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Sam leaves Town X at 9 am and drives due north at 50 mph towards Town

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Sam leaves Town X at 9 am and drives due north at 50 mph towards Town [#permalink]

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Sam leaves Town X at 9 am and drives due north at 50 mph towards Town Y. An hour later, Julie leaves Town X and drives due south toward Town Z. At what time, are the two cars 90 miles apart?

(1) The distance from Town Y to Town Z is 210 miles.
(2) Sam average speed is 12% slower than Julie's.
[Reveal] Spoiler: OA

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Sam leaves Town X at 9 am and drives due north at 50 mph towards Town [#permalink]

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New post 04 May 2017, 05:58
(1) The distance from Town Y to Town Z is 210 miles.
Since we need to find out the position of Sam and Julie,
it is not enough to know the distance between the towns,
in order to calculate at what time the cars are 90 miles apart(Insufficient)

(2) Sam average speed is 12% slower than Julie's.
Since we know that Sam is 12% slower than Julie, we can find out the speed at which Julie travels.
In the one hour Sam leaves he travels 50 miles towards Town X. We can find out
,using the relative speed, how much more time it will take them to travel exactly 90 miles apart (Sufficient)(Option B)

Correcting solution!
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Last edited by pushpitkc on 04 May 2017, 06:54, edited 1 time in total.

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Re: Sam leaves Town X at 9 am and drives due north at 50 mph towards Town [#permalink]

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Bunuel wrote:
Sam leaves Town X at 9 am and drives due north at 50 mph towards Town Y. An hour later, Julie leaves Town X and drives due south toward Town Z. At what time, are the two cars 90 miles apart?

(1) The distance from Town Y to Town Z is 210 miles.
(2) Sam average speed is 12% slower than Julie's.


Nice question, Bunuel!

This is an expanding gap question, with both people leaving Town X and traveling in OPPOSITE DIRECTIONS.

Target question: At what time, are the two cars 90 miles apart?

Given: Sam leaves Town X at 9 am and drives due north at 50 mph towards Town Y. An hour later, Julie leaves Town X and drives due south toward Town Z.

Statement 1: The distance from Town Y to Town Z is 210 miles.
This information is irrelevant. There need not even be a Town Y and a Town Z.
All we need to know is that the two people are heading in opposite directions.
What we DO need is Julie's speed
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Sam average speed is 12% slower than Julie's
In other words, Sam's speed is 88% that of Julie's speed
Sam's speed is 50 miles per hour, so we can write: 50 = 88% of Julie's speed
IMPORTANT: We COULD use this information to calculate Julie's speed. Once we know each person's speed, we can determine how long it will take for the GAP to increase to 90 miles, which means we COULD answer the target question with certainty. Of course, we won't actually perform all of those tedious calculations, since we need only determine whether we have enough information to answer the target question.
So, statement 2 is SUFFICIENT

Answer:
[Reveal] Spoiler:
B


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Re: Sam leaves Town X at 9 am and drives due north at 50 mph towards Town [#permalink]

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GMATPrepNow wrote:
Bunuel wrote:
Sam leaves Town X at 9 am and drives due north at 50 mph towards Town Y. An hour later, Julie leaves Town X and drives due south toward Town Z. At what time, are the two cars 90 miles apart?

(1) The distance from Town Y to Town Z is 210 miles.
(2) Sam average speed is 12% slower than Julie's.


Nice question, Bunuel!


Hello Brent,

I may sound silly but this is my doubt; Are we safe to assume that either Sam or Julie, may be even both, did not make any stops or vary their speeds once they departed from their respective places? I couldn't see the word "Constant Speed" anywhere and the word "Average Speed" added fuel to my confusion.

Cheers!

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Re: Sam leaves Town X at 9 am and drives due north at 50 mph towards Town [#permalink]

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Diwakar003 wrote:

Hello Brent,

I may sound silly but this is my doubt; Are we safe to assume that either Sam or Julie, may be even both, did not make any stops or vary their speeds once they departed from their respective places? I couldn't see the word "Constant Speed" anywhere and the word "Average Speed" added fuel to my confusion.



To avoid ambiguity, it would probably be useful to add "constant."

Cheers,
Brent
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Re: Sam leaves Town X at 9 am and drives due north at 50 mph towards Town [#permalink]

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New post 06 May 2017, 18:05
Bunuel wrote:
Sam leaves Town X at 9 am and drives due north at 50 mph towards Town Y. An hour later, Julie leaves Town X and drives due south toward Town Z. At what time, are the two cars 90 miles apart?

(1) The distance from Town Y to Town Z is 210 miles.
(2) Sam average speed is 12% slower than Julie's.


We are given that Sam leaves Town X at 9 a.m. and drives at a rate of 50 mph toward Town Y, and that Julie leaves Town X and drives toward Town Z. We must determine at what time the two cars are 90 miles apart.

We can use the following formula:

distance of Sam + distance of Julie = 90

Statement One Alone:

The distance from Town Y to Town Z is 210 miles.

Knowing the distance from Town Y to Town Z does not help us determine at what time the two cars are 90 miles apart. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

Sam’s average speed is 12% slower than Julie's.

Since Sam’s speed is 12% slower than Julie’s, we can let Julie's speed = r and create the following equation:

0.88r = 50

r = 50/0.88

Also, since Sam left at 9 a.m. and Julie left an hour later, we can let Julie’s time = t and Sam’s time = t + 1. Thus:

distance of Sam + distance of Julie = 90

50(t + 1) + 50/0.88(t) = 90

Since we see that we have enough information to determine t, statement two alone is sufficient to answer the question.

Answer: B
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Re: Sam leaves Town X at 9 am and drives due north at 50 mph towards Town [#permalink]

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New post 16 Oct 2017, 12:52
We should always assume the cities are 90+ miles apart in case like this? I used statement 1 to be sure the distance would reach 90 eventually.

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Re: Sam leaves Town X at 9 am and drives due north at 50 mph towards Town   [#permalink] 16 Oct 2017, 12:52
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Sam leaves Town X at 9 am and drives due north at 50 mph towards Town

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