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