If m and n are integers, is mn 0 ? (1) m/n is an integer (2) |m|

Question

If m and n are integers, is mn > 0 ?

(1) m/n is an integer.
(2) |m| < |n|

belagavi · Answer

Edit : I initially had not considered that when m/n is an integer, m could also be zero. So i have updated my answer.

We need to find out if mn > 0. That is do m and n have different signs.

Statement 1: m/n is an integer. This means that n is a factor of m. m and n could have different or the same signs but the only condition is that |m| >= |n| or m = 0, because if its not the case
we will be entering decimal territory. We have no idea about the signs of m and n so Insufficient.

Statement 2: |m| < |n|. This tells us nothing about the signs.Insufficient .

According to statement 1 |m| >= |n| or m = 0, but according to statement 2 |m| < |n|. So the only thing that makes sense is that m = 0.
Which means mn = 0.

So answer is C.

gmatophobia · Answer

We know that m and n are integers.

Individually the statements are insufficient, as the sign of m and n are not known.

However when we we combine

1) we know that |m| < |n|

2)  \frac{m}{n}  is  an integer .

This can only happen if m = 0

Is mn > 0 - No !

IMO C

Bunuel · Answer

Official Solution: If m and n are integers, is mn > 0 ? (1) \frac{m}{n} is an integer. This statement is clearly insufficient. For example, consider m = 1 and n = 1 , and m=1 and n=-1 . (2) |m| < |n| This statement implies that n is further from 0 than m . This statement is also clearly insufficient. For example, consider m = 1 and n = 2 , and m=1 and n=-2 . (1)+(2) \frac{m}{n} being an integer implies that m is a multiple of n , and |m| < |n| implies that m is smaller in magnitude than n . The only way for m to be a multiple of n and have a smaller magnitude than n is if m is 0. Thus, m = 0 , which provides a NO answer to the question of whether mn > 0 . Sufficient. Answer: C

If m and n are integers, is mn > 0 ? (1) m/n is an integer (2) |m| <

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions