Is the product of a and b equal to 1?

hi,

why can't we use this approach?

a*b*a = a
a*b=a/a
a*b= 1

You cannot reduce this by a, because you'll loose a possible root a = 0. Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.

HI Bunuel, chetan2u

I am little confused here. when we combine 2 statements in Data sufficiency questions, we usually take the common elements between two. Why not in this question?

I know it might be a stupid question.

Thanks in Advance
Harsh

Hi chetan2u

Pls help

Hi Harsh

Let me solve it for you.

Is ab=1?

1) \(a^2b=a........a^2b-a=0........a(ab-1)=0\)
So either a=0 or ab=1 or both.
Solutions can be
{a,ab}={0,0}; {1,1}; {2,1}; {-1000,1}
That is, a could be anything when ab=1
2) similarly \(ab^2=b........b^2a-b=0........b(ab-1)=0\)
So either b=0 or ab=1 or both.
Solutions can be
{b,ab}={0,0}; {1,1}; {2,1}; {-1000,1}
That is, b could be anything when ab=1

Combined
There is no common area in the two statements, because statement I talks of a being 0 while b talks of b being 0.
So possible solutions
{a,b,ab}={0,0,0}
Or {a,b,ab}={1,1,1}={-1,-1,1}

So ab can be 0 or 1.


Had the statement II been : (a-2)(ab-1)=0, so either a=2 or ab=1 or both.
Then we would have common portion as ab=1, and C would be the answer.

Hi Bunuel

If a=0, would not ab=0 as well?

Yes, if a = 0, then ab = 0 but not sure what you are implying there.

Hi
i have a doubt , in DS question option C is using both (i)&(ii) right
so doesnt it mean both the statements should be satisfied, in that case
(i) either ab=1 or a=0
(ii)either ab=1 or b=0
while using both should we consider the overlap between both the conditions
and here would that be 'ab=1'

We have two possible answers a=0 ,b=0
or a=1, b=1