GMAT Club Test M01

[gmatwork]

Is the product of A and B equal to 1?

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


For 1: A(AB-1)=0

Either A=0 OR AB=1

--- AB can be 0 or 1.

Not Sufficient.

2. B(AB-1)=0

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

OA - E


This problem is from gmatclub online tests. Can someone please explain me how to combine the solutions together?

a) One way to combine is to say A =0 , B =0 and AB = 1 which means that still we can't determine the value of AB

b) Another way of looking at it is that both equations have to hold true......if both have to hold true shouldn't we just pick the overlapping solution and pick only AB= 1 after combining the two equations

Please clarify the confusion.

[mithunsam]

We need to consider two cases
1) A and B are of same sign
2) A and B are of different signs

Our question -> Is AB = 1?

Statement 1
a) If A and B are of same sign
A*B*A = A => A^2*B = A => AB = 1

b) If A and B are of different signs
A*B*A = A => A^2*B = -A => AB = -1
[A^2 is always +ve. Either A or B has to be -ve. Therefore, A^2*B will be -A]

We have two values for AB. Statement 1 is insufficient

Statement 2
a) If A and B are of same sign
B*A*B = B => B^2*A = B => AB = 1

b) If A and B are of different signs
B*A*B = B => B^2*A = -B => AB = -1
[B^2 is always +ve. Either A or B has to be -ve. Therefore, B^2*A will be -B]

We have two values for AB. Statement 2 is insufficient

Together statement 1 & 2 gives AB = 1 or -1. Therefore, both statements together are insufficient.

[Note - There is a third case -> AB=0. We can ignore this case now, as the above two cases are sufficient enough to arrive at E.]

[jnelson0612]

Great work,mithunsam.

[piyush.net]

Is the product of A and B equal to 1?

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


For 1: A(AB-1)=0

Either A=0 OR AB=1

--- AB can be 0 or 1.

Not Sufficient.

2. B(AB-1)=0

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

Combining 1 and 2

I put the value of A from statement 1 in the statement 2
statement 2 : B*A*B = B
=> B * (A*B*A) * B = B
=> (AB)^2 = 1
=> AB= 1 or AB = -1
Not sufficient.
Hence E

[tim]

i disagree that (AB)^2 = 1. it is possible that BOTH variables equal 0. the answer remains E regardless..