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# If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?

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If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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14 Apr 2011, 03:14
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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

Topic locked. Open discussions at if-m-0-and-n-0-is-m-x-n-x-m-n-93967.html
[Reveal] Spoiler: OA

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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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14 Apr 2011, 03:50
whichscore wrote:
If m>0 and n>0, is (m+x)/(n+x) greater than m/n ?
1. m < n
2. x > 0

$$\frac{m+x}{n+x} > \frac{m}{n}$$

$$\frac{m+x}{n+x} - \frac{m}{n} > 0$$

$$\frac{mn+nx-mn-mx}{n(n+x)} > 0$$

A: Does $$\frac{x(n-m)}{n(n+x)} > 0$$?

1. $$m<n$$

$$m-n<0$$
$$n-m>0$$

But, what if $$x<0 \hspace{2} & \hspace{2} |x|<n$$
Then the answer to the question would be No.

If $$x>0$$
Then the answer to the question would be Yes.
Not Sufficient.

2. $$x>0$$

Denominator is +ve.
Numerator must be +ve to make the expression true.

$$n-m>0$$
$$n>m$$ should be true to make the expression true. But, it is not given which of the two is greater.

If n>m, the answer would be Yes.
If n<m, the answer would be No.

Combining both statements:
Denominator becomes +ve.
Numerator also becomes +ve as m<n
Answer to the question is Yes.
Sufficient.

Ans: "C"
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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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14 Apr 2011, 04:26
1) Insufficient.
Lets consider m = 1 n = 2
If x = 0 The answer is NO
If x = 1 The answer is YES

2) Insufficient
consider m = n = 1 x = 1 The answer is NO
Consider m = 1 n = 2 x = 1 The answer is YES

1) + 2) Consider m = 1 n = 2 x = 1 The answer is YES. Sufficient

whichscore wrote:
If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?
1. m < n
2. x > 0

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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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14 Apr 2011, 05:24
As per (1)

m = 2, n = 3

m/n = 2/3

if x = -2, then 0/1 < 2/3

if x = 0 then (m+0)/(n +0) = m/n

if x = 2 then (2 + 2)/(3+2) = 4/5 > 2/3

(1) is insufficient

As per (2)

x > 0, but it's possible that m = n , and hence (m+x)/(n+x) = m/n

(2) is insufficient

(1) and (2) together

if x = 1, m = 2, n = 3

(2 + 1)/(3 + 1) = 3/4 hence m/n < (m+x)/(n+x)

if x = 2, m = 2, n = 3 then (2 + 2)/(3+2) = 4/5 > 2/3 hence m/n < (m+x)/(n+x)

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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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14 Apr 2011, 06:12
Rephrasing given expression we have ((n-m)x)/(n(n+x)) >0?

1. Not sufficient as we don't know anything about x.

2. Not sufficient as we don't know anything about m,n

Together we have n>m & x>0 . sufficient to answer.

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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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14 Apr 2011, 14:31
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whichscore wrote:
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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17345 [7], given: 232 Senior Manager Joined: 08 Nov 2010 Posts: 394 Kudos [?]: 128 [0], given: 161 WE 1: Business Development Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink] ### Show Tags 15 Apr 2011, 12:20 great explanation. thanks karishma. _________________ Kudos [?]: 128 [0], given: 161 Manager Joined: 16 May 2011 Posts: 71 Kudos [?]: 18 [0], given: 2 Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink] ### Show Tags 06 Mar 2012, 07:30 Why cant we cross multiply to get; mn + nx > mn + mx, simplify, resulting is n>m?? is this totally wrong? Kudos [?]: 18 [0], given: 2 Math Expert Joined: 02 Sep 2009 Posts: 41886 Kudos [?]: 128668 [2], given: 12181 Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink] ### Show Tags 06 Mar 2012, 08:08 2 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. Hope it's clear. _________________ Kudos [?]: 128668 [2], given: 12181 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7674 Kudos [?]: 17345 [0], given: 232 Location: Pune, India Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink] ### Show Tags 06 Mar 2012, 11:17 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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07 Mar 2012, 10:53
@flute, thanks for the solution.

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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

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26 Dec 2015, 18:31
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)

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Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?   [#permalink] 26 Dec 2015, 18:31
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