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# M01 #36

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08 Oct 2008, 09:02
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Is the product of $$A$$ and $$B$$ equal to 1?

1. $$ABA= A$$
2. $$BAB =B$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

I don't agree with the answer. what do you guys think?

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08 Oct 2008, 09:35
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Is the product of A and B equal to 1?

1. ABA= A
2. BAB =B

(C) 2008 GMAT Club - m01#36

I don't agree with the answer. what do you guys think?

(1) ABA = A
= ABA - A = 0
= A(AB-1) = 0
This means A=0 or AB=1 ---- Not Sufficient.

(2) BAB = B
= BAB - B = 0
= B(AB-1) = 0
This means B=0 or AB=1 ---- Not Sufficient.

Combined - A=0 or B=0 or AB=1 ---Not Sufficient.

E
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Re: One more .... help needed [#permalink]

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07 Jul 2010, 05:04
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Is the product of A and B equal to 1?

Question: $$ab=1$$?

(1) $$a^2b=a$$ --> $$a^2b-a=0$$ --> $$a(ab-1)=0$$ --> either $$a=0$$ or $$ab=1$$. Two different answers, not sufficient.

(2) $$ab^2=b$$ --> $$ab^2-b=0$$ --> $$b(ab-1)=0$$ --> either $$b=0$$ 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.

onedayill wrote:
A/A cancels out to be 1
this means A*B = 1

When you cancel $$a$$, what you are actually doing is dividing both parts of the equation by variable $$a$$, thus assuming with no ground for it that this variable does not equal to zero.

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 can not divide by zero.
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16 Sep 2010, 17:21
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Is the product of A and B equal to 1?

Question: $$ab=1$$?

(1) $$a^2b=a$$ --> $$a^2b-a=0$$ --> $$a(ab-1)=0$$ --> either $$a=0$$ (and $$b=any \ value$$, 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 $$a=any \ value$$, including zero) so in this case $$ab=0\neq{1}$$ OR $$ab=1$$. Two different answers, not sufficient.

(1)+(2) As from (1) $$a(ab-1)=0$$ and from (2) $$b(ab-1)=0$$ then $$a(ab-1)=b(ab-1)=0$$ --> 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.

Side note on dividing (1) by $$a$$ and (2) by $$b$$: 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 can not divide by zero.

Hope it helps.
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19 Jan 2010, 04:01
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It's not a good practice to divide the parts of an equation by the unknown (A or B here) because this unknown can be 0. As we know, division by 0 can't be done.
jainanurag78 wrote:
I think it should be D. Why can we divide A*B*A=A by A on both the sides and it would give us AB =1 same with the S2.

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08 Oct 2008, 19:52
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amitdgr wrote:
Is the product of A and B equal to 1?

1. ABA= A
2. BAB =B

(C) 2008 GMAT Club - m01#36

I don't agree with the answer. what do you guys think?

(1) ABA = A
= ABA - A = 0
= A(AB-1) = 0
This means A=0 or AB=1 ---- Not Sufficient.

(2) BAB = B
= BAB - B = 0
= B(AB-1) = 0
This means B=0 or AB=1 ---- Not Sufficient.

Combined - A=0 or B=0 or AB=1 ---Not Sufficient.

E

Putting Both statements together shouldn't it be sufficient?
You know for sure that the only answers are 0 and 1. and if either A or B is 0, hten definetly the other is 1, IN this case answer is always zero right?

No they are not sufficient. The question asks is AB=1 ?

In data sufficiency with "is...?" questions we should arrive at either YES or NO. We cannot have both answers (ie) YES and NO from a single statement.

Statement 1 says --- > AB can be zero or one. So we can have No (AB is not 1) and Yes(AB is 1). so not sufficient
Statement 2 says --- > AB can be zero or one. This is also not sufficient.
Combined also says --> AB can be zero or one. So combined also not sufficient.

That is why we choose E. We are not able to arrive at definitive YES or NO with the given information.
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19 Feb 2011, 02:42
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BLUEMINT wrote:
Is the product of A and B equal to 1?

1. A*B*A = A
2. B*A*B = B

Can anyone explain the funda how we should consider the possibility of A & B being 0 ?

[Reveal] Spoiler:
OA E

Is the product of A and B equal to 1?

Question: $$ab=1$$?

(1) $$a^2b=a$$ --> $$a^2b-a=0$$ --> $$a(ab-1)=0$$ --> in order a product to be zero ether of multiples (or both) must be zero --> so, either $$a=0$$ (and $$b=any \ value$$, 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 $$a=any \ value$$, including zero) so in this case $$ab=0\neq{1}$$ OR $$ab=1$$. Two different answers, not sufficient.

(1)+(2) As from (1) $$a(ab-1)=0$$ and from (2) $$b(ab-1)=0$$ then $$a(ab-1)=b(ab-1)=0$$ --> 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.

