reciprocal of 2 consecutive integers.....

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willbeatthegmat: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Sat Sep 20, 2008 5:48 am; Thanked: 5 times

by willbeatthegmat » Wed Feb 11, 2009 6:38 am

If the reciprocal of 2 consecutive integers r added to one another , wat is the sum in terms of greater integer x?

OA [spoiler](2x-1)/(x^2-x)[/spoiler]

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Source: Beat The GMAT — Problem Solving | Wed Feb 11, 2009 6:38 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Wed Feb 11, 2009 6:53 am

Well, you've got two consecutive integers, with x being the greatest. That means that x -1 is the other one. The reciprocals are 1/x and 1/(x - 1) respectively.
Add 1/x + 1/(x - 1) and you get (x + x - 1)/[x(x - 1)] = (2x - 1)/(x^2 - x).

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marcusking: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Feb 04, 2009 6:09 am; Location: Louisville, KY; Thanked: 8 times

by marcusking » Wed Feb 11, 2009 7:00 am

Great job danaj, that really helped me. one question though how did you get the numerator for (x + x - 1)/[x(x - 1)] ?

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dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Wed Feb 11, 2009 7:05 am

marcusking wrote:Great job danaj, that really helped me. one question though how did you get the numerator for (x + x - 1)/[x(x - 1)] ?

1/x + 1/(x - 1)

Once you give these a common denominator you come up with the following:

(x-1)/x(x-1) + x/x(x-1)

Now you can combine them since they have the same denominator

(x - 1 + x) / x(x-1)

(2x-1)/(x^2-x)

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willbeatthegmat: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Sat Sep 20, 2008 5:48 am; Thanked: 5 times

by willbeatthegmat » Wed Feb 11, 2009 7:10 am

too good...danaj..u made it look so simple....i think i just didn't understand d question...

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marcusking: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Feb 04, 2009 6:09 am; Location: Louisville, KY; Thanked: 8 times

by marcusking » Wed Feb 11, 2009 7:15 am

thanks dmateer25, once I wrote it out on paper it became very obvious.

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