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mstone: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Fri Jan 29, 2010 6:06 am

by mstone » Wed Feb 03, 2010 11:15 am

Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. 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

How would you solve this by picking numbers?

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Source: Beat The GMAT — Problem Solving | Wed Feb 03, 2010 11:15 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Feb 03, 2010 11:20 am

mstone wrote:Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. 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

How would you solve this by picking numbers?

say aaron walks a miles, aaron has to jog a miles too

time taken to walk a miles =a/x
time taken to run a miles = a/y

total time taken t = a(1/x+1/y)

a = t/(1/x+1/y) = xyt/(x+y)

C for me

Always borrow money from a pessimist, he doesn't expect to be paid back.

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mstone: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Fri Jan 29, 2010 6:06 am

by mstone » Wed Feb 03, 2010 11:26 am

C is correct. But, is there a way to solve this with picking numbers for x, y and t?

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Wed Feb 03, 2010 11:33 am

mstone wrote:Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. 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

How would you solve this by picking numbers?

since no restriction given take any value
let x=1
y=2
and dis=d
t=t1+t2
t1=d/x=d
t2=d/y=d/2
t=d+d/2
---->d=2t/3
now put x=1 and y=2 in option to get same value of d

option c is correct

however this q is much easy to solve algebraically than plugging no's

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Feb 03, 2010 11:34 am

mstone wrote:C is correct. But, is there a way to solve this with picking numbers for x, y and t?

Say Aaron goes for 5 Km jog in the morning at 5Km/hr and comes back at 2 Km/hr

now x = 5 y =2

he takes 1 hour to go and 2.5 hours to come back

t = 3.5 hours

Now you want to check which of the option equals 5

A) 5*3.5/2 does not equal 5 --- ruled out
B) 5+3.5/5*2 does not equal 5 -- ruled out
C) 5*3.5*2/7 = 5 ---- Hold
D) 5+2+3.5/5*2 does not equal 5 --- ruled out
E) 2 + 3.5/5 - 3.5/2 does not equal 5 --- ruled out

C is the only option

Always borrow money from a pessimist, he doesn't expect to be paid back.

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fibbonnaci: MBA Student; Posts: 403; Joined: Tue Dec 22, 2009 7:32 pmFollowed by: 22 members; Thanked: 98 times

by fibbonnaci » Wed Feb 03, 2010 11:34 am

you can solve in any way that strikes you first. choose the one that suits you. i chose the plugging in concept.

VIC approach:

Note the distance is same. a= say 10 km (a= distance from home to some point P)
x= 5 km/hr, y= 2 km/hr.
The total time he takes to cover 10 km for and back is 7 hrs= t

Now lets plug in these variables into the answer choices and see the one that gives the distance( ie. 10 km) as the answer.

a) xt / y => (5*7/2 = 35/2 = eliminated)

b) x + t / xy (57/10 = eliminated!)

c) xyt / x + y (70/7 = 10 = correct! my answer)

d) x+y+t / xy (14/10 = eliminated)

e) y + t / x - t/y (another junk answer. eliminated)

hope this helps!

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Osirus@VeritasPrep: GMAT Instructor; Posts: 1578; Joined: Thu May 28, 2009 8:02 amFollowed by: 34 members; Thanked: 128 times; GMAT Score:760

by Osirus@VeritasPrep » Wed Feb 03, 2010 11:34 am

This may sound like a dumb question but how did you guys get good at solving those problems algebraiclly? I'm in the same boat as mstone. I have to plug in with those questions, I have difficulty just solving it with algebra. How can I improve?

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fibbonnaci: MBA Student; Posts: 403; Joined: Tue Dec 22, 2009 7:32 pmFollowed by: 22 members; Thanked: 98 times

by fibbonnaci » Wed Feb 03, 2010 11:44 am

hey osirus, you are plugging in numbers so that it is easy to deal and comprehend. there is no worry until you are picking the rite numbers. you are by no way left behind with this method. Remember, on the D- Day, you need to hit the rigth answer in the shortest time possible.

While during practice if you do want to solve it algebraically, just resist the temptation of plugging in numbers. here the algebraic method is no different from plugging in numbers, just that now you have variables to look at. you might have to make few rearrangements to get the final view of the correct answer but at the end it all boils down to the same thing.

You also need to be strong with the basics to know how to approach in that method. you can try brushing up your basics and trying to attempt such questions algebraically. But i advise you not to try to figure it out in the test. Gmat is not bothered on the method. take your shortcuts but hit the rite answer should be your mantra (of course keep your basics solid!)

Hope this helps!

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Osirus@VeritasPrep: GMAT Instructor; Posts: 1578; Joined: Thu May 28, 2009 8:02 amFollowed by: 34 members; Thanked: 128 times; GMAT Score:760

by Osirus@VeritasPrep » Wed Feb 03, 2010 11:48 am

fibbonnaci wrote:hey osirus, you are plugging in numbers so that it is easy to deal and comprehend. there is no worry until you are picking the rite numbers. you are by no way left behind with this method. Remember, on the D- Day, you need to hit the rigth answer in the shortest time possible.

While during practice if you do want to solve it algebraically, just resist the temptation of plugging in numbers. here the algebraic method is no different from plugging in numbers, just that now you have variables to look at. you might have to make few rearrangements to get the final view of the correct answer but at the end it all boils down to the same thing.

Hope this helps!

Thanks for this. I really appreciate it. I think I will just practice. The problem I encountered on test day, was when I was given a problem where I had no clue how to even pick the numbers, so knowing how to just use straight algebra would have helped.

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Wed Feb 03, 2010 11:51 am

osirus0830 wrote:This may sound like a dumb question but how did you guys get good at solving those problems algebraiclly? I'm in the same boat as mstone. I have to plug in with those questions, I have difficulty just solving it with algebra. How can I improve?

i guess plugging no. is the smartest way to solve

dnt master the 100 best moves
master the only move u are best at
u will always find that u are a winner

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