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

(1) \(ab=bc\)

(2) \(a\ne c\)

Answer: C

Source: Veritas Prep

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

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## Your Answer

**A**

**B**

**C**

**D**

**E**

## Global Stats

**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

Cheers,

Brent