If a + b + c < 0, is c < 1 ?

[BTGModeratorVI]

If a + b + c < 0, is c < 1 ?

(1) c < a + b – 1
(2) a + b − 1 > 0

Answer: D
Source: Kaplan

[Jay@ManhattanReview]

If a + b + c < 0, is c < 1 ?

(1) c < a + b – 1
(2) a + b − 1 > 0

Answer: D
Source: Kaplan

Let's take each statement one by one.

(1) c < a + b – 1

1 + c < a + b;
Adding c to both the sides, we have
2c + 1 < a +b + c

Since a + b + c < 0, we have 2c + 1 < 0 => c < –1/2. Sufficient.

(2) a + b − 1 > 0

=> a + b > 1
Adding c to both the sides, we have

a + b + c > 1 + c

Since a + b + c < 0, we have c + 1 < 0 => c < –1. Sufficient.

Correct answer: D

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

If a + b + c < 0, is c < 1 ?

(1) c < a + b – 1
(2) a + b − 1 > 0

Answer: D
Source: Kaplan

Given: a + b + c < 0

Target question: Is c < 1?

Statement 1: c < a + b – 1
Take: a + b + c < 0
Subtract a and subtract b from both sides to get: c < -a - b
Now add this inequality to the statement 1 inequality: c < a + b – 1
We get: 2x < -1
Divide both sides by 2 to get: c < -1/2
If c < -1/2, then c is definitely less than 1
So, the answer to the target question is YES, x IS less than 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a + b − 1 > 0
Take: a + b − 1 > 0
Rewrite as: 0 < a + b - 1
Add c to both sides to get: c < a + b + c - 1
Add 1 to both sides to get: c + 1 < a + b + c
We already know that a + b + c < 0
So, we can add this info to our inequality to get: c + 1 < a + b + c < 0
This tells us that c + 1 < 0
Subtract 1 from both sides to get: c < -1
If c < -1, then c is definitely less than 1
So, the answer to the target question is YES, x IS less than 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent