Problem Solving

For any numbers A and B, AB = A+B - AB. If AB = 0, which of the following CANNOT be a value of B?

a) 2

b) 1

c) 0

d) -1

e) -3/2


Do you recommend plugging in the answer choices once you narrow down that -A = B? What's the most efficient way of solving this problem? Correct answer is B

If AB = 0, then

AB = A+B-AB
0 = A+B - 0
0 = A+B

Also, if AB = 0, then A, B, or both, is zero. If this is true you must then ask yourself;

If A=0;

0=0+B, B has to equal zero.

If B=0;

0=A+0, A must equal zero.

So A and B must both be equal to zero.

I think the question is flawed. Or point out my error in reasoning. I may have drank to much last night lol.

wcheng57 wrote: Do you recommend plugging in the answer choices once you narrow down that -A = B? What's the most efficient way of solving this problem? Correct answer is B

I just wanted to add;

Your came to the right conclusion with, -A=B.

But again if AB=0 then A, B, or both is equal to zero.

If A=0;

-0=B, B must be equal to zero.

If B=0;

-A=0, A must be equal to zero.

We can conclude that not matter what, the two numbers must be equal to zero.

Finally figured it out. The correct answer is choice B.

AB = A+B - AB, which also means 2AB = A+B

Given that AB = 0, then we can say that 2AB - AB = AB = A+B

Since A+B = AB, then of all the answers given, B cannot be which value. The correct is B CANNOT be 1. Why?

Since A+B = AB, when B=1, then A+1=A (THAT IS NEVER TRUE!!!)

If you plug in the other 4 values for B, it is possible that A+B = AB is still valid.

Since A+B = AB, when B=1, then A+1=A (THAT IS NEVER TRUE!!!)

b isn't possible because, again, AB=0 so A, B, or both is equal to zero.

b) assume that B is 1 so A must be zero, A+B=0. 0+1=/=0. So b) cannot be a value of B. But neither can 2(a), 1(b), -1(d), -3/2(e), for the same reason;

A+B=AB, and AB=0, so;
A+B=0

(a) 0+2=2, not 0, so (a) is true.

(b) 0+1=1, not 0, so (b) is true.

(d) 0-(-1)=1, not 0, so (d) is true.

(e) 0-(-3/2)=3/2, not 0, so (e) is true.

What I'm getting at is that as much as b is true so much a, d, e.

What is the source of the problem?

This was an actual GMAT question from a GMAT Test Paper exam that I bought from mba.com. I only have the correct answers, but no explanation. However, if you look at my reasoning below again, answer choice B is correct.


The question states the following: For any numbers A and B, AB = A+B - AB. If AB = 0, what CANNOT be the value of B?

Based on the given info, we can say this:

If AB = 0, then we can logically conclude that either A or B is equal to 0. But, that doesn't help us if you end up just plugging in the solutions, because all the answer choices seem plausible. You need to use BOTH equations given to solve the problem.

So, I did the following work:

Given that AB = A+B - AB (general equation) Then, 2AB = A+B

If AB=0, then plugging 0 in place of AB into the general equation, we get 0=A+B

From that, we can also logically say that 2AB - AB = AB = 0 = A+B

Since A+B = AB, then of all the answers given, B cannot be which value. The correct is B CANNOT be 1. Why?

If you plug in the 5 values for B, B CANNOT equal 1 because since A+B = AB, when B=1, then A+1=A (THAT IS NEVER TRUE!!!)

wcheng57 wrote:This was an actual GMAT question from a GMAT Test Paper exam that I bought from mba.com. I only have the correct answers, but no explanation. However, if you look at my reasoning below again, answer choice B is correct.


The question states the following: For any numbers A and B, AB = A+B - AB. If AB = 0, what CANNOT be the value of B?

Based on the given info, we can say this:

If AB = 0, then we can logically conclude that either A or B is equal to 0. But, that doesn't help us if you end up just plugging in the solutions, because all the answer choices seem plausible. You need to use BOTH equations given to solve the problem.

So, I did the following work:

Given that AB = A+B - AB (general equation) Then, 2AB = A+B

If AB=0, then plugging 0 in place of AB into the general equation, we get 0=A+B

From that, we can also logically say that 2AB - AB = AB = 0 = A+B

Since A+B = AB, then of all the answers given, B cannot be which value. The correct is B CANNOT be 1. Why?

If you plug in the 5 values for B, B CANNOT equal 1 because since A+B = AB, when B=1, then A+1=A (THAT IS NEVER TRUE!!!)

Okay, you still haven't negated my point.

Sorry I just really want to get this one nailed down.

Any two numbers that multiply to zero means that one of those numbers is 0.

Any number plus 0 and has a sum of 0 means that both numbers must be zero, because any non-zero number plus zero cannot possibly equal zero. How is it possible that B, or A for that matter, could be anything but 0? You keep talking about A+B = AB without addressing the fact that AB=0. I understand that if we AB does not equal zero then your absolutely correct, but if AB = 0 then you couldn't possibly right.

You are not addressing this point.

sk818020 wrote:
Any two numbers that multiply to zero means that one of those numbers is 0.

Any number plus 0 and has a sum of 0 means that both numbers must be zero, because any non-zero number plus zero cannot possibly equal zero. How is it possible that B, or A for that matter, could be anything but 0? You keep talking about A+B = AB without addressing the fact that AB=0. I understand that if we AB does not equal zero then your absolutely correct, but if AB = 0 then you couldn't possibly right.

You are not addressing this point.

I think the thing that makes this problem confusing is the way it's worded. I agree with you that when AB = 0, A or B would equal to 0. What the question provides is the general equation, plus a specific case (AB=0). I don't think it's asking necessarily that if AB = 0 exclusively, then what value cannot be B. If that were the case, then you're absolutely right. B could equal to any of the answer choice values because A would be equaled to 0 every time. That was my initial thought process too, but that would mean there is no correct answer.

However, I realized that the question is actually asking the following: when you get to A+B = AB, it is asking at this point, what value CANNOT be B. If you were to again put 0 in place of AB, then yes, you'll get A+B=0, so A=B=0. But, the point of the question is for you to get to this point and plug in the values to see which answer choice will make A+B=AB invalid. And when B=1, that is the only possible choice b/c A+1 DOES NOT equal A times 1.

The question provides a general equation and enough info from a specific case to allow you to arrive at a different general equation, so that you can use that new general equation to find the correct answer. After all, AB=A+B-AB does allow other possibilities other than A=B=0. AB=0 just happens to be one specific case that fits into the given general equation. So, the problem wants to know what value of B will absolutely not work.

Does that make more sense?

If AB=0
=> A+B-AB= 0
=> A+B = AB
=> B= A(B-1)
=> A = B/(B-1)

Therefore, B cannot be equal to 1

Ans. (B)

@nxanand: The logic can be extended to ensure that B cannot be other numbers as well, like below:

A + B = 0 = 2AB
=> B = 2AB - A
=> B = A (2B - 1)
=> A = B/(2B - 1)

With the above set of equations, B cannot be 1/2.

For A + B to be 0 and AB also to be 0, the only possible values I see for A and B are O and O. Not sure whether the Q is correct...

Well the question says "for any numbers A & B , AB= A+B-AB.. So, I think the LHS AB is not exactly A*B but some function defined .. say A$B = A +B -AB, given A$B = 0, which of the following CANNOT be a value of B?...makes sense..