Harsh9676 wrote:
Harsh9676 wrote:
Bunuel wrote:
Official Solution:
Question: is \(ab=1\)?
(1) \(a^2b=a\)
\(a^2b-a=0\);
\(a(ab-1)=0\): either \(a=0\) (and \(b=\text{any value}\), including zero) so in this case \(ab=0\neq 1\) OR \(ab=1\). Two different answers, not sufficient.
(2) \(ab^2=b\)
\(ab^2-b=0\);
\(b(ab-1)=0\): either \(b=0\) (and \(a=\text{any value}\), including zero) so in this case \(ab=0 \neq 1\) OR \(ab=1\). Two different answers, not sufficient.
(1)+(2) either \(a=b=0\), so in this case \(ab=0 \neq 1\) and the answer to the question is NO, OR \(ab=1\) and the answer to the question is YES. Two different answers, not sufficient.
Answer: E
HI
Bunuel,
chetan2uI 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
chetan2uPls 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.
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