variable question

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arpitad: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sat Nov 05, 2011 10:01 amFollowed by: 1 member; Thanked: 1 times

by arpitad » Wed Jan 18, 2012 12:35 pm

Aaron will jog from home at x miles per hour and then walk back home by the same route at y mph. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

a. xt/y
b. x+t/xy
c. xyt/x+y
d. x+y+t/xy
e. y+t/x - t/y

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Source: Beat The GMAT — Problem Solving | Wed Jan 18, 2012 12:35 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Wed Jan 18, 2012 1:19 pm

very sensuous question

time jogged and time walked are 1/x and 1/y
combined time is t=1/x+1/y, t=(x+y)/xy, txy=x+y and distance is 1 (whole)=txy/(x+y)

[spoiler]why sensuous? Because ... [/spoiler]it could be also (x+y)/txy which ever GMAT likes in A-E

arpitad wrote:Aaron will jog from home at x miles per hour and then walk back home by the same route at y mph. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

a. xt/y
b. x+t/xy
c. xyt/x+y
d. x+y+t/xy
e. y+t/x - t/y

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Wed Jan 18, 2012 9:00 pm

We could also substitute numbers..

Say x=y=1mph.. therefore t=2hrs

now we spend 1 hr jogging.. sub x=y=1 and t=2..

Only C gives us 1hr.

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ArunangsuSahu: Master | Next Rank: 500 Posts; Posts: 382; Joined: Thu Mar 31, 2011 5:47 pm; Thanked: 15 times

by ArunangsuSahu » Wed Jan 18, 2012 11:39 pm

t=d*(x+y)/xy

d=xyt/x+y

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mj78ind: Master | Next Rank: 500 Posts; Posts: 265; Joined: Mon Dec 28, 2009 9:45 pmFollowed by: 2 members; Thanked: 26 times; GMAT Score:760

by mj78ind » Thu Jan 19, 2012 7:07 am

arpitad wrote:Aaron will jog from home at x miles per hour and then walk back home by the same route at y mph. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

a. xt/y
b. x+t/xy
c. xyt/x+y
d. x+y+t/xy
e. y+t/x - t/y

Let the distance to be traveled one way be "a", then
a/x + a/y = t (since a/x = time jogging, a/y = time walking)

Hence a = txy/(x+y)

Hence C

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Fri Jan 20, 2012 11:20 am

You could also pick numbers to help solve the problem in a different way than it was asked. if you set Distance = 20 and x = 5 and y = 2 you find that he jogs for 4 hours, walks for 10 hours for a total time spend of 14 hours.

So t = 14, x=5 and y = 2

Plug those numbers into the answer choices and only C xyt/x+y will give you the 20 as your distance from home.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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