OG-17 (DIAGNOSTIC TEST)

Expert replies

acegmat29: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Dec 11, 2016 10:57 am

by acegmat29 » Sat Apr 29, 2017 4:55 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

Like this post

Source: Beat The GMAT — Problem Solving | Sat Apr 29, 2017 4:55 am

GMAT/MBA Expert

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 » Sat Apr 29, 2017 5:06 am

acegmat29 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

As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach or via an ALGEBRAIC approach.

Here's an algebraic approach:

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

Like this post

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 » Sat Apr 29, 2017 5:46 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

Like this post

Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Sat Apr 29, 2017 8:00 am

Dear Experts,

What does the stem ask for? I understood it as if I will use the total time to find NEW distance form home? How can In interpret t correctly?

Thanks

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Apr 29, 2017 9:02 am

Hi acegmat29,

This question can be solved by TESTing VALUES. I'm going to give you a couple of hints so that you can attempt this question on your own...

1) Since this question has so many variables, you want to make sure that the variables are easy to work with. Try using X = 3 miles/hour and Y = 2 miles/hour and set each distance at 6 miles.
2) You'll have to do some simple calculations to figure out the time traveled in each direction and the total time (T), which you'll need to answer the question.
3) TEST those values in the answer choices; you're looking for answer that equals 6.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Wed May 03, 2017 11:45 am

Mo2men wrote:Dear Experts,

What does the stem ask for? I understood it as if I will use the total time to find NEW distance form home? How can In interpret t correctly?

Thanks

We can infer that the time t is defined as the total time spent jogging and walking. It's as if he knows exactly how long he wants to spend, and knows exactly the speeds at which he'll jog and walk. And based on that, he wants to determine how far he can go.

So there's no such thing as "new" or "old" distance. Imagine that before he leaves the house, he has a plan: "I want to go a total of t hours, and my speeds are x for jogging and y for walking. So that means I can jog a distance of d miles, then turn around and walk back the same d miles."

Did that help?

I posted a full algebraic solution here: https://www.beatthegmat.com/og-13-24-t288366.html#765096

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Apr 27, 2018 9:38 am

acegmat29 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

We can let d = the distance traveled when walking and jogging.

Thus, the jogging time is d/x and the walking time is d/y. Since the total time is t:

d/x + d/y = t

Multiply the entire equation by xy:

dy + dx = txy

d(y + x) = txy

d = txy/(y + x)

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review