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# M01 #36

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Re: Data Sufficiency - Simultaneous Equations [#permalink]

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12 Apr 2011, 09:32
amp0201 wrote:
Is the product of A and B equal to 1?

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

1. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
2. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
4. EACH statement ALONE is sufficient
5. Statements (1) and (2) TOGETHER are NOT sufficient

1.
$$A^2B-A=0$$
$$A(AB-1)=0$$

Either A=0 OR AB=1
If A=0; AB=0
OR AB=1
AB can be 0 or 1.
Not Sufficient.

2.
$$B^2A-B=0$$
$$B(AB-1)=0$$

Either B=0 OR AB=1
If B=0; AB=0
OR AB=1
AB can be 0 or 1.
Not Sufficient.

Combining both statements:

Either A and B are both 0 OR AB=1
If A and B are both zeros: AB=0
or AB=1
Not Sufficient.

Ans: "E"
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Re: Data Sufficiency - Simultaneous Equations [#permalink]

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12 Apr 2011, 09:42
How can AB can be 0 or 1 ?

in (1) - A= 0 or AB =1 and (2) B = 0 or AB = 1 so combining (1) & (2) => can't we say AB=1 and hence C.
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Re: Data Sufficiency - Simultaneous Equations [#permalink]

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12 Apr 2011, 09:46
amp0201 wrote:
How can AB can be 0 or 1 ?

in (1) - A= 0 or AB =1 and (2) B = 0 or AB = 1 so combining (1) & (2) => can't we say AB=1 and hence C.

Is the product of A and B equal to 1?
1. A * B * A = A
2. B * A * B = B
*************************

Substitution:
A=0, B=0
A * B * A = A
0*0*0=0
True
B * A * B = B
0*0*0=0
True.

A=1, B=1
A * B * A = A
1*1*1=1
True
B * A * B = B
1*1*1=1
True.

Makes more sense now?
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Re: Data Sufficiency - Simultaneous Equations [#permalink]

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12 Apr 2011, 19:06
1. A * B * A = A

=> A(AB -1) = 0

=> A = 0 or AB = 1, so not sufficient

2. B * A * B = B

=> B(AB-1) = 0

=> B = 0 or AB = 1, so not sufficient

(1) and (2) combined says that A = 0, or B = 0 or AB = 1

Which can mean that either AB = 0, or AB = 1

Not sufficient

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Re: Data Sufficiency - Simultaneous Equations [#permalink]

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14 Apr 2011, 05:52
1. Not sufficient.

A=0 or AB=1
2. Not sufficient.

B=0 or AB = 1

Together we have A=0,B=0 or AB=1. Still not sufficient.

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02 May 2011, 07:38
1
KUDOS
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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20 Sep 2011, 05:59
dzyubam wrote:
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.

For all who think we can divide both sides by A to have AB=1;
Ok, we can try it, but just like absolute values, we have to consider two scenarios:

1) A is NOT equal to 0 : Well here AB=1

2) A is EQUAL to zero. Here since we can not divide, we have to find other ways to manipulate the statements. We arrive at A(AB-1)=0. Analyzing it, we can see AB can be both 1 and 0. Insuf.

I think D is irrelevant and if we are gonna become dubious b/w two choices, they are more likely to be C and E. As you know the general guideline is to choose C b/w C and E on tough questions when it comes to guessing. Solving it, I couldn't make my brain free of the thought that the statements together may be suf.
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22 Sep 2011, 21:50

1) A=0 or AB=1

2) B=0 or AB=1

C) AB=1 is the only solution that satisfies both statements --> Does AB=1? --> YES
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22 Sep 2011, 21:55
E)

1) A=0 (meaning AB=0) OR AB=1

2) B=0 (meaning AB=0) OR AB=1

Yes, E) is the correct answer. Even putting the two statements together, there are two possibilities for the value of AB (0 OR 1)
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20 Sep 2012, 06:11
What are wonderful question !
Reminds me of the Mona lisa.. Wonderfully simple in its presentation, yet on closer inspection, the painting reveals so many subtleities.
Anyway, the key point to remember is that , on the GMAT,
a) If the questions pertains to the "=" symbol, never ever cancel terms on both ends unless one is sure that the variable is not equal to 0. Remember that there is no such mathematical action as "Cancellation". Cancellation is division in disguise.
b) If the question pertains to the ">" or "<" symbol, never ever divide, or cross multiply unless one is certain that the variable being acted upon is >0. Remember that there is no such mathematical operation as "Cross multiplying". It is multiplication in disguise

Apply the FOIN tests to ensure that you have covered all the values that a variable may assume :-
F - Fraction
o - ZERO
i - Integer or Irrational
N - Negative
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22 Sep 2012, 03:12
well, i first chose E but on a second thought, i chose A , cos, drug related is an entity and others' is another entity that must be recognised as well. so i go for A, i hope am right.
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22 Sep 2012, 07:53
Yettilicious2 wrote:
well, i first chose E but on a second thought, i chose A , cos, drug related is an entity and others' is another entity that must be recognised as well. so i go for A, i hope am right.

The correct answer is E. Check this: m01-71305-20.html#p875154
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23 Sep 2012, 08:24
when you take it combined, you say:

either (A=0 and B=0) or (AB=1) ----not sufficient.
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19 Sep 2013, 05:25
This is golden Rule--

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 or its sign. We can not divide by zero.
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20 Sep 2013, 05:07
guttal007 wrote:
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.

I thought of this in the beginning, but A or B might equal zero, which makes dividing by A or B undefined. There is nothing in the question that tells you that A and B are not zero.
I think if the questions states that A and B are not zero, then your solution will be correct.

best,
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23 Sep 2013, 22:01
Is the product of $$A$$ and $$B$$ equal to 1?

1. ABA= A
2. BAB =B

1) ABA=A

ABA-A=0
A(BA-1)=0
ie A=0 OR AB-1=0
ie AB=1

2) BAB=B

BAB-B=0
B(AB-1)=0
ie B=0 OR AB-1=0
ie AB=1

So, combination of both of these two results in as follows:
A=B=0 or AB=1.
Both are insufficient.
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26 Mar 2014, 10:05
Bunuel wrote:
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.

Hi Bunnel,
per my understanding when we combine the solution from 2 equations we look for common solution.
from 2 equations we have a=0 OR b=0 OR ab=1
a=0, is not a solution since it doesn't satisfy II
b=0, is not a solution since it doesn't satisfy I
ab=1 satisfy both I and II so this is the solution or we have single solution for the problem.
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26 Mar 2014, 10:28
dangeyg wrote:
Bunuel wrote:
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.

Hi Bunnel,
per my understanding when we combine the solution from 2 equations we look for common solution.
from 2 equations we have a=0 OR b=0 OR ab=1
a=0, is not a solution since it doesn't satisfy II
b=0, is not a solution since it doesn't satisfy I
ab=1 satisfy both I and II so this is the solution or we have single solution for the problem.

When we consider two statements together we should take the values which satisfy both statements. For this question $$ab=1$$ satisfies both statement, but $$a=b=0$$ also satisfies both statements. So what you call "common solution" for this question is: $$ab=1$$ OR $$ab=0\neq{1}$$.

Hope it's clear.
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Re: M01 #36   [#permalink] 26 Mar 2014, 10:28

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# M01 #36

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