BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

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.

Cheer<i class="em em-v"></i>
Top
Post new topic Post Reply
• Page 1 of 1