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If mn < np < 0, is n < 1?

Expert replies
by M7MBA » Fri Apr 13, 2018 6:22 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty

If mn < np < 0, is n < 1?

(1) n is an integer
(2) m < p

The OA is C.

How can I determine the value of n? I really don't have an idea of how to solve this DS question. <i class="em em-confused"></i>
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Source: — Data Sufficiency |

by [email protected] » Fri Apr 13, 2018 5:28 pm
Hi M7MBA,

We're told that (M)(N) < (N)(P) < 0. We're asked if N is less than 1. This is a YES/NO question and can be answered with a mix of Number Properties and TESTing VALUES.

To start, since (M)(N) and (N)(P) are both less than 0, we know that one of the variables in each pair MUST be POSITIVE and the other MUST be NEGATIVE. Notice that "N" appears in both products - so there are two possible outcomes to consider (including how M relates to P):
N = POSITIVE, M = NEGATIVE and P = NEGATIVE and M < P
N = NEGATIVE, M = POSITIVE and P = POSITIVE and M > P

1) N is an integer

IF...
N is a POSITIVE integer, then the answer to the question is NO.
N is a NEGATIVE integer, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) M < P

With Fact 2, we know that we're dealing with the first option (above), so N MUST be POSITIVE. However, we don't know if N is an integer or not.
IF...
N = 1, then the answer to the question is NO.
N = 1/2, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know...
N is an integer
N is positive
Thus, N must be at least 1 and the answer to the question is ALWAYS NO.
Combined, SUFFICIENT

Final Answer: C

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Rich
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