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# GMAT Diagnostic Test Question 25

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Re: GMAT Diagnostic Test Question 25 [#permalink]  01 Oct 2010, 15:24
kseel wrote:
Maybe I'm just misreading this, but something seems off to me.

The first trip takes x amount of time at s speed for both buses from opposite directions. If P is not city M - then why would they ever meet outside the city on one of the buses sides? It seems like the wording means they are going to the city N and stopping.

Same with the second part, how will they meet away from city N if they are coming from opposite directions and not passing through?

M >-----------------N----------------X(second bus home)

given the wording, it seems to me P lies somewhere in between M and N or N and X. Am I misreading it?

Otherwise, I understand the math. Just wondering why they would ever meet outside the city.
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Re: GMAT Diagnostic Test Question 25 [#permalink]  09 Oct 2010, 09:43
I solved it in the following way:

Assumed distance between M and N to be = 2D miles
Distance travelled by each bus = D miles
Time taken to cover the distance = 2 hours
Speed of each bus = D/2 miles per hour

Since the meeting point has now moved 24 miles away from point P, hence Distance travelled by one bus would be (D+24) miles and the Distance travelled by the other bus would be (D-24) miles.
The time difference between the two buses is one hour (24+36).
Time = Distance/Speed
[(D+24)/(D/2)] - [(D-24)/(D/2)] = 1
Solving the equation gives D = 96 miles

The distance between M and N is thus 2D = 192 miles.
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Re: GMAT Diagnostic Test Question 25 [#permalink]  17 Oct 2010, 10:04
tingle15 wrote:
I solved it in the following way:

Assumed distance between M and N to be = 2D miles
Distance travelled by each bus = D miles
Time taken to cover the distance = 2 hours
Speed of each bus = D/2 miles per hour

Since the meeting point has now moved 24 miles away from point P, hence Distance travelled by one bus would be (D+24) miles and the Distance travelled by the other bus would be (D-24) miles.
The time difference between the two buses is one hour (24+36).
Time = Distance/Speed
[(D+24)/(D/2)] - [(D-24)/(D/2)] = 1
Solving the equation gives D = 96 miles

The distance between M and N is thus 2D = 192 miles.

This problem has driven me crazy for more than 1 hr now, I am trying to find what is the issue in my understanding..

Worst, I am getting 3 diff answers..
I assume total dist i.e. dist bet cities = D. Total time = 240 min. Constant speed for both buses = D/240.

RTD Chart

T R D
240 D/240 D
156 (i.e.120+36) D/240 (D/2) + 24 For bus leaving early, no need to care abt other bus
96 (i.e. 120-24) D/240 (D/2) - 24 For bus leaving late, no need to care abt other bus

1st Linear equation for D (bus leaving early):
(156D)/240 = (D/2) + 24=>D=160
2nd Linear equation for D (bus leaving late):
(96D)/240 = (D/2) - 24=>D=240
3rd case, same as tingle15 above:
( (D/2) + 24 ) /(D/240) - ( (D/2) - 24 ) /(D/240) = 156 - 96=>D=192 (OE).

Also, since speed is constant, even using simple direct proportion, we get D=160:
36->24
240->D
=>D=160

Can Bunuel/somebody pls explain the mistake here/if the no. 24 in the question should be changed..Worst, I hope there is no calculation mistake on my part..

Thanks.
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Re: GMAT Diagnostic Test Question 25 [#permalink]  09 Dec 2010, 13:53
Sorry to dig out this question... I tried to simplify it to the greatest degree.
To me, since the other bus has 1 hour advantage and travels 24 miles farther, alludes that 1 hour of trip=24 miles. Since they traveled 4 hours total, it would equal 96 miles. I do understand above explanations, but just wanted to expose the pitfall some may have fell into.
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Re: GMAT Diagnostic Test Question 25 [#permalink]  09 May 2011, 12:20
Can someone help me with my flaw in logic please?

24minutes /60 minutes = .4 hours
36 minutes / 60 min = .6 hours

NOT .5!!

So, bus one (we'll call M) drove 1.6 hours to get to p-24
Bus two (bus N) drove 24 minutes + 36 minutes + the 1.6 hours that M was driving = 2.6 hours.

1.6*M = P - 24
2.6*N = P + 24
So, 2N = P and 2M = P...

2.6N - P - 24 = 2N - P yields: .6N = 24 > N = 40 mph

1.6M - P + 24 = 2M - P yields: 24 = .4M > M = 60 mph

2h * 60 mph = 120 miles (bus M)
2h * 40mph = 80 miles (bus N)

= 200 miles?

The biggest issue I am having is how they are getting 1.5, 2.5, etc. 36 minutes / 60 minutes = .6 hours not .5 HOURS!

Thanks!
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Re: GMAT Diagnostic Test Question 25 [#permalink]  09 May 2011, 17:54
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.

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)
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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.
Re: GMAT Diagnostic Test Question 25   [#permalink] 18 Jan 2012, 08:32
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