A piece of work can be done by 10 boys in 6 days working 4 hours each

Question

A piece of work can be done by 10 boys in 6 days working 4 hours each day. How many minimum possible number of boys are needed to complete another work which is three times more if they work for same integer number of hour and day, say x hour and x days?
(1) 5
(2) 10
(3) 12
(4) 15
(5) 30

Kurtosis · Accepted Answer

Total work done = 10 * 6 * 4 = 240 units

New work = Three times more than current work

New work = Current work + 3(Current work)
New work = 4*240 = 960 units

Number of boys * x * x = 960

960 can be factorized as 2^6 * 3 * 5 --> 2^6 can be expressed as x^2 i.e. (2^3)^2

Minimum number of boys = 3 * 5 = 15

Answer: D

mdacosta · Answer

Vyshak -- I understand everything up to: "# of boys * x * x = 960"

How are you able to replace (2^3)^2 for x^2 like that? I'd think each boy does (1)(6)(4) = 24 units of work, so 960 / 24 = 40 boys

Can you help me understand please? Thank you :D

Michael

Kurtosis · Answer

Hi Michael,

The question states that the number of hours worked and the number of days taken to complete the work are same. When you take 6 hrs and 4 days or vice versa, it violates the given condition. When we factorize we should express one number as a square of an integer. We are able to express only 2^3 in this way.

etienneg · Answer

Hello all! This is my first post, please excuse if I am not following protocol etc

I misunderstood this statement: another work which is three times more - is this phrased correctly? I understood that the work was 3x times 240, ie 720 (which is 5 boys working 12 hours over 12 days) I understand how "three times" is not exactly the same as "three times more", however, this is how people speak when they mean 3x times; they use both to mean the same thing. English is not my first language and so it is quite possible that I misunderstand the subtlety of this. My concern is more if I should look out for something like this on the test, or if it will be more clear in the GMAT?

GGMU · Answer

Vyshak  I don't seem to understand why have you considered New work =  Current work  + 3(Current work)

In question stem it is mentioned that How many minimum possible number of boys are needed to complete  another work which is three times more

Kurtosis · Answer

Hi,

If new work(x') is three times current work then you can consider x' = 3x. If new work is 3 times more than current work then it means that the difference between new work and current work is three times.

GGMU · Answer

Vyshak  Then my solution will be something like this. Correct me if I am wrong:

Rate=?; Time= 24hrs; Work=1
So Rate= 1/24 for 10 boys
So Rate= 1/240 for 1 boy

Now let there be n boys for new work
Rate= n/240; Time=t ; New Work= 1+3 
So (n/240)*t=4
So nt=960
Now for n to be minimum t should be maximum.
960=2^6 * 3 * 5
Since days=hrs, we can only have days =2^3 and hrs=2^3
so 960/(2^3*2^3)=15

chetan2u · Answer

Hi,
  the most important point here is to note that 3 times more than x means x+3x or 4x..

First find the boys-hour required for initial work  = 10*6*4 = 240 
Now the new work is 3 times more, so boys hour required  = 240+3*240 = 960 ..
Now x*x*boys =  960 = 64 *3*5 = 8^2 *3*5. .
 We are looking for minimum possible number of boys, equate two sides 
so x= 8 and boys = 15

D

Kinshook · Answer

A piece of work can be done by 10 boys in 6 days working 4 hours each day.

How many minimum possible number of boys are needed to complete another work which is three times more if they work for same integer number of hour and day, say x hour and x days?

Man-hours required to finish the work = 10*6*4 = 240 man-hours

Let the minimum possible number of boys be n.

Man-hours required to finish 3 times more work = 240 + 3*240 = 960 = n*x*x = nx^2

nx^2 = 960 = 2^6*3*5

Minimum n = 3*5 = 15; x = 2^6 = 64

IMO D

Wadree · Answer

Original work =   ×   ×   = 6 × 4 × 10 = 240

So... another work =   +   = 4 times original work = 4 × 240 = 960

So....we gotta make em work same day and hour.....and keep   at minimum....
So..... another work = 960 = 5 × 2 × 3 × 2 × 4 × 4 =   ×   ×   =   ×   ×   
So.....   = 4 × 2 = 8 .... and   = 4 × 2 = 8 ..... 5 and 3 are different primes.....so we cant increase   and   anymore while keeping em da same..... so   = 5 × 3 = 15 .......

! nah id win!

A piece of work can be done by 10 boys in 6 days working 4 hours each

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