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# If a,b and x are integers greater than zero

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If a,b and x are integers greater than zero [#permalink]  10 Sep 2018, 22:15
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Question Stats:

80% (02:08) correct 20% (01:09) wrong based on 5 sessions
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)$$\frac{a-1}{a+b-1}$$
[Reveal] Spoiler: OA
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Re: If a,b and x are integers greater than zero [#permalink]  12 Sep 2018, 19:09
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AchyuthReddy 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)$$\frac{a-1}{a+b-1}$$

As it is mentioned
a, b and x are integers greater than zero

so a,b,x can be equal, consecutive numbers or any other possible value matching the criteria.

Now we can glance down straight to the answer choice we can eliminate option B, D and E. Option A is the possible contender.

Option B : if x is subtracted from numerator than the value will be < $$\frac{a}{a+b}$$
Option D : we are squaring the value but remember we are also squaring the denominator so the value will be < $$\frac{a}{a+b}$$
Option E: Again if 1` is subtracted it will only reduce the value so it will always be < $$\frac{a}{a+b}$$

Now for option C:: Let dig some value such as all numbers are considered equal, after solving it < $$\frac{a}{a+b}$$

So only option left is A, we can put some value such as a = b =c = x =1, or any integer value greater than 1, it will always be > $$\frac{a}{a+b}$$
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Re: If a,b and x are integers greater than zero   [#permalink] 12 Sep 2018, 19:09
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