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

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Math Expert
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16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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26 Jan 2015, 05:41
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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.

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Math Expert
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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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26 Jan 2015, 08:24
ans B.. statement 2 is sufficient
statement 1 .. if mules work as efficiently as horses, it will take atleast 9 min so depending on the % of being slow would give ans >15min or <15 min..
statement gives speed of mules too sufficient
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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26 Jan 2015, 12:29
Answer D (Not sure if that's right)
The problem tells us that 16 horses need 24 min's to do the job - thus one horse would need 16x24 min's to do the same job alone. 12 horses would need (16x24)/12 = 32 minutes to do the full job. A quarter of an hour is 15 minutes. After 14 minutes 12 mules join the horses. If the mules work faster than the horses it might be possible that they could finish the job in fewer than 15 minutes - but if they work at an equal or slower rate it is not possible (24 mules/horses with the same speed would need 32/2=16 minutes).
Statement (1) is sufficient as it tells us that the mules work at a slower rate.
Statement (2) tells us that the 12 mules need (48x16)/12 = 64 minutes to do the full job. As 64 minutes > 24 minutes the work rate of the mules is slower than that of the horses. Sufficient

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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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26 Jan 2015, 13:14
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we know that 16*(1/x)=1/24
so -> for 1 horse its 384(=x) minutes.
for 12 horses its 12/384=1/32 -> 32 minutes.
after 14 minutes they still ned 18 minutes to finish the job.
we add some mule power to finish this job faster, but we need to determine if we can save 4 minutes so that the time(rest)<15 minutes.

(1) -> mules are slower, but are they just slighty slower, then we COULD finish the job under 15 minutes, or are they hardcore slow. we dont know, but in this case both is possible and lead to 2 different answer -> not sufficient.

(2) -> we got an number which we could use to calculate if we can save 4 minutes or not. this leads us to 1 answer -> suff.
B
i did not calculate anything in part 2, because I needed 1.5 minutes to calculate the beginning. (its already late in Germany)

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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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26 Jan 2015, 20:07
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Expert's post
Answer D (Not sure if that's right)
The problem tells us that 16 horses need 24 min's to do the job - thus one horse would need 16x24 min's to do the same job alone. 12 horses would need (16x24)/12 = 32 minutes to do the full job. A quarter of an hour is 15 minutes. After 14 minutes 12 mules join the horses. If the mules work faster than the horses it might be possible that they could finish the job in fewer than 15 minutes - but if they work at an equal or slower rate it is not possible (24 mules/horses with the same speed would need 32/2=16 minutes).
Statement (1) is sufficient as it tells us that the mules work at a slower rate.
Statement (2) tells us that the 12 mules need (48x16)/12 = 64 minutes to do the full job. As 64 minutes > 24 minutes the work rate of the mules is slower than that of the horses. Sufficient

hi... the point you are missing is that the amount of work left which is not full but 18/32=9/16....
so if both are equally or mules are just slightly slower, they will take 9/16*16=9 mins...
therefore if they are slightly slow it may take <15 min.. or >15 if very slow...
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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27 Jan 2015, 13:54
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Bunuel 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.

Kudos for a correct solution.

I think B is the answer:

Approach is as follows;
from stem

Horses........minutes............total work
16..............24....................16*24 = 384 units
12..............14....................12*14 = 168 units --> work left = 384 - 168 = 216 units of work is left.

from 1:
mules work slower than horses and 216 units of work is completed by horses and mules together. In 15 mins horses do 12*15 = 180 units of work. Mules do less than 180 units in 15 mins from this statement. together, they can do more than or less than 216 units in 15 mins ---> if mules are too slow.

from 2:
48 mules can do 384 units of work in 16 mins.
12 mules can do 384 units of work in 16*4 = 64 mins
12 mules can do 216 unis of work in 64*216/384 = 36 mins
12 horses can do 216 units of work in 24*(16/12)*(216/384) = 18 mins (equation is from stem as 16 horses take 24 mins for 384 units of work)

as 12 horses and 12 mules do the work simultaneously: and horses take 18 mins and mules take 36 mins, combined they take (36*18)/(36+18) mins = 12 mins

B

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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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02 Feb 2015, 05:22
Expert's post
1
This post was
BOOKMARKED
Bunuel 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.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

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 started h [#permalink]

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02 Feb 2015, 06:09
Hi,

Would the following logic be ok during the test or no :

without even computing anything, statement A doesnt give any real info, only 'slower' but it can be much slower, or a lot slower.
statement B does give the rate of the mule, and thus can allow us to make some computation and answer the question (but we wont since we don't need the actual answer).
thus, only statement B is helpful.
done in 20seconds.

would this be correct or can there be a case where only statement A is helpful ? such as a situation where the only fact of knowing that the mule are slower can tell us the answer?

thank you !

