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If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? 1. m < n 2. x > 0
It is useful to understand that when you add the same positive number to the numerator and denominator of a positive fraction, it moves towards 1.
Say 1/2 = 0.5 I add 1 to both numerator and denominator, it becomes 2/3 = 0.67 i.e. closer to 1 than 1/2 Say 3/2 = 1.5 I add 1 to both numerator and denominator, it becomes 4/3 = 1.33 i.e. closer to 1
When you add the same negative number (or in other words, subtract the same positive number) to the numerator and denominator of a positive fraction, it moves away from 1.
Say 1/2 = 0.5 I add -1 to both numerator and denominator, it becomes 0 i.e. farther from 1 than 1/2 Say 3/2 = 1.5 I add -1 to both numerator and denominator, it becomes 2/1 i.e. farther from 1
Once you understand this, the question takes a few seconds.
1. m < n The fraction m/n must be less than 1. So if x is positive, the fraction will increase and move towards 1. If x is negative, the fraction will decrease to move away from 1. Not sufficient.
2. x > 0 x is positive but we do not know whether the fraction is greater than 1 or less than 1. If m/n is greater than 1, it will decrease and move towards 1. If m/n is less than 1, it will increase and move towards 1.
Using both together, m/n is less than 1 and x is positive so we are adding the same positive number to both numerator and denominator. Hence (m+x)/(n+x) will be greater than m/n to move towards 1. Answer (C) _________________
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? 1. m [#permalink]
06 Mar 2012, 07:08
1
This post received KUDOS
Expert's post
dchow23 wrote:
Why cant we cross multiply to get; mn + nx > mn + mx, simplify, resulting is n>m?? is this totally wrong?
Cross-multiplying (m+x)/(n+x)>m/n would be wrong, since we don't know whether n+x is positive or negative: if n+x>0 then we would have as you've written mn+nx>mn+mx BUT if n+x<0 then when multiplying by negative number we should flip the sign of the inequity and write mn+nx<mn+mx.
General rule: never multiply or divide inequality by a variable (or by an expression with variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality.
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? 1. m [#permalink]
06 Mar 2012, 10:17
Expert's post
dchow23 wrote:
Why cant we cross multiply to get; mn + nx > mn + mx, simplify, resulting is n>m?? is this totally wrong?
Yes, cross multiplying is incorrect here. We do not know whether (n+x) is positive or negative. We know that m and n are positive but we know nothing about x. When you multiply an inequality by a positive number, the inequality sign stays the same but when you multiply an inequality by a negative number, the inequality sign flips. So before you multiply/divide an inequality by a variable, you need to know whether the variable is positive or negative. _________________
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]
26 Dec 2015, 17:03
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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]
26 Dec 2015, 17:31
whichscore wrote:
If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?
(1) m < n (2) x > 0
I think lot of folks have suggested great solution, but me not great with math followed following, which helped me get to the answer fairly quickly.
Really to solve this we needed to both about X and about relationship between M&N. So, I tried using number, since we were given X,Y>0 but not given if X>0 or X<0 or M>N or M<N.
case 1: M>N, say 5/4 = 1.25 now X>0 or X<0 for X>0, say 3 (5+3)/(4+3) = 1.143 (values comes down)
for x < 0, say -3 (5-3)/(4-3) = 2 (value goes up)
case 2: M<N, say 3/4 = 0.75 now X>0 or X<0 for X>0, say 3 (3+3)/(4+3) = .85 (value goes up)
for x < 0, say -2 (3-2)/(4-2) = 2 (values comes down)
gmatclubot
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?
[#permalink]
26 Dec 2015, 17:31
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