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

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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

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

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09 Feb 2017, 00:40

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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

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

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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)

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

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09 Feb 2017, 11:23

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

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

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

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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"?

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"?

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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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.

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

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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.

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.

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).

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

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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

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

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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

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

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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