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655-705 (Hard)|   Algebra|         
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Bunuel
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Is the product of a and b equal to 1? 02 Oct 2019, 05:42
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65% (hard)

Question Stats:

50% (01:26) correct 50% (01:12) wrong based on 558 sessions

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Is the product of \(a\) and \(b\) equal to 1?


(1) \(a*b*a=a\)

(2) \(b*a*b=b\)


M01-36

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E
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Bunuel
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Is the product of a and b equal to 1? 02 Oct 2019, 05:43
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Bunuel
Is the product of \(a\) and \(b\) equal to 1?


(1) \(a*b*a=a\)

(2) \(b*a*b=b\)


M01-36
Show more

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
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Is the product of a and b equal to 1? 02 Oct 2019, 06:10
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Bunuel
Is the product of \(a\) and \(b\) equal to 1?


(1) \(a*b*a=a\)

(2) \(b*a*b=b\)


M01-36
Show more

Case A: a can be 0 or 1, equation still holds; so Insufficient.
Case B: b can be 0 or 1, equation still holds; so Insufficient.

A+B

Yes, iff a=b=1

No, if a=b=0, Still insufficient.
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Is the product of a and b equal to 1? 07 Oct 2019, 00:29
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hi,

why can't we use this approach?

a*b*a = a
a*b=a/a
a*b= 1
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Is the product of a and b equal to 1? 07 Oct 2019, 00:37
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anitakhairunnisa
hi,

why can't we use this approach?

a*b*a = a
a*b=a/a
a*b= 1
Show more

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.
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Is the product of a and b equal to 1? 08 Aug 2020, 11:30
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Bunuel
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Is the product of \(a\) and \(b\) equal to 1?


(1) \(a*b*a=a\)

(2) \(b*a*b=b\)


M01-36

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
Show more


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
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Is the product of a and b equal to 1? 27 Feb 2021, 22:51
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Harsh9676
Bunuel
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Is the product of \(a\) and \(b\) equal to 1?


(1) \(a*b*a=a\)

(2) \(b*a*b=b\)


M01-36

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, 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
Show more

Hi chetan2u

Pls help
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Is the product of a and b equal to 1? 28 Feb 2021, 00:12
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Harsh9676
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Bunuel


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, 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
Show more


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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Is the product of a and b equal to 1? 01 Apr 2021, 20:04
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Bunuel
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Is the product of \(a\) and \(b\) equal to 1?


(1) \(a*b*a=a\)

(2) \(b*a*b=b\)


M01-36

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
Show more

Hi Bunuel

If a=0, would not ab=0 as well?
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Is the product of a and b equal to 1? 01 Apr 2021, 22:33
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Bunuel
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Is the product of \(a\) and \(b\) equal to 1?


(1) \(a*b*a=a\)

(2) \(b*a*b=b\)


M01-36

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

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

Yes, if a = 0, then ab = 0 but not sure what you are implying there.
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Is the product of a and b equal to 1? 19 Oct 2022, 03:45
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Bunuel
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Is the product of \(a\) and \(b\) equal to 1?


(1) \(a*b*a=a\)

(2) \(b*a*b=b\)


M01-36

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
Show more


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'
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Is the product of a and b equal to 1? 28 Aug 2023, 22:44
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anitakhairunnisa
hi,

why can't we use this approach?

a*b*a = a
a*b=a/a
a*b= 1
Show more
We have two possible answers a=0 ,b=0
or a=1, b=1
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Is the product of a and b equal to 1? 07 Dec 2024, 05:24
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