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Which expression has the greatest value?

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Which expression has the greatest value?

by vinni.k » Thu Jan 17, 2013 7:30 am
Which expression has the greatest value?

(A). 1876452/1876455
(B). 1883456/1883459
(C). 1883491/1883494
(D). 1883446/1883449
(E). 1883453/1883456

answer is C.

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by GMATGuruNY » Thu Jan 17, 2013 8:35 am
vinni.k wrote:Which expression has the greatest value?

(A). 1876452/1876455
(B). 1883456/1883459
(C). 1883491/1883494
(D). 1883446/1883449
(E). 1883453/1883456

answer is C.

Thanks & Regards
Vinni
Each of the answer choices is of the following form:
x/(x+3).

Plug in EASY VALUES for x and look for a PATTERN.
If x=1, x/(x+3) = 1/4.
If x=2, x/(x+3) = 2/5.
If x=3, x/(x+3) = 1/2.

As the value of x increases, the value of x/(x+3) also increases.
Thus, to maximize x/(x+3), we must maximize the value of x (the numerator).
Of the five answer choices, C has the greatest numerator.

The correct answer is C.
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by Tommy Wallach » Fri Jan 18, 2013 12:40 am
Believe it or not, this pattern (when there's a constant difference between the denominator and numerator in a fraction, the number gets bigger as the numerator and denominator get bigger) is actually worth just knowing, as it comes up now and again in questions. Similarly, it's worth knowing that when the difference between the numerator and denominator is the same, but the numerator is bigger than the denominator (i.e. an improper fraction), the bigger they get, the smaller the resultant number.

For example 5/4 > 6/5 > 7/6

Good luck!

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by vinni.k » Fri Jan 18, 2013 3:11 am
Thank you :D

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by Brent@GMATPrepNow » Fri Jan 18, 2013 8:16 am
vinni.k wrote:Which expression has the greatest value?

(A). 1876452/1876455
(B). 1883456/1883459
(C). 1883491/1883494
(D). 1883446/1883449
(E). 1883453/1883456

answer is C.
Here's a slightly different way to look at it.

Notice that all 5 fractions are in the form (x-3)/x

Important: (x-3)/x = (x/x) - (3/x) = 1 - (3/x)

We can see that, in order to maximize 1 - (3/x), we need to minimize 3/x.
3/x is minimized when x (the denominator) is the largest value possible.

Among the answer choices, C has the greatest denominator, so 1883491/1883494 must have the biggest value.

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Brent
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