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If it took a bus 4 hours to get from town A to town B, what

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If it took a bus 4 hours to get from town A to town B, what [#permalink]

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06 Oct 2010, 12:48
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If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

(1) In the first 2 hours the bus covered 100 miles.
(2) The average speed of the bus for the first half of the distance was twice its average speed for the second half.

OLD VERSION OF THIS QUESTION:

If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

(1) In the first 2 hours the bus covered 100 miles.
(2) The average speed of the bus for the first half of the distance was twice its speed for the second half.

(C) 2008 GMAT Club - m16#8

I am always really struggling with these... I can easily determine (at least something...) that it has to be C,E - but I usually have to guess then! Any help greatly appreciated! THANKS
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jul 2013, 00:05, edited 1 time in total.
Edited the question.

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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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06 Oct 2010, 13:56
AndreG wrote:
If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles.
2. The average speed of the bus for the first half of the distance was twice its speed for the second half.

(C) 2008 GMAT Club - m16#8

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

I am always really struggling with these... I can easily determine (at least something...) that it has to be C,E - but I usually have to guess then! Any help greatly appreciated! THANKS

To know the average speed, we need total distance & total time. We know time=4h, so just need distance

(1) We only know 100miles covered in first 2 hours. Don't know about rest of the distance covered. Insufficient

(2) Avg speed was halfed in the second half. But we dont know what it actually was, so can't put a number to it. Insufficient

(1+2) Avg speed in first 2hours 50mph, distance is 100miles. Lets say distance covered in total is x.
For x/2 it went for speed s ... time taken = (x/2s)
For x/2 it went for speed s/2 ... time taken = (x/s)
(x/s) + (x/2s) = 4hrs ... (x/2s) = 4/3 hrs
Which means for 4/3 hours it went for speed s and then for the rest of the time the speed doubled.
So consider the first 2hours, (4/3)*s + (2/3)*(s/2) = 100 ... s=300/5=60
We know, we can know s/2 ... we can find out total distance covered = 60*(4/3) + 30*(8/3) = 160
So we can find out average speed = 160/4 = 40miles/hour
Sufficient

Where did u get E from ?
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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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06 Oct 2010, 14:03
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shrouded1 wrote:
AndreG wrote:
If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles.
2. The average speed of the bus for the first half of the distance was twice its speed for the second half.

(C) 2008 GMAT Club - m16#8

I am always really struggling with these... I can easily determine (at least something...) that it has to be C,E - but I usually have to guess then! Any help greatly appreciated! THANKS

To know the average speed, we need total distance & total time. We know time=4h, so just need distance

(1) We only know 100miles covered in first 2 hours. Don't know about rest of the distance covered. Insufficient

(2) Avg speed was halfed in the second half. But we dont know what it actually was, so can't put a number to it. Insufficient

(1+2) Avg speed in first 2hours 50mph, distance is 100miles. Lets say distance covered in total is x.
For x/2 it went for speed s ... time taken = (x/2s)
For x/2 it went for speed s/2 ... time taken = (x/s)
(x/s) + (x/2s) = 4hrs ... (x/2s) = 4/3 hrs
Which means for 4/3 hours it went for speed s and then for the rest of the time the speed doubled.
So consider the first 2hours, (4/3)*s + (2/3)*(s/2) = 100 ... s=300/5=60
We know, we can know s/2 ... we can find out total distance covered = 60*(4/3) + 30*(8/3) = 160
So we can find out average speed = 160/4 = 40miles/hour
Sufficient

Where did u get E from ?

I can justify E:

If (2) were: The constant speed of the bus for the first half of the distance was twice its constant speed for the second half.

Then for (1)+(2) we would have: $$s_1*\frac{4}{3}+\frac{s_1}{2}*(2-\frac{4}{3})=100$$ --> we can find $$s_1$$ so we can find $$d$$ ($$d=2*s_1*\frac{4}{3}$$). But as it is we don't know whether the average speed after first $$\frac{4}{3}$$ hours till 2 hours from the start was $$\frac{s_1}{2}$$ or less or more, we just know that the average speed from first $$\frac{4}{3}$$ hours till 4 hours from the start was $$\frac{s_1}{2}$$.

Hope it's clear.
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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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06 Oct 2010, 14:06
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Tricky !

But I think the Q should probably be re-phrased as :
The average speed of the bus for the first half of the distance was twice its average speed for the second half.

