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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  [#permalink]

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New post 17 Sep 2018, 02:08
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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) \(\frac{a-1}{a+b-1}\)

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Re: If a, b and x are integers greater than zero, then which of the follow  [#permalink]

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New post 17 Sep 2018, 07:33
Assume the value 1 each.
Ans A
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Re: If a, b and x are integers greater than zero, then which of the follow  [#permalink]

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New post 17 Sep 2018, 09:50
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Bunuel wrote:
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) \(\frac{a-1}{a+b-1}\)


--------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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Re: If a, b and x are integers greater than zero, then which of the follow  [#permalink]

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New post 19 Sep 2018, 22:30
pandeyashwin wrote:
Assume the value 1 each.
Ans A



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!
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If a, b and x are integers greater than zero, then which of the follow  [#permalink]

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New post 19 Sep 2018, 23:16
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sarahfiqbal wrote:
pandeyashwin wrote:
Assume the value 1 each.
Ans A



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!

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.
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Re: If a, b and x are integers greater than zero, then which of the follow  [#permalink]

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New post 20 Sep 2018, 04:20
1
Bunuel wrote:
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) \(\frac{a-1}{a+b-1}\)



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
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Re: If a, b and x are integers greater than zero, then which of the follow  [#permalink]

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New post 07 Oct 2018, 22:24
sarahfiqbal wrote:
pandeyashwin wrote:
Assume the value 1 each.
Ans A



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!


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.
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Re: If a, b and x are integers greater than zero, then which of the follow &nbs [#permalink] 07 Oct 2018, 22:24
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