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

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pm; Thanked: 11 times; Followed by:8 members

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

by gmattesttaker2 » Mon Apr 28, 2014 10:52 pm

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

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Source: Beat The GMAT — Data Sufficiency | Mon Apr 28, 2014 10:52 pm

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by [email protected] » Tue Apr 29, 2014 12:48 am

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.

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Rich

Contact Rich at [email protected]

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

by Scott@TargetTestPrep » Thu Jan 14, 2021 4:25 am

gmattesttaker2 wrote: ↑
Mon Apr 28, 2014 10:52 pm
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

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