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

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by Brent@GMATPrepNow » Sat Oct 26, 2019 7:59 am
BTGmoderatorDC wrote:For nonnegative integers a, b, and c, what is the value of the product abc?

(1) ab = bc
(2) a≠c
Target question: What is the value of the product abc?

Statement 1: ab = bc
Let's TEST some values.
There are several values of a, b and c that satisfy the condition that ab = bc. Here are two:
Case a: a = 0, b = 0 and c = 0. In this case, the answer to the target question is abc = (0)(0)(0) = 0
Case b: a = 1, b = 1 and c = 1. In this case, the answer to the target question is abc = (1)(1)(1) = 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a≠c
Let's TEST some values.
Since we aren't told anything about the value of b, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that ab = bc
Rewrite as: ab - bc = 0
Factor to get: b(a - c) = 0
This means that EITHER b = 0 OR (a - c) = 0

Statement 2 tells us that a≠c
So, it CANNOT be the case that a-c = 0
This means it MUST be the case that b = 0
If b = 0, then abc = 0
The answer to the target question is abc = 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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Brent
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by deloitte247 » Sun Oct 27, 2019 1:09 pm
What is the value of the product abc?
First, let find the value for each of a, b and c.
Statement 1: ab = bc
ab =bc + 0
ab - bc = 0
b(a-c) = 0
$$If\ b=1,\ a=2;\ and\ b=3;\ b(a-c)=6\ne0$$
$$If\ b=0,\ a=3;\ and\ b=4;\ b(a-c)=0$$
$$If\ b=2,\ a=5;\ and\ b=5;\ b(a-c)=0$$
$$If\ b=6,\ a=6;\ and\ b=6;\ b(a-c)=0$$
$$If\ b=7,\ a=5;\ and\ b=3;\ b(a-c)=14\ne0$$
Thus, the information provided is not enough to arrive at a definite value, hence, statement 1 IS NOT SUFFICIENT.

Statement 2:
$$a\ne c$$
$$If\ a\ne c,\ then\ abc=2\cdot3\cdot4\ or\ 3\cdot4\cdot5\ or\ $$ any other variant with any other integer, hence, statement 2 is NOT SUFFICIENT.

Combining both statements;
Statement 1: b(a-c) = 0
Statement2: $$a\ne c$$
If 'a' and 'c' are different values for b(a-c) to b=0, then b=0.
If b=0, then the product of a, b, and c will also equal to zero (0). Notwithstanding the value of 'a' and 'c', both statements combined ARE SUFFICIENT.

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