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Re: Data Sufficiency - Simultaneous Equations [#permalink]
 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
Please justify your answer, as I am not sure if the OA is correct. Thanks. 1. A^2B-A=0A(AB-1)=0Either 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=0B(AB-1)=0Either 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]
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]
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]
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 Answer - E
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Re: Data Sufficiency - Simultaneous Equations [#permalink]
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. Answer is E. Posted from my mobile device 
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Re: Test m01 36/37 [#permalink]
02 May 2011, 07:38
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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 = 0A<>0 --> AB = 1 --> B = 1/A 2) B*A*B = B B=0 --> A is any number --> AB = 0B<>0 --> AB = 1 --> B = 1/A 1&2) Combination of both statements results in 2 possible solutions: A=0 and B=0 --> AB = 0A<>0 and B<>0 --> AB = A * 1/A = 1So, insufficient too.
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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. 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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answer is definitely C)
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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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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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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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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when you take it combined, you say:
either (A=0 and B=0) or (AB=1) ----not sufficient.
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close