Discussed here: m01-71305.html and here: tricky-one-98413.html

Hope it's clear.
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08 Oct 2008, 19:26
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amitdgr wrote:
Is the product of A and B equal to 1?

1. ABA= A
2. BAB =B

(C) 2008 GMAT Club - m01#36

I don't agree with the answer. what do you guys think?

(1) ABA = A
= ABA - A = 0
= A(AB-1) = 0
This means A=0 or AB=1 ---- Not Sufficient.

(2) BAB = B
= BAB - B = 0
= B(AB-1) = 0
This means B=0 or AB=1 ---- Not Sufficient.

Combined - A=0 or B=0 or AB=1 ---Not Sufficient.

E

Putting Both statements together shouldn't it be sufficient?
You know for sure that the only answers are 0 and 1. and if either A or B is 0, hten definetly the other is 1, IN this case answer is always zero right?

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09 Oct 2008, 02:29
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Its (E)

S1: ABA = A (A could be 0) or alternatively 1/2 * 2 * 1/2
S2: BAB = B (B could be 0) or alternativelt 1/2 * 2 * 1/2

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02 May 2011, 07:38
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Expert's post
The fastest way to solve the problem is to construct 2 examples:
1) A=1, B=1
2) A=0, B=0

Both examples satisfy first and second conditions but AB could be 1 or 0. So, it's E.

I agree that explanation is a bit unclear.

Now, let's try a strict solution:

1) A*B*A = A
A=0 --> B is any number --> AB = 0
A<>0 --> AB = 1 --> B = 1/A

2) B*A*B = B
B=0 --> A is any number --> AB = 0
B<>0 --> AB = 1 --> B = 1/A

1&2) Combination of both statements results in 2 possible solutions:

A=0 and B=0 --> AB = 0
A<>0 and B<>0 --> AB = A * 1/A = 1
So, insufficient too.
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08 Oct 2008, 22:24
What is the OA ?
IMO ans is D.

ABA = A.
=> ABA/A = 1
=> AB = 1 ... Suff.

BAB = B.
=>BAB/B = 1
=> BA = 1
=> AB = 1 .... Suff.

Hence either of them is sufficient
Hence D.

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10 Oct 2008, 17:38
This is a good Q

We are saying that either A is 0 or AB=1. I was tempted to chose D because AB=1 from both and I dont care about A or B by themselves.

But the catch is either A is 0 or AB=1. We don't know which one of them is correct. either of them will satisfy the condition. If A =1 AB =0 irrespective of B. Hence AB can be both 0 or 1.

E is correct.

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18 Jan 2010, 17:20
I think it should be D. Why can we divide A*B*A=A by A on both the sides and it would give us AB =1 same with the S2.

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Re: One more .... help needed [#permalink]

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04 Jul 2010, 10:50
Both are insufficient as you don't know what the values of A or B are?

Statement one would be sufficient if we knew the values.

As A*B=A/A which would give you the same answer.

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Re: One more .... help needed [#permalink]

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04 Jul 2010, 11:21
susuana wrote:
Both are insufficient as you don't know what the values of A or B are?

Statement one would be sufficient if we knew the values.

As A*B=A/A which would give you the same answer.

A/A cancels out to be 1
this means A*B = 1
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Re: One more .... help needed [#permalink]

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04 Jul 2010, 11:40
onedayill wrote:
susuana wrote:
Both are insufficient as you don't know what the values of A or B are?

Statement one would be sufficient if we knew the values.

As A*B=A/A which would give you the same answer.

A/A cancels out to be 1
this means A*B = 1

Sneaky!

Onedayill -- what if A = B = 0?

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Re: One more .... help needed [#permalink]

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07 Jul 2010, 05:26
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Bunuel wrote:
Question: $$ab=1$$?

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 can not divide by zero.

Gottcha, Thanks once again!!!
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Re: One more .... help needed [#permalink]

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12 Jul 2010, 07:48
E.
AB = 1 doesn't mean A= 1 , B =1
They can be inverse of each other. E.g. A =2 , B = 1/2.
Question doesn't say both are integers in which case AB =1 will imply A=B=1 and each one will be sufficient in that case.
Also, you can't cancel out A with A because you don't know if A# 0.

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16 Sep 2010, 14:57
Its D, ABA =A (Cancel A on both sides then Product of AB is equal to 1)
BAB=B (Cancel B on both sides then product of AB =1)
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16 Sep 2010, 15:06
nageshshiv wrote:
Its D, ABA =A (Cancel A on both sides then Product of AB is equal to 1)
BAB=B (Cancel B on both sides then product of AB =1)

You can't cancel A or cancel B
If you do that you automatically assume A is not equal to 0
Similarly for B

Notice that A=B=0 will satisfy both equations

So the answer is def E. You cannot say for sure that AB=1.
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Re: M01 #36   [#permalink] 16 Sep 2010, 15:06

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# M01 #36

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