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X number of men can finish a piece of work in 30 days

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X number of men can finish a piece of work in 30 days  [#permalink]

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New post 09 Feb 2017, 00:09
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X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15

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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 09 Feb 2017, 03:06
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saswata4s wrote:
X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15


Hi,

X number of men can finish a piece of work in 30 days. ==> Total work = 30X Men days. -- (1)

If there were 6 men more, the work could be finished in 10 days less. ==> Total work = (X+6)*20 days -- (2)

By (1) and (2) we have:

30X = (X+6)*20 => 10X = 120 => X = 12 men.

Thanks.
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 09 Feb 2017, 00:40
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2
saswata4s wrote:
X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15


y-#of days one man will finish the work.

\(\frac{x}{y} = \frac{1}{30}\)

\(y = 30x\)

\(\frac{x + 6}{y} = \frac{1}{20}\)

\(\frac{x + 6}{30x} = \frac{1}{20}\)

\(20x + 120 = 30x\)

\(x = 12\)

Answer C
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 09 Feb 2017, 11:23
1
1
saswata4s wrote:
X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15


rate of 1 man per day=1/30x
(x+6)*1/30x*20=1
x=12
C
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 10 Feb 2017, 00:18
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saswata4s wrote:
X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15


Using Ratios:

X men do 1/30th of the work per day.

X+6 men will do 1/20th of the work per day.

So ratio of men in the two cases is (1/30)/(1/20) = 2/3

On the ratio scale, the additional 1 is actually 6 so the multiplier is 6. Hence original number of men = 2*6 = 12

Answer (C)
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 14 Feb 2017, 20:25
VeritasPrepKarishma wrote:
saswata4s wrote:
X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15


Using Ratios:

X men do 1/30th of the work per day.

X+6 men will do 1/20th of the work per day.

So ratio of men in the two cases is (1/30)/(1/20) = 2/3

On the ratio scale, the additional 1 is actually 6 so the multiplier is 6. Hence original number of men = 2*6 = 12

Answer (C)


Hi Karishma, can you break this down a bit more? I understand the ratio of rates is 2/3, but what did you mean "on the ratio scale, the additional 1 is actually 6"?
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 15 Feb 2017, 01:37
cara0910 wrote:
VeritasPrepKarishma wrote:
saswata4s wrote:
X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15


Using Ratios:

X men do 1/30th of the work per day.

X+6 men will do 1/20th of the work per day.

So ratio of men in the two cases is (1/30)/(1/20) = 2/3

On the ratio scale, the additional 1 is actually 6 so the multiplier is 6. Hence original number of men = 2*6 = 12

Answer (C)


Hi Karishma, can you break this down a bit more? I understand the ratio of rates is 2/3, but what did you mean "on the ratio scale, the additional 1 is actually 6"?


Sure. Take a look at this post:

https://www.veritasprep.com/blog/2011/0 ... of-ratios/

You have the ratio scale, a multiplier and the actual values.

e.g. On the ratio scale, A:B = 2:3.
If the multiplier is 6, actual values are A = 6*2 = 12 and B = 6*3 = 18
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 15 Feb 2017, 10:51
saswata4s wrote:
X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 15


We are given that X men can complete a job in 30 days. Since rate = work/time, the rate of the X men is 1/30. We are also given that if 6 more men were added, the work could be finished in 10 fewer days (i.e., the work could be finished in 20 days). Thus the rate of X + 6 men would be 1/20. To determine X, we create the following proportion:

X/(1/30) = (X + 6)/(1/20)

30X = 20(X + 6)

30X = 20X + 120

10X = 120

X = 12

Answer: C
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X number of men can finish a piece of work in 30 days  [#permalink]

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New post Updated on: 20 Feb 2017, 09:42
VeritasPrepKarishma wrote:

You have the ratio scale, a multiplier and the actual values.

e.g. On the ratio scale, A:B = 2:3.
If the multiplier is 6, actual values are A = 6*2 = 12 and B = 6*3 = 18


Thanks! This was a good read.

Originally posted by okfan01 on 15 Feb 2017, 20:37.
Last edited by okfan01 on 20 Feb 2017, 09:42, edited 1 time in total.
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 15 Feb 2017, 23:07
You can straight away apply a formula here.

(M1D1H1)/W1 = (M2D2H2)/W2

Where M1, M2 = Number of men/women
H1,H2 = Number of hours worked
D1,D2 = Number of days worked
and
W1,W2 = Work done

Here, the case will be

(X)30 = (X+6)(20)
X=12
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 17 Feb 2017, 12:39
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Hi saswata4s,

This question can be solved by TESTing THE ANSWERS. Since the numbers involved in the prompt are all EVEN numbers (and there are no fractions or decimals involved), then it's likely that the correct answer will also be an even number. This is essentially a rate question, so it will help to think in those terms...

