The SAT question 99% of students get wrong… can you solve it? #digitalsat #satprep

[brendangardiner]

Every engineer knows the answer is D. Every project manager thinks the answer is C

[wonderingatom]

The answer is D. It isn't stated anywhere if the task(s) at hand could be performed in parallel to gain the efficiency assumed. If the work was sequential with defined times, then you could end up saving no time at all.

[thenetherlord]

If it said that the days where proportional, I would say C, but I said D because you cannot measure human efficiency

[Insecurity]

The answer is D. The people are more likely to get distracted while completing the job and thus, may complete the job slower.

[TDomonkos]

I don't think 99% gets this wrong, I immediatly knew the answer when I looked at it

[henningjorgensen]

The answer is D, nothing in the description says anything about if the job is scalable at all.

[Alexander-vllg]

I would answer D. Completing jobs looks like a bell curve where the more people you add the less time you save until eventually adding people to the job is insignificant. For example. If you said "How many days will it take 3000 men and 2500 women to complete it" According to your explanation the answer would be 0.06 days. And I think that's wrong. There's going to be a minimum amount of time required to complete any job.

[alcoremortis]

by this logic, nine women working together could birth a baby in a month.

[adean]

Imagine they're running a chemical reaction that lasts 15 days or something

[riccardozanoni]

It's obviously D. The amount of cases in which the number of people performing a task and the time required follow a perfect negative correlation is probably close to zero.

[brentgroen]

if it takes 10 minutes to boil 3 eggs, how long does it take to boil 30 eggs.
depending on how many eggs can be boiled at once its anywhere between 10 and 100 minutes
if you can boil all the eggs at once, its 10
if you can boil 3 at once, its 100.

its the exect same thing as this ecuation here, and as its uncertain weather you can boil more than 3 eggs at once.
Thus its option D

[vfe]

In fact D is correct. For example: If you have job to support 15 days tour for tourists or if you growing something (technology process time), moving something depending on transportation systems/times

(wo)manhour is only one factor in job ;) If you have task to change one bulb then it realy dont go faster with 9 helpers :D

[daancompen]

Let’s look at it this way. I had a school project where we had to test the effect of leaving out a polymer for a couple of weeks seeing what effect the time had on said polymer. If we were with 20x as many people that time would still not have shortened

[XianRoblox]

I had the same answer, but different solution.
First, add the men and women, so 22 people in 15 days, change it to a fraction, which makes 22/15. Second, add the 30 and the 25 to get 55. Now, since we don't know how many days yet, we do x, so 55/x. Switch the denominators, so 22/x and 55/15. Cross multiply the 22 and 15 to get 330, and then divide by 55 to get the answer of 6.

[misternoodle]

D is the correct answer 99% of the time. There are so many variables in a job outside of the number of workers. Not only do you have to consider those, but realistically speaking, efficiency per worker tends to go down as you add more people. On top of that, if the people aren't structured correctly for the job, you run into what is known by some as the "Ant Colony Problem" that further drives lower productivity. There are very few jobs out there that can be scaled perfectly with people.

[sefaq]

Answer should be D since we dont have enough information. The Law of Diminishing Returns proves that a proportional increase in Input is never equal to that same proportional gain in output. It's always rather a lower proportion, hence realistically it cannot be C.

[moonman]

12 men + 10 women = 22 people
22 people * 15 days = 330 "man-days"

30 men + 25 women = 55 people
330 "man-days" / 55 people = 6 days

[usmanchughtai]

Two methods: #1 - Logical Deduction

If 12 men and 10 women can complete the job in 15 days, then diving by 2 means that 6 men and 5 women can complete the job in 30 days since you have half the labor.

Looking at the other expression we see that 6 men go into 30 men, 5 times (oh my) and 5 women go into 25 women 5 times as well.

Meaning we just divide the original 30 day completion by 5 since we have 5x the aid. The answer is C

#2 - SAT time sensitive solution.
Add up the total number of men and women of each side and divide those numbers by each other to find the duplicator.
(12 + 10) / (30 + 25) = 2/5

Multiply that constant by the initial number of days to arrive at your answer.

[thoughtsengineer]

More detailed explanation (in general proof):

So the velocity to complete the job is V = W/t, where W is the about of work and t the about of time it takes to complete such work. Assuming approximately constant velocity.

Let’s say Vm and Vw are the average velocity for men and women respectively to do any work, then the total velocity for 12men and 10women to complete the task is:
V1 = 12*Vm + 10*Vw
Likewise, for 30men and 25women:
V2 = 30*Vm + 25*Vw

Substitute V1=W/t1 (t1 = time to complete all work W = 15); and V2=W/t2 (t2= time to complete same work W):

W/t1 = 12*Vm + 10*Vw
W/t2 = 30*Vm + 25*Vw

Solve for t1 and t2, and get the final system of equation:
t1 = W /(12*Vm + 10*Vw)
t2 = W/(30*Vm + 25*Vw)

You can now see why multiplying the first equation both sides by 1/(2.5) = 2/5 will get you the 2nd equation. And thus the answer for t2.

BUT, if there wasn’t any easy common factor, then you would do this instead (longer):

since t1 is given and t2 is the question, you can just make up values for Vm and Vw, plug them in the first equation to find W (for this particular speed), then plug them in the 2nd equation to get the result:

Example, easier math (but any number works): Vm=1/6 and Vw=1/5:

t1 = W /[12*Vm + 10*Vw]
15 = W /[12*(1/6) + 10*(1/5)] = W/[2 + 2] = W/4
Solve for W = 60.

Plug these for the other equation:
t2 = W/[30*Vm + 25*Vw]
t2 = 60/[30*(1/6) + 25*(1/5)] = 60/[5 + 5]
t2 = 6

Q.E.D.

[samuels]

I believe this question could be rewritten to be less vague, it needs to clearly indicate that the job progresses at a rate linearly proportional to the number of workers.
_"If 12 men and 10 women can complete a job in 15 days, _*_but 6 men and 5 women would take 30 days, _*_ how many days would it take for 30 men and 25 women to complete the same job?"_