Makes it sound as if the speed in the second half was constant (since it is refered to simply as twice the speed in the second half)
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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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06 Oct 2010, 18:04
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AndreG wrote:
If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles.
2. The average speed of the bus for the first half of the distance was twice its speed for the second half.

I thought it was C, and then I realized why it's E. I bolded the reason above. I read it too quickly and thought that (2) said "for the first half of the trip", thinking it covered 100 miles in 2 hours in the first half of the trip, which is 50 mph, and then it went 25 mph for the second half of the trip... so C. But it's actually the first half of the total distance, which is impossible to figure out. It could have gone only 150 miles. It could have gone 300. We don't know. So it's E.

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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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07 Oct 2010, 01:00
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TehJay wrote:
AndreG wrote:
If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles.
2. The average speed of the bus for the first half of the distance was twice its speed for the second half.

I thought it was C, and then I realized why it's E. I bolded the reason above. I read it too quickly and thought that (2) said "for the first half of the trip", thinking it covered 100 miles in 2 hours in the first half of the trip, which is 50 mph, and then it went 25 mph for the second half of the trip... so C. But it's actually the first half of the total distance, which is impossible to figure out. It could have gone only 150 miles. It could have gone 300. We don't know. So it's E.

Thats not true, as you can see above.
The only critical assumption is that the speed is not constant in the second half of the distance. If you assume that then you can still solve this and get (c)
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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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08 Oct 2010, 11:15
shrouded1 wrote:
TehJay wrote:
AndreG wrote:
If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

1. In the first 2 hours the bus covered 100 miles.
2. The average speed of the bus for the first half of the distance was twice its speed for the second half.

I thought it was C, and then I realized why it's E. I bolded the reason above. I read it too quickly and thought that (2) said "for the first half of the trip", thinking it covered 100 miles in 2 hours in the first half of the trip, which is 50 mph, and then it went 25 mph for the second half of the trip... so C. But it's actually the first half of the total distance, which is impossible to figure out. It could have gone only 150 miles. It could have gone 300. We don't know. So it's E.

Thats not true, as you can see above.
The only critical assumption is that the speed is not constant in the second half of the distance. If you assume that then you can still solve this and get (c)

That's true... here assumption is constant speed
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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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08 Oct 2010, 11:46
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According to my calculation B is the ans..
from option 2.
take time as t1--for ist half...t2 for 2nd half....we know t1+t2 =4..
speed s1= 2s for 1st half ..., s2=s for 2nd half...
so s1/s2 =2= t2/t1..
so t1= 4*1/3 and t2= 4*2/3
hence 2s*4/3 + s*8/3 =100..
we can calculate s...hence we get avf speed for 1st ad 2nd half..
so avg speed too..

plz suggest

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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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08 Oct 2010, 11:49
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sudhanshushankerjha wrote:
According to my calculation B is the ans..
from option 2.
take time as t1--for ist half...t2 for 2nd half....we know t1+t2 =4..
speed s1= 2s for 1st half ..., s2=s for 2nd half...
so s1/s2 =2= t2/t1..
so t1= 4*1/3 and t2= 4*2/3
hence 2s*4/3 + s*8/3 =100..
we can calculate s...hence we get avf speed for 1st ad 2nd half..
so avg speed too..

plz suggest

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Re: GMAT CLUB TEST m16#8 - Speed-time-distance [#permalink]

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08 Oct 2010, 12:01
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Yaa got..ans will be E only...Thanx

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Re: If it took a bus 4 hours to get from town A to town B, what [#permalink]

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10 Dec 2012, 20:18
am i correct in assuming that total distance d will be less than 200 miles? if after 4/3 hours we've reached the midpoint and STILL have not reached 100 miles (that is only reached at the 2 hour point), ergo 100 < d < 200.
Now, we can definitively say that the bus' average speed for the first 4/3 hours (s1) was less than 75 mph, otherwise it would have hit 100 at the 4/3 hour point and not the 2 hour point. We can also say that s1 must have been more than 37.5 mph b/c, if it was any less, the speed required to make up the 100 miles in the remaining 2/3 of an hour would be netted out over the 8/3 to be more than .5 s1. So unlike the above commenter said before, there are very clear limits to s1 and d, although not enough to definitively answer the question.

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Re: If it took a bus 4 hours to get from town A to town B, what   [#permalink] 10 Dec 2012, 20:18
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