a, b, and c are three integers such that a

Question

a, b, and c are three integers such that a < b < c. Is (a + b) less than c?

(1) ab is negative
(2) a + b is negative

OptimusPrepJanielle · Answer

Statement 1: ab < 0 This means that a and b have opposite signs. Since a < b < c Therefore a < 0 and b > 0 and c > b > 0 Since b is positive and a is negative, therefore we are subtracting something from b Hence (a + b) < b Therefore (a + b) < c Sufficient Statement 2: a + b < 0 If a and b both < 0 (a + b) will be a quantity that would be less than both a and be Hence (a + b) < c If a < 0 and b > 0 In this case, (a + b) will be a quantity that is less than b Hence (a + b) < c Sufficient Option D

KarishmaB · Answer

Imagine the three numbers on the number line:

............. a .............. b .................... c ....................

Is (a + b) < c?

(1) ab is negative
It means one and only one of a and b is negative. Since a is to the left of b on the number line, a must be negative and b positive. So c must be positive too and greater than b.
(a + b) must be smaller than b because a is negative. So a+b is definitely smaller than c.
Sufficient.

(2) a + b is negative
Either a is negative or both a and b are negative. 
If only a is negative, (a+b) is between a and b on the number line.
If both a and b are negative, (a+b) is to the left of a. 
In both cases, a+b is to the left of c so it is definitely smaller than c
Sufficient

Answer (D)

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a, b, and c are three integers such that a < b < c. Is (a + b) less th

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