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## OG-17 (DIAGNOSTIC TEST)

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 1 member reply
acegmat29 Newbie | Next Rank: 10 Posts
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#### OG-17 (DIAGNOSTIC TEST)

Sat Apr 29, 2017 4:55 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
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

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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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.

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

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GMATGuruNY GMAT Instructor
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Sat Apr 29, 2017 5:46 am
Quote:
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.

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Mo2men Legendary Member
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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

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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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.

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ceilidh.erickson GMAT Instructor
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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: http://www.beatthegmat.com/og-13-24-t288366.html#765096

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