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
The OA is D.
Please, can any expert explain this DS question for me? I don't understand why that is the correct answer. Thanks.
a, b, and c are three integers such...
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We have to determine whether (a + b) < c.swerve wrote: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
The OA is D.
Please, can any expert explain this DS question for me? I don't understand why that is the correct answer. Thanks.
(1) ab is negative.
Since ab is negative, only one between a and b is negative. Since we know that a < b, the only possibility is that a is negative and b is positive. Let's determine the value of (a + b). Since a is negative and b is positive, we can deduce that (a + b) = b - |a|. Since b < c, we can deduce that (b - |a|) < c. Sufficient.
(2) a + b is negative.
Case 1: a and b both are negative.
Thus, a < b < c can be deduced as -|a| < -|b| < c. For this relationship to hold true, if c is a non-negative number, then a + b = -|a + b| < c. However if c is also a negative number, then a + b = -|a + b| < -|c|.
Case 2: Only one between a and b is negative. Since a < b, only a can be negative and b would be positive. This is the same case as discussed in Statement 1.
Sufficient.
The correct answer: C
Hope this helps!
-Jay
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