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# GMAT Diagnostic Test Question 25

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Re: GMAT Diagnostic Test Question 25 [#permalink]  10 May 2011, 03:30
itsagulati wrote:
Sure.

Let's say 12p.m. is the scheduled departure...

Bus M was scheduled to leave at 12, but was delayed 24 min (.4 hours...24min / 60min). So, this left at 12:24 p.m.

Bus N was scheduled to leave at 12 p.m. as well, but left 36 minutes early at 11:24 a.m.
Bus N takes at LEAST 2 hours to get to point P. Thus, it cannot arrive before 1:24 p.m., however, we know that bus N travels farther since we are going past point P (or you can look at it as M can at best reach half way to point P since it has only been going for an hour at 1:24 p.m.). Thus, you go to 2 p.m. which is the original area they would have met at point P, but bus M is not to point P since delayed (it is 24 miles short) and bus N has been going longer than 2 hours which is how it gets to be P+24.lost you here

Let me know if that helps or further confuses..i realize that was incredibly wordy.

Also, in case that equation wasn't clear...
Bus M only gets to drive 1.6 hours (delayed 24 min, 24 min / 60 = .4, 2-.4 = 1.6 hours). And 36 min early departure + 24 min. the delay that bus N didn't experience = 1 hour extra that bus N gets to drive over bus M. Thus:

Bus M: 1.6x = P - 24 (24 miles shorter than point P) and...
Bus N: 2.6x = p + 24 (went 24 miles past point P in the 1 hour extra it had compared to bus M)

M leaves @ 12:24PM
N leaves @ 11:24AM

As you rightly said: N travels P/2 distance until 12:24PM, when M starts its journey.

Let's try to understand this using a line. Let the two extreme points be X and Y.

I. X(M)---------------------------P---------------------------(N)Y @11:24AM, where XP=YP

II. X(M)---------------------------P------------(N)R--------------Y @12:24PM, because N left early and covered half of YP; PR=RY=1/4*XY

III. X--------------------(M)(N)T-------P-------------R-------------Y @Some time after 1:24PM. The important thing to note here is that the point, let's call it T, where "MN" have met is again midway from X and R in the immediately previous line(II). Why? Because M and N travels with same constant speed.

PR+PT=XT [:Note: T is midway from X and R]
PR+24=XT
PR=1/2*PY=1/2*1/2*(XY) [:note: P is midway from X and Y]
XT=PR+24=1/4*XY+24 --------------------------1

Also,
XT=XY-TY=XY-(PY+PT)=XY-(1/2*XY+24)=1/2*XY-24---------------------2

Equate 1 and 2:
1/4*XY + 24 = 1/2*XY - 24
1/4*XY=48
XY=48*4=192
******************************************************

See it another way;
XT= 3/8*XY
M travels XY in 4 hours
M would travel 3/8*XY in (3/8)*4=1.5 hours
Thus, M and N meet 1.5 hours after M starts its journey i.e. @1:54PM
********************************************************

Please let me know if something is unclear.
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Re: GMAT Diagnostic Test Question 25 [#permalink]  10 May 2011, 04:12
Its a blinder.In the second journey, 1 bus should be ahead of the other as it has 1 hr lead.More so, the speeds have not changed too.
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Re: GMAT Diagnostic Test Question 25 [#permalink]  03 Dec 2011, 13:05
this was tricky....moreover it dosent look like a 600 level ques......Should have been 700+...

Or may be i am confused because of the wordings....
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Re: GMAT Diagnostic Test Question 25 [#permalink]  18 Jan 2012, 08:32
Great question, but I'd agree: There's no way this would be a 600-level-question. 700 sounds about right.
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Re: GMAT Diagnostic Test Question 25 [#permalink]  15 Jun 2013, 19:17
I tried something else and it doesn't add up.

Expressed in minutes, on day one, the distance to P is 120*s (120mins=2 hrs, s=speed)

Then for bus 1 on the second day, distance covered is (120-24)*s =96s

So shouldn't distance to P (120*s) minus 24 miles equal 96s? As in 120s-24=96s, which would calculate to s=1mile/min=60mph
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Re: GMAT Diagnostic Test Question 25 [#permalink]  16 Jun 2013, 01:27
Dixon wrote:
I tried something else and it doesn't add up.

Expressed in minutes, on day one, the distance to P is 120*s (120mins=2 hrs, s=speed)

Then for bus 1 on the second day, distance covered is (120-24)*s =96s

So shouldn't distance to P (120*s) minus 24 miles equal 96s? As in 120s-24=96s, which would calculate to s=1mile/min=60mph

The point is that we cannot say that bus 1 traveled 96 minutes on the second day.

BELOW IS REVISED VERSION OF THIS QUESTION:

A bus leaves city M and travels to city N at a constant speed, at the same time another bus leaves city N and travels to city M at the same constant speed. After driving for 2 hours they meet at point P. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

A. 48
B. 72
C. 96
D. 120
E. 192

Say the distance between the cities is d miles.

Since both buses travel at the same constant speed and leave the cities at the same time then they meet at the halfway, so the first meeting point P, is \frac{d}{2} miles away from M (and N).

Next, since the buses meet in 2 hours then the total time to cover d miles for each bus is 4 hours.

Now, on the second day one bus traveled alone for 1 hour (36min +24min), hence covered 0.25d miles, and 0.75d miles is left to cover.

The buses meet again at the halfway of 0.75d, which is 24 miles from \frac{d}{2}:

Hence, \frac{d}{2}-24=\frac{0.75d}{2} --> d=192 miles.

Also discussed here: a-bus-from-city-m-is-traveling-to-city-n-at-a-constant-speed-86478.html

Hope it helps.
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Re: GMAT Diagnostic Test Question 25   [#permalink] 16 Jun 2013, 01:27
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