BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Aron

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 510
Joined: Thu Aug 07, 2014 2:24 am
Thanked: 3 times
Followed by:5 members

Aron

by j_shreyans » Sat Apr 04, 2015 9:51 pm
Aron 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 Aron 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

OAC
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Apr 05, 2015 2:50 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)
Let the distance = 10 miles.
Let x = 5 miles per hour and y = 2 miles per hour.
Time for Aaron to jog 10 miles at a rate of 5 miles per hour = d/r = 10/5 = 2 hours.
Time for Aaron to walk 10 miles at a rate of 2 miles per hour = d/r = 10/2 = 5 hours.
t = total time spent jogging and walking = 2+5 = 7 hours.

The question stem ask for the distance that Aaron jogs (10 miles).
This is our target.
Now plug x=5, y=2 and t=7 into the answer choices to see which yields our target of 7.
Only C works:
(xyt)/(x+y) = (5*2*7)/(5+2) = 10.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 05, 2015 7:17 am
j_shreyans wrote:Aron 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 Aron 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

OAC
As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach (as Mitch has done) or via an ALGEBRAIC approach.
Typically, when the answer choices look complex (as they do here), I find the INPUT-OUTPUT approach easier.
However, the algebraic approach isn't too bad.

Let's let d = the number of miles (distance) that Aaron jogs.
This means that d also = the distance that Aaron walks.

Let's start with a WORD EQUATION:
total time = (time spent jogging) + (time spent walking)
In other words: t = (time spent jogging) + (time spent walking)
Since time = distance/speed, we can write: t = d/x + d/y [our goal is to solve this equation for d]
The least common multiple of x and y is xy, so we can eliminate the fractions by multiplying both sides by xy. When we do so, we get...
txy = dy + dx
Factor right side to get: txy = d(x + y)
Divide both sides by (x+y) to get: txy/(x+y) = d
So, the correct answer is C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1