Let's TEST Answer A: 10 workers

IF... 10 workers require 30 days to complete a job, then that is (10)(30) = 300 worker-days of effort to complete the task.
With 10+6 = 16 workers, we would need 300/16 = 18 3/4 days to complete the task. This difference does NOT match what we were told (it's supposed to be 20 days). Eliminate Answer A.

Let's TEST Answer C: 12 workers

IF... 12 workers require 30 days to complete a job, then that is (12)(30) = 360 worker-days of effort to complete the task.
With 12+6 = 18 workers, we would need 360/18 = 20 days to complete the task. This is an exact match for what we were told, so this MUST be the answer.

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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 17 Feb 2017, 23:37
EMPOWERgmatRichC wrote:
Hi saswata4s,

This question can be solved by TESTing THE ANSWERS. Since the numbers involved in the prompt are all EVEN numbers (and there are no fractions or decimals involved), then it's likely that the correct answer will also be an even number. This is essentially a rate question, so it will help to think in those terms...

Let's TEST Answer A: 10 workers

IF... 10 workers require 30 days to complete a job, then that is (10)(30) = 300 worker-days of effort to complete the task.
With 10+6 = 16 workers, we would need 300/16 = 18 3/4 days to complete the task. This difference does NOT match what we were told (it's supposed to be 20 days). Eliminate Answer A.

Let's TEST Answer C: 12 workers

IF... 12 workers require 30 days to complete a job, then that is (12)(30) = 360 worker-days of effort to complete the task.
With 12+6 = 18 workers, we would need 360/18 = 20 days to complete the task. This is an exact match for what we were told, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich


Hi EMPOWERgmatRichC,

Quote:
This question can be solved by TESTing THE ANSWERS.


I think if options are in increasing/decreasing order then we should start checking with middle option, i.e. (C). It helps us to eliminate two other options in one shot.

Thanks.
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 18 Feb 2017, 14:12
Hi ganand,

When TESTing THE ANSWERS, it helps to consider all of the information that you're given (including the 'design' of the answer choices and the specific question that is asked) when choosing which answer to TEST first. To that end, starting with Answer C is often not the best option (as 80% of the time you'll be forced to check a second option to get to the correct answer).

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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 16 Apr 2017, 13:23
(1): X*(1/m) = 1/30 (X men do 1/30 work a day)
(2): (X+6)*(1/m) = 1/20 ((X + 6) men do 1/20 work a day)
(1)/(2) = X/(X+6) = 2/3 --> 3X = 2X + 12 --> X = 12
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 16 Apr 2017, 23:23
1/20-1/30=1/60
So 6 men will make 1/60 more job per day which makes 1 men do 1/360 job per day
360/30= 12 men as original number
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 06 Jun 2017, 11:55
What if you consider the total units to be 600 and so with
X men -30 days - 600 units then in 1 day he makes 20 units.
therefore for X men it is 20X units / day
X+6 men - 20 days - 600 units then in 1 day he makes 30 units
therefore for X+6 men it is 30 (X+6)=30X+180. Then equate the two to get the value of X. But i am unable to get the answer.
Can someone please let me know why is my method wrong and where am i getting deviated. Thank you :oops:
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Re: X number of men can finish a piece of work in 30 days  [#permalink]

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New post 06 Jun 2017, 23:36
muthappashivani wrote:
What if you consider the total units to be 600 and so with
X men -30 days - 600 units then in 1 day he makes 20 units.
therefore for X men it is 20X units / day
X+6 men - 20 days - 600 units then in 1 day he makes 30 units
therefore for X+6 men it is 30 (X+6)=30X+180. Then equate the two to get the value of X. But i am unable to get the answer.
Can someone please let me know why is my method wrong and where am i getting deviated. Thank you :oops:

Hi muthappashivani,

Please refer the highlighted part.

x men 30 days - 600 units => x men in 1 day - 20 units => 1 men in 1 day - 20/x units. --- (1)

x+6 men 20 days - 600 units => x+6 men in 1 day - 30 units => 1 men in 1 day - 30/(x+6) units. ---(2)

Equate (1) and (2), we have:

\(\frac{20}{x} = \frac{30}{x+6} \Rightarrow 30x = 20x + 120 \Rightarrow x = 12\)

Hope it helps.

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