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16 horses can haul a load of lumber in 24 minutes. 12 horses

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16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Feb 2013, 01:27
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16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.
[Reveal] Spoiler: OA

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Last edited by daviesj on 22 Feb 2013, 02:21, edited 1 time in total.
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Feb 2013, 02:18
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let work done by one horse in one min. be 1 unit
so total work = 16*24*1 = 384 units
quarter hour = 15 minutes
work done 12 horses in 15 min = 12*15*1 = 180 units
work left = 384 - 180 = 204 units
works done by 48 maules in 16 min = 384
works done by 12 maules in 1 min = 384x(12/48)x(1/16) = 6 units
so, work left after 15 minutes = 204 - 6 = 198 units

Hence, will take more than 15 minutes
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Feb 2013, 02:19
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daviesj wrote:
16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

1. Mules work more slowly than horses.
2. 48 mules can haul the same load of lumber in 16 minutes.

OA after some discussion.


16 horses can haul a load of lumber in 24 minutes.

So, 12 horses can haul the load in 32 minutes
and 24 horses can haul the load in 16 minutes.

So unless the mules are faster than the horses to a certain extent (in this instance they should be mules from Krypton), it is not possible to complete the work in 15 minutes.

1) Sufficient
2)The speed of the mules is given. The statements never contradict each other. So, we do not need to do any calculations to compare it with that of the horses. This statement is sufficient.

Answer is D.

EDIT:

AFTER seeing the OA, I realize that I could have misunderstood the question. If the question is asking for whether the work can be completed in an additional 15 minutes AFTER the initial 14 minutes, then I guess the working would be different.

12 horses can haul the load in 32 minutes.
So, in 14 minutes they would have hauled \frac{14}{32} of the load and the remaining is \frac{18}{32} of the load.

24 horses will be able to complete this remaining work in \frac{18}{32}*16 ie 9 minutes

1) If the mules are only slightly slower than the horses, the work can be finished in under 15 minutes. If the mules are abysmally slower than the horses, it will take more than 15 minutes. Insufficent.

2) The speed of the mules is given and hence whether the work can be finished in under 15 minutes or not can be calculated. Sufficient.

Answer is B.

However, IMHO the presence of this confusion alone makes this question a poor quality one.
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Feb 2013, 03:23
daviesj wrote:
OA is B.

Solution edited.. :)
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Feb 2013, 03:26
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Let the work being done by each horse in a givn period of time be called horsepower(HP). Now, given that 16 horses can do some work in 24 minutes. Thus, let this be 16*24 HP. Now, for 12 horses to the same work, we would require,

16*24 = 12*x

or x = 32 minutes.

Now, for 14 minutes, there are 12 horses and they do 12*14 HP work. So the remaining work is(32-14)*12 HP = 18*12 HP

Now, we don't know the relation between the rate of work of mules and that of the horses.

From F.S 1 , we know that mules work at a much smaller rate than the horses.

Scenario 1: Assume(against the option given) that the mules work at the same rate as that of the horses. Thus, 12 mules can be considered as 12 horses. Thus, the time taken for doing 18*12 HP of work :

18*12 = (12+12)*x

or x = 9 minutes.

Thus, as it is given that the rate of work of mules is smaller than that of horses, the time taken will definitely more than 9 minutes.

Assuming that mules work at half the rate of horses,

12 mules = 6 horses.

Thus, 18*12 = (12+6)*x

x = 12 minutes.

Let the rate of work of mules be 1/12th of the horse.

12 mules = 1 horse

Thus, 18*12 = (12+1)*x

x= 16.6 minutes.

Thus, F.S 1 not sufficient.

From F.S 2, you can get the relation between the rates of mule and horse. No need to solve. Sufficient.

B.
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Feb 2013, 03:28
(Question Source: VeritasPrep)

This is what VeritasPrep has to say about OA.

The correct response is (B).
The answer is always “yes.” Let’s consider how “big” this lumber-haul job is first. To load the lumber, it took 16 horses x 24 minutes = 384 horse-minutes of work. If mules do it, it takes 48 mules x 16 minutes = 768 mule-minutes of work. Notice that 384 is half of 768! That means that one horse can do the work of two mules.

In 14 minutes, 12 horses will do 12 x 14 = 168 horse-minutes of work. That leaves 384 – 168 = 216 horse-minutes of work left to do.

To complete the job, we have 12 horses and 12 mules. The 12 mules do the work of 6 horses, so 12 horses and 12 mules will do the work at the same rate 18 horses would:

18 horses x ___ minutes =216 horse-minutes of work

216/18 = 12 minutes to complete the remaining work.

If you chose (A), this information is not sufficient. Without knowing how much slower mules work than horses, we cannot answer the question.

If you chose (C), the second statement alone is sufficient.

If you chose (D), the first statement doesn’t tell us anything about the mule’s work-rate.

If you chose (E), the second statement is sufficient because we are given the rates of both animals. You may want to get more practice on challenging work-and-rate word problems to review this difficult concept in more detail.
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Feb 2013, 03:30
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daviesj wrote:
16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.


Total work = 16*24 = 384 horse minutes;

Work done by 12 horses in 14 minutes = 12*14 = 168 horse minutes.

Work left = 384 - 168 = 216 horse minutes.

Work done by 12 horses in 15 minutes = 12*15 = 180 horse minutes (work done by 12 horses in quarter-hour).

From (1) we know that 12 mules works slower than 12 horses, so in 15 minutes they can do less than 180 horse minutes work.

Hence, together in 15 minutes they can do less than 360 horse minutes work.

So, in 15 minutes together they can do less as well as more that the amount of the work that is left (216 horse minutes).

