What is the value of ab?

Question

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

carcass · Answer

1) clearly insuff

2) also manipulate it is insuff

1) + 2)  a= 1   b = 0

a*b=0

C suff for me

Bunuel · Answer

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.

amy888 · Answer

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?

Bunuel · Answer

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.

chetan2u · Answer

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

BelalHossain046 · Answer

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.

BelalHossain046 · Answer

a^2=a means either a=0 or a=1.
Only these Two values are possible.

cjhyou700 · Answer

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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What is the value of ab?

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