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.

Answer (C)

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