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What is the value of ab?

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Maxswe
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What is the value of ab? [#permalink] New post   Updated on: 09 Dec 2012, 11:06
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73% (01:24) correct 27% (01:25) wrong based on 406 sessions
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What is the value of ab?

(1) a = b + 1
(2) a^2 = b + 1
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Official Answer
C

Originally posted by Maxswe on 09 Dec 2012, 10:45.
Last edited by Bunuel on 09 Dec 2012, 11:06, edited 1 time in total.
OA added.
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Re: What is the value of ab? [#permalink] New post   09 Dec 2012, 11:01
1) clearly insuff

2) also manipulate it is insuff

1) + 2) \(a= 1\) \(b = 0\)

\(a*b=0\)

C suff for me
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Re: What is the value of ab? [#permalink] New post   09 Dec 2012, 11:09
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Maxswe wrote:
What is the value of ab?

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


Each statement alone is clearly insufficient. When taken together we have that a=a^2, which implies that a=0 or a=1.
If a=0 --> ab=0;
If a=1 --> b=0 --> ab=0.

Sufficient.

Answer: C.

P.S. Please provide OA's when posting questions.
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Re: What is the value of ab? [#permalink] New post   01 Apr 2014, 23:45
I had a question on this question. I thought the answer should be B.

a^2=b+1...then a^2-1=b
a^2-1 can be factored and would equal (a+1)(a-1)
then (a+1)(a-1)=b
in this case a = -1 or 1. When plugging both -1 or 1 in b is always zero.

therefore ab will always equal 0.

Is it wrong to factor out the equation in the second statement?
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Re: What is the value of ab? [#permalink] New post   02 Apr 2014, 00:09
Expert Reply
amy888 wrote:
I had a question on this question. I thought the answer should be B.

a^2=b+1...then a^2-1=b
a^2-1 can be factored and would equal (a+1)(a-1)
then (a+1)(a-1)=b
in this case a = -1 or 1. When plugging both -1 or 1 in b is always zero.

therefore ab will always equal 0.

Is it wrong to factor out the equation in the second statement?


Factoring is correct but the derivation is not.

(a+1)(a-1)=b does not mean that a=-1 or a=1, it would be so if we knew that b=0. I mean if it were (a+1)(a-1)=0, then yes, for the product of two multiples, a+1 and a-1, to be 0 either of them must be zero, hence a=-1 or a=1.
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What is the value of ab? [#permalink] New post   17 Aug 2017, 19:53
Expert Reply
Gnpth wrote:
What is the value of ab?

1. \(a= b+1\)

2. \(a^2= b+1\)



Each statement individually can be seen is not sufficient.
Let's see what so we get when combined

a=b+1 and \(a^2=b+1..... So ...a=a^2.....a^2-a=0....a(a-1)=0\)
Thus a is 0 or 1...

If a =0, a*b=0 irrespective of value of b otherwise b=a-1=-1
If a=1, b=a-1=1-1=0... So a*b=1*0=0

So in each case ANSWER is 0
Sufficient

C
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Re: What is the value of ab? [#permalink] New post   07 Nov 2019, 22:29
Statement 1: a=b+1
If b=1, a=2, so ab=2
If b=2, a=3, so ab=6
INSUFFICIENT

Statement 2:a^2=b+1
If a=2, b=3 so ab=6
If a=3, b=8 so ab=24
INSUFFICIENT.

COMBINING:
a=b+1........(1)
a^2=b+1........(2)
SUBSTITUTING the value (b+1) in statement 2, we get
a^2=a
Or, a^2-a=0
Or, a(a-1)=0
Either a=0 or a=1

If a=1, b=0 (according to statement 1). So, ab=0.
If a=0, b=-1 (according to statement 1). So, ab=0.
Always ab=0.
C is SUFFICIENT.
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Re: What is the value of ab? [#permalink] New post   07 Nov 2019, 22:31
a^2=a means either a=0 or a=1.
Only these Two values are possible.
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Re: What is the value of ab? [#permalink] New post   17 Jul 2022, 20:44
I have a doubt on this question. What if b=-2.
a=1
a=-2+1=1

Because the question does not state that b cannot be negative.
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Re: What is the value of ab? [#permalink] New post   06 Sep 2023, 11:27
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Re: What is the value of ab? [#permalink]
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