That's why (1) is not sufficient.

Hope it's clear.
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Feb 2013, 19:55
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daviesj wrote:
16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.


In my last week's post, I have discussed the basics of how to handle such work questions.
http://www.veritasprep.com/blog/2013/02 ... variation/

16 horses ........ 24 mins .......... 1 work
12 horses ......... 14 mins .......... ? work

Work done = 1*(14/24)*(12/16) = 7/16 work

Leftover work = 9/16

(1) Mules work more slowly than horses.

Say, consider when mules work almost as efficiently as horses. 12 mules is equivalent to 12 horses in that case.

16 horses ........ 24 mins .......... 1 work
24 horses ......... ?? mins .......... 9/16 work

Time taken = 24*(16/24)*(9/16) = 9 mins
If the mules work slower, time taken will be more till the point when mules work so slowly that they do no work. Since 12 horses take 2 mins to do 1/16th work, they will take 18 mins to complete 9/16 work. So depending on how fast/slow the mules are, time taken could be less/more than 15 mins. Not sufficient

(2) 48 mules can haul the same load of lumber in 16 minutes.
We now know exactly how fast/slow the mules are. So this must be sufficient to say whether time taken was less or more than 15 mins. Sufficient

Answer (B)
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 03 Apr 2014, 03:02
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 22 Jun 2014, 21:17
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I am not sure about the above clarification, please can you explain about the above ratio proportion calculation.


Did you check the link I gave above? It discusses this method. You will understand the calculations only if you first go through that post.
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16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 25 Jun 2014, 04:57
VeritasPrepKarishma wrote:
daviesj wrote:
16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.


In my last week's post, I have discussed the basics of how to handle such work questions.
http://www.veritasprep.com/blog/2013/02 ... variation/

16 horses ........ 24 mins .......... 1 work
12 horses ......... 14 mins .......... ? work

Work done = 1*(14/24)*(12/16) = 7/16 work

Leftover work = 9/16

(1) Mules work more slowly than horses.

Say, consider when mules work almost as efficiently as horses. 12 mules is equivalent to 12 horses in that case.

16 horses ........ 24 mins .......... 1 work
24 horses ......... ?? mins .......... 9/16 work

Time taken = 24*(16/24)*(9/16) = 9 mins
If the mules work slower, time taken will be more till the point when mules work so slowly that they do no work. Since 12 horses take 2 mins to do 1/16th work, they will take 18 mins to complete 9/16 work. So depending on how fast/slow the mules are, time taken could be less/more than 15 mins. Not sufficient

(2) 48 mules can haul the same load of lumber in 16 minutes.
We now know exactly how fast/slow the mules are. So this must be sufficient to say whether time taken was less or more than 15 mins. Sufficient

Answer (B)


sorry for asking dumb question , i have read the blog but i always get confuse in the realtion thing, for e.g in this case ( how is time taken realted to horses ? it is inversly propotional i.e if more horses are there time taken will be less..............but how is time taken related to work to be done ( do we say if work to be done is less the time taken would be less ? so it is directly propotional but here we have taken work to be done as inversly proptional .
i always get confused in this. please help :oops:
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses [#permalink] New post 25 Jun 2014, 21:04
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tyagigar wrote:
VeritasPrepKarishma wrote:
daviesj wrote:
16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.


In my last week's post, I have discussed the basics of how to handle such work questions.
http://www.veritasprep.com/blog/2013/02 ... variation/

16 horses ........ 24 mins .......... 1 work
12 horses ......... 14 mins .......... ? work

Work done = 1*(14/24)*(12/16) = 7/16 work

Leftover work = 9/16

(1) Mules work more slowly than horses.

Say, consider when mules work almost as efficiently as horses. 12 mules is equivalent to 12 horses in that case.

16 horses ........ 24 mins .......... 1 work
24 horses ......... ?? mins .......... 9/16 work

Time taken = 24*(16/24)*(9/16) = 9 mins
If the mules work slower, time taken will be more till the point when mules work so slowly that they do no work. Since 12 horses take 2 mins to do 1/16th work, they will take 18 mins to complete 9/16 work. So depending on how fast/slow the mules are, time taken could be less/more than 15 mins. Not sufficient

(2) 48 mules can haul the same load of lumber in 16 minutes.
We now know exactly how fast/slow the mules are. So this must be sufficient to say whether time taken was less or more than 15 mins. Sufficient

Answer (B)


sorry for asking dumb question , i have read the blog but i always get confuse in the realtion thing, for e.g in this case ( how is time taken realted to horses ? it is inversly propotional i.e if more horses are there time taken will be less..............but how is time taken related to work to be done ( do we say if work to be done is less the time taken would be less ? so it is directly propotional but here we have taken work to be done as inversly proptional .
i always get confused in this. please help :oops:


To make it easier for yourself, you can ignore proportionality. Think in terms of logic.
You need to find the time taken. Your number of horses has increased from 16 to 24. So now you will need less time to finish the same work. So you multiply your old time with a fraction less than 1 which is 16/24.
Also, the work required to be done has decreased. From 1 to 9/16 (less than 1). So time required to complete the work would be less. This means we will multiply with a fraction less than 1 to make the time less. So you multiply by (9/16)/1 = 9/16.

Note that since horses required and time taken are inversely proportion, you multiplied by 16/24 (first line/second line). Since work to be done and time taken is directly proportional, we multiplied by (9/16)/1 (second line/first line). You will obviously not go wrong if you use proportionality but you might want to just stick to logic to keep it simple.
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses   [#permalink] 25 Jun 2014, 21:04
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