If a, b and x are integers greater than zero, then which of the follow

Question

If a, b and x are integers greater than zero, then which of the following must be greater than  \frac{a}{a+b} ?

(A)  \frac{a+x}{a+b+x}

(B)  \frac{a-x}{a+b+x}

(C)  \frac{2a}{2a+2b+x}

(D)  (\frac{a}{a+b})^{2}

(E)  \frac{a-1}{a+b-1}

BrentGMATPrepNow · Accepted Answer

--------ASIDE---------------------------------------
Here's a nice property of fractions:    If a, b and k are positive, then (a + k)/(b + k) approaches 1 as k gets bigger.    
For example, the fraction (2 +11 )/(3 +11 ) is closer to 1 than 2/3 is.
Likewise, the fraction (1 +7 )/(2 +7 ) is closer to 1 than 1/2 is.
-----ONTO THE QUESTION!!!-------------------------------------

Since a and b are positive, we know that a+b > a
So, the fraction a/(a+b) must be less than 1

So, based on the above   property  , if we add a positive number to numerator and denominator, the resulting fraction will be closer to 1 than the original fraction is.

Check the answer choices. . . .
(A) (a  + x )/(a + b  + x )
Since x is positive, we know that (a  + x )/(a + b  + x ) will be closer to 1 than a/(a+b) is.
Since a/(a+b) is less than 1, we know that (a  + x )/(a + b  + x ) will be greater than a/(a+b)

Answer: A

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pandeyashwin · Answer

Assume the value 1 each.
Ans A

sarahfiqbal · Answer

Can you please clarify, how did you know to assume the value 1 for each? Is this a rule somewhere? Or some sort of pre-thinking that I am not aware of? Thanks!

pandeyashwin · Answer

The condition for this question is : a , b, x > 0 & they are integers.

Therefore we are free to assume any values we like as long as it follows the given condition.

I assumed 1 each because it's the easiest one to calculate. 
But if you get more than 1 correct option with your assumption, you should assume different set of values such as a = 1 , b= 2 ,c = 3 to rule out the wrong choices.

GMATinsight · Answer

It's a basic concept that if x/y < 1
  then (x+a)/(y+a) > x/y because same number added in numerator and denominator increases numerator by greater percentage than the percentage that it increases the denomenator

Hence, Answer Option A

shaarang · Answer

Rather than assuming one for each term, know that a fundamental rule of fractions is that adding the same number to both numerator and denominator brings the fraction closer to that number.

So, adding x to both numerator and denominator brings the fraction closer to x. The value of x doesn't matter. Since we know it's an integer (1 or greater) and a/a+b is a fraction, adding x will bring the fraction closer to x, therefore, increasing it.

ScottTargetTestPrep · Answer

Solution:
 
Using a = 2, b = 3, and x = 1, we see that a/(a + b) = 2/5. Now let’s check the given choices.

A) (a + x)/(a + b + x) = 3/6 = 1/2 → This is greater than 2/5.

B) (a - x)/(a + b + x) = 1/6 → This is NOT greater than 2/5.

C) 2a/(2a + 2b + x) = 4/11 → This is NOT greater than 2/5.

D)  ^2 = (2/5)^2 = 4/25 → This is NOT greater than 2/5.

E) (a - 1)/(a + b + 1) = 1/4 → This is NOT greater than 2/5.

(Note that you could choose any integer values greater than 0 for a, b, and x, and the same answer - choice A - will be correct.)

Answer: A

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If a, b and x are integers greater than zero, then which of the follow

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If a, b and x are integers greater than zero, then which of the follow

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