If m

Question

If  m < x < n  and  p < y < r , is  \frac{x}{y} < 0 ?

(1)  −|n− m| = |n| − |m| < 0

(2)  |p− r| = |p| − |r| > 0

Project PS Butler 
 Subscribe to get Daily Email -   Click Here  |  Subscribe via RSS -   RSS

Are You Up For the Challenge: 700 Level Questions

nick1816 · Answer

Statement 1- −|n− m| = |n| − |m| < 0 We get, |m|>|n| and mn>0 Also we know that m 0 |p|>|r| and pr>0 Also, p

eakabuah · Answer

Given that m0 From statement 2, we can conclude that |p|>|r|, implying that p<0 and r<0, hence y<0. We know nothing about x, so statement 2 is insufficient. 1+2 Sufficient because a negative number divided by a negative number results in a positive number. Hence x/y>0. The answer is C.

Archit3110 · Answer

given 
 m < x < n  and  p < y < r ,
target is to check whether  \frac{x}{y} < 0

#1
 −|n− m| = |n| − |m| < 0 
with given condition 
 m < x < n

only possibility is m & n being both -ve ; eg m= -5 and n =-3
-l-3+5l=l-3l-l-5l 
-2=-2
but no info about y so insufficient

#2
 |p− r| = |p| − |r| > 0

given condition 
 p < y < r 
r=-3 and p=-5
l-5+3l=l-5l-l-3l
2=2
but no info about x
insufficient
from 1 &2
we can say that value of x & y would fall in range of -ve values so  \frac{x}{y} < 0  is  NO 
hence option C is sufficient

sujoykrdatta · Answer

m < x < n and p < y < r Thus, we need information about m, n and also about p, r. Thus, we definitely need to combine the statements. From 1: -|n - m| = |n| - |m| < 0 => |n - m| = |m| - |n| > 0 => |m| > |n| Also: |n - m| = |m - n| = |m| - |n| => m and n are both of the same sign (both positive or both negative) However, we already have: m < n Thus, m is a negative number and hence, n is negative but smaller magnitude than m For example: m = -6, n = -2 => x is negative (since y lies between m and n) From 2: |p− r| = |p| − |r| > 0 => |p| > |r| Also: |p - r| = |p| - |r| => p and r are both of the same sign (both positive or both negative) However, we already have: p < r Thus, p is a negative number and hence, r is negative but smaller magnitude than m For example: p = -6, r = -2 => y is negative (since y lies between p and r) Thus: x/y > 0 Answer C

sauravleo123 · Answer

m0 y#0 and y>0 Insufficient Both statements together x<0 and y>0 Sufficient C

DaniyalAlwani · Answer

sujoykrdatta

Also: |n - m| = |m - n| = |m| - |n| => m and n are both of the same sign (both positive or both negative).

I really struggle in these questions of mod; please explain me this? 
And also, how important is mod for gmat?

sujoykrdatta · Answer

Best way to understand is to take some numbers: First of all, |m-n| = |n-m| since even if we multiply the inside of a mod by a '-1', there is no change - after all, mod removes the effect of the negative. Now, we need to check: |m - n| = |m| - |n| .... (A) Say m=4,n=1: both sides of (A) above equal 3 Say m=-4,n=-1: both sides of (A) above equal 3 Say m=4,n=-1: left side equals 5 while the right side equals 3 => not equal Thus, only when m and n were both positive or both negative, i.e. m and n are of same sign, (A) holds true Mod => pretty important

Posted from my mobile device

sujoykrdatta · Answer

Forgot to tag you - please check my response above

Posted from my mobile device

rye · Answer

nick1816

Can you please tell why you have not selected values of m and n , i.e. m = - 0.75 and n = 0.25 In this case ImI > InI. The original eqn. m < n still holds valid. Thus x can be +ve or -ve and not just -ve.

Same goes for Condition 2, i.e. y can be +ve or -ve since IpI > IrI where r can be either +ve or -ve, and p is always -ve.

Will appreciate any help?

nick1816 · Answer

rye 
(1) −|n−m|=|n|−|m|<0

or |n−m|=|m|−|n|

Now put the values you consider for m and n

|n−m|=|0.25-(-0.75)|=1

|m|−|n|= |-0.75|-|0.25| = 0.5

So the values you consider doesn't satisfy the statement 1. Same goes with other case. If you still have any doubt, you can ask.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If m < x < n and p < y < r, is x/y < 0?

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