For nonnegative integers a, b, and c, abc = ?

[gmattesttaker2]

Hello,

Can you please tell me if my solution is correct:

For nonnegative integers a, b, and c, what is the value of the product abc?

1) ab = bc
2) a is not equal to c

OA: C


1) ab = bc
b could be 0 or positive
b = 0 => abc = 0
b = +ve => a = c => abc = some +ve value



2) In-suff.


1 and 2 => b = 0 => abc = 0



I was just wondering if this is correct?

Thanks a lot,
Sri

[[email protected]]

Hi Sri,

Yes, your approach is correct. You've used Number Properties to make quick work of this DS prompt. It's also worth pointing out the importance of the value 0 when dealing with these types of questions. By TESTing 0 (either with literal values or with Number Property theory), you can avoid many long calculations and focus more on the inherent patterns that the question was built on.

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

Hello,

Can you please tell me if my solution is correct:

For nonnegative integers a, b, and c, what is the value of the product abc?

1) ab = bc
2) a is not equal to c

OA: C


1) ab = bc
b could be 0 or positive
b = 0 => abc = 0
b = +ve => a = c => abc = some +ve value



2) In-suff.


1 and 2 => b = 0 => abc = 0



I was just wondering if this is correct?

Thanks a lot,
Sri

Solution:

Statement One Alone:

ab = bc

If a = 1, b = 0 and c = 2, then abc = 0. However, if a = 2, b = 1 and c = 2, then abc = 4. Since we could have more than one possible value for abc, statement one alone is not sufficient.

Statement Two Alone:

a ≠ c

Since we don’t know the value of b, we can’t determine the value of abc. Statement two alone is not sufficient.

Statements One and Two Together:

Let’s rewrite the equality as ab - bc = 0. Factoring out b, we have b(a - c) = 0. Using the zero product property, this can only be true if b = 0 or a - c = 0. Since a ≠ c, a - c ≠ 0. In other words, b must be 0. If b is 0, then regardless of the values of a and c, we will have abc = 0.

Answer: C