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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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02 Feb 2015, 07:55
hycday wrote:
Hi,

Would the following logic be ok during the test or no :

without even computing anything, statement A doesnt give any real info, only 'slower' but it can be much slower, or a lot slower.
statement B does give the rate of the mule, and thus can allow us to make some computation and answer the question (but we wont since we don't need the actual answer).
thus, only statement B is helpful.
done in 20seconds.

would this be correct or can there be a case where only statement A is helpful ? such as a situation where the only fact of knowing that the mule are slower can tell us the answer?

thank you !

hi, ....
you cannot take this as a routine. It may not have mattered here with the kind of numbers we have...
but it will not be true if i change only one value in the original question ..

16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 1 minute, 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.

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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14 Nov 2016, 00:43
help help help!!!! :(
i am solving it as follows but i am stuck:

16H=1/24 thus, 1H does 1/(16*24) L/min, so 12 horses do 12H=1/(16*2) L/min

in 14 mins, the 12H will do 7/16 L, thus remains 9/16L.

so, 12H+12M= ((1/16*2)+(12M))*15=.....

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Re: 16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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08 Jul 2017, 05:16
Cuco wrote:
chetan2u wrote:
hycday wrote:
Hi,

Would the following logic be ok during the test or no :

without even computing anything, statement A doesnt give any real info, only 'slower' but it can be much slower, or a lot slower.
statement B does give the rate of the mule, and thus can allow us to make some computation and answer the question (but we wont since we don't need the actual answer).
thus, only statement B is helpful.
done in 20seconds.

would this be correct or can there be a case where only statement A is helpful ? such as a situation where the only fact of knowing that the mule are slower can tell us the answer?

thank you !

hi, ....
you cannot take this as a routine. It may not have mattered here with the kind of numbers we have...
but it will not be true if i change only one value in the original question ..

16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 1 minute, 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.

Actually, hycday's logic still works with the changes you made to the original question.... With the given information we can still calculate the time it would take 12 horses and 12 mules working together to finish the job, hence B is sufficient. Whether it takes more, or less, than 15 min is indifferent, the fact is that with the information provided in B we can calculate the time it would take the animals to finish the job, so B is sufficient.

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16 horses can haul a load of lumber in 24 minutes. 12 horses started h [#permalink]

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19 Oct 2017, 06:37

Let h - time taken by single horse to load (in minutes)
m - time taken by single mule to load (in minutes)

Given: 16 horses -> 24 mins => time taken by single horse is (16 * 24) = 384 minutes
so amount of job completed by 1 horse in 1 min => 1/384
amount of job completed by 12 horse in 1 min => 12/384
amount of job completed by 12 horses in 14 min => (14 * 12/384) = 9/16

So before mules join (7/16) of work completed,

now , amount of job completed by 1 mule in 1 min => 1/m
amount of job completed by 12 mules in 1 min => 12/m

now the question is remaining job, (9/16) will be completed less than 15 mins?

(9/16)/ ( (12/384) + (12/m)) < 15 ? ---------------------- (1)

Statement 1:
mules work slower than horses,

now if considering hypothetical situation, mules at same speed as horse., them m = 384(time taken by single horse to complete full job)
Eqn --- (1) becomes , (9/16) / ((12/384) + (12/384)) = 9 minutes (which is less than 15 mins)
so, if mules work at same speed as horses, remaining job will be completed in 9 minutes, but given mules work slower than horses, we don't know how slow, so time taken could be < 15 or >= 15 minutes, we can't say -> Insufficient.

Statement 2:
48 mules can haul the same load of lumber in 16 minutes.
so time taken by single mule to do whole job = (16 * 48) minutes (which is the value of "m")

We can substitute the value of "m" in equation --- -(1) and can find remaining job time taken, and accordingly we will be able to say <15 or >= 15

Sufficient.

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16 horses can haul a load of lumber in 24 minutes. 12 horses started h   [#permalink] 19 Oct 2017, 06:37
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