Problem Solving

Hi, can someone please explain the solution to this problem? The OG Solution doesn't really help me understand thoroughly.

Problem: At a loading dock, each worker on the night crew loaded (3/4) as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

Answer choices:
(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8


The answer is (e). Thanks!

E

I solved this by picking numbers.

Say the Day Boxes /worker = 20 boxes
then Night Boxes / worker = 20 * 3/4 = 15 boxes

Now, say the Day workers = 30 workers
then the Night workers = 30 * 4/5 = 24 workers

Now we find how many boxes loaded in total by all workers -

Day Crew = 20 * 30 = 600
Night Crew = 15 * 24 = 960

So, to find the fraction of boxes loaded by the day crew -

600 / 960 = 5/8 = E.

Hi,

This question can also be solved using algebraic expressions (in case you are not familiar with picking numbers;

Day shift; 1 worker can load x boxes
y workers can load xy boxes

Night shift; 1 worker can load (3/4)x boxes
(4/5)y workers can load (3/4)(4/5)xy or (3/5)xy boxes


So Day/All = xy/((3/5)xy + xy)

The answer is 5/8

niraj_a wrote:E

I solved this by picking numbers.

Say the Day Boxes /worker = 20 boxes
then Night Boxes / worker = 20 * 3/4 = 15 boxes

Now, say the Day workers = 30 workers
then the Night workers = 30 * 4/5 = 24 workers

Now we find how many boxes loaded in total by all workers -

Day Crew = 20 * 30 = 600
Night Crew = 15 * 24 = 960

So, to find the fraction of boxes loaded by the day crew -

600 / 960 = 5/8 = E.

Just to clarify....

Night Crew = 15 * 24 = 360

Night Crew (360) + Day Crew (600) = 960

Problem: At a loading dock, each worker on the night crew loaded (3/4) as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

Answer choices:
(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

I also picked numbers to plug in. I always do for these work problems. I used 12 for the number of boxes the day crew loaded b/c its simple and divisble by 3/4

Day Crew 4 boxes
Night crew 3 boxes (3/4 of day crew's boxes)

For the number of workers I plugged in a number divisible by 4/5

Day Crew 5 workers
Night Crew 4 workers (4/5 of Day Crew's workers)

So day Crew loaded 4 boxes X 5 workers = 20 boxes
Night crew loaded 3 boxes X 4 workers= 12 boxes
20 + 12 = total boxes loaded =32
Day crew loaded 20 of the 32 total boxes
20/32 = 5/8

If you actually want to follow the methodical route,

Lets,
Crew Night Cn
Day Crew Cd
Boxes loaded per Night Crew Bn
Boxes loaded per Day Crew Bd
Total Boxes loaded by Night Crew Tn
Total