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

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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.

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

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