Which expression has the greatest value?

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

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.

Thanks & Regards
Vinni

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Source: Beat The GMAT — Problem Solving | Thu Jan 17, 2013 7:30 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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Tommy Wallach: GMAT Instructor; Posts: 451; Joined: Thu Jan 21, 2010 11:58 amFollowed by: 120 members; Location: New York City; Thanked: 188 times; GMAT Score:770

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!

-t

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ManhattanGMAT

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Fri Jan 18, 2013 3:11 am

Thank you

Regards
Vinni

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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