (2): |a| + b + a + |b|= a + b --> |a| + |b| = 0. The sum of two non-negative values (|a| and |b|) to be 0, each must be 0, thus a=b=0 --> ab=0. Sufficient.

Hope it's clear.

Bunuel - Thanks for the reply. I understood the way you did that. Could you please go through my explanation once please and see if that is also fine or have I done soemthing wrong? also is there a way to combine the two statements without literally adding them...I mean the way I solved it..I reached at b=0 and 2a from Ist statement and a=0, and 2b from IInd statement....is there a way I can combine them from this point? I am usually we look for a common point from the outcomes of two statements when we combine them, can we do that here. Thanks.

Kind regards..
Math Expert
Joined: 02 Sep 2009
Posts: 47983
Re: What is the value of ab?  [#permalink]

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02 May 2013, 03:55
1
tirbah wrote:
Bunuel wrote:
What is the value of ab?

(1) |a| + b = a. Just plug numbers to see that this statement is NOT sufficient: if a=b=0, then ab=0 but if a=-1 and b=-2, then ab=2. Not sufficient.

(2) a + |b| = b. The same here. Not sufficient.

(1)+(2) Sum (1) and (2): |a| + b + a + |b|= a + b --> |a| + |b| = 0. The sum of two non-negative values (|a| and |b|) to be 0, each must be 0, thus a=b=0 --> ab=0. Sufficient.

Hope it's clear.

Bunuel - Thanks for the reply. I understood the way you did that. Could you please go through my explanation once please and see if that is also fine or have I done soemthing wrong? also is there a way to combine the two statements without literally adding them...I mean the way I solved it..I reached at b=0 and 2a from Ist statement and a=0, and 2b from IInd statement....is there a way I can combine them from this point? I am usually we look for a common point from the outcomes of two statements when we combine them, can we do that here. Thanks.

Kind regards..

Your reasoning for (1) and (2) is correct:
(1) |a| + b = a.
a<0 --> b=2a
a>=0 --> b=0

(2) a + |b| = b
b<0 --> a=2b (b=a/2)
b>=0 --> a=0

(1)+(2) If a<0, then from b=2a, b<0 too. Thus we have that when a<0 and b<0, then b=2a and b=a/2, which cannot be true. So,we are left with a=b=0.

Hope it's clear.
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Manager
Joined: 01 Feb 2012
Posts: 86
Re: What is the value of ab?  [#permalink]

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02 May 2013, 06:11
Bunuel wrote:
tirbah wrote:
Bunuel wrote:
What is the value of ab?

(1) |a| + b = a. Just plug numbers to see that this statement is NOT sufficient: if a=b=0, then ab=0 but if a=-1 and b=-2, then ab=2. Not sufficient.

(2) a + |b| = b. The same here. Not sufficient.

(1)+(2) Sum (1) and (2): |a| + b + a + |b|= a + b --> |a| + |b| = 0. The sum of two non-negative values (|a| and |b|) to be 0, each must be 0, thus a=b=0 --> ab=0. Sufficient.

Hope it's clear.

Bunuel - Thanks for the reply. I understood the way you did that. Could you please go through my explanation once please and see if that is also fine or have I done soemthing wrong? also is there a way to combine the two statements without literally adding them...I mean the way I solved it..I reached at b=0 and 2a from Ist statement and a=0, and 2b from IInd statement....is there a way I can combine them from this point? I am usually we look for a common point from the outcomes of two statements when we combine them, can we do that here. Thanks.

Kind regards..

Your reasoning for (1) and (2) is correct:
(1) |a| + b = a.
a<0 --> b=2a
a>=0 --> b=0

(2) a + |b| = b
b<0 --> a=2b (b=a/2)
b>=0 --> a=0

(1)+(2) If a<0, then from b=2a, b<0 too. Thus we have that when a<0 and b<0, then b=2a and b=a/2, which cannot be true. So,we are left with a=b=0.

Hope it's clear.

Yes I understood it now...Thank you so much.
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Re: What is the value of ab?  [#permalink]

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31 Jul 2018, 19:56
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