If m/n

Question

If  m/n < 1  which of the following must be greater than 1 ?

(A)  \frac{m}{n^2}

(B)  \frac{m}{2n}

(C)  \frac{n}{m^2}

(D)  \frac{n}{m}

(E) None of the above

GMATBusters Collection

GMATinsight · Answer

Given:  m/n < 1

(A)  \frac{m}{n^2}  If m/n = 1/2, m/n^2 = 1/4 i.e. NOT greater than 1 so ELIMINATED

(B)  \frac{m}{2n}  If m/n = 1/2, m/2n = 1/4 i.e. NOT greater than 1 so ELIMINATED

(C)  \frac{m}{n^2}  If m/n = 1/2, m/n^2 = 1/4 i.e. NOT greater than 1 so ELIMINATED (By mistake it is same option as Option A)

(D)  \frac{n}{m}  If m/n = -1, n/m = -1 i.e. NOT greater than 1 so ELIMINATED

(E) None of the above CORRECT OPTION

TestPrepUnlimited · Answer

Remember that we have two possible cases:  \frac{m}{n}  is between 0 and 1, or  \frac{m}{n}  is negative.
If  \frac{m}{n}  is negative then this means m and n have opposite signs. We will check if the answers are forced to be positive first.
(A) m negative n positive, then A is negative. 
(B) m negative n positive, then B is negative.
(C) n negative m positive, then C is negative.
(D) n negative m positive, then D is negative.

Therefore in all cases we can't even pass the "must be positive" test, E is the answer.

purab15 · Answer

The logic was in this case m, n will have opposite sign.

arushi118 · Answer

KarishmaB  can you please help with how to proceed with these type of questions? I got the correct answer but it took me 3 minutes 20 seconds.

KarishmaB · Answer

Think of the number line. m/n < 1 means it lies in the region to the left of 1 so it could be something like 1/2 or -1/2 or -3/2 or 4/-3 etc. If m/n is negative, all four available terms could stay negative. If m is negative, then m/n^2, m/2n and n/m are negative too. If n is negative, then n/m^2 is negative too So none of them need to be greater than 1. Answer (E) Mind you, in actual GMAT Quant questions, 'None of the above' is never an option. Here is a video discussing relations on number line: https://youtu.be/YmoRR8OL4_c

If m/n < 1 which of the following must be greater than 1 ?

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 Problem Solving (PS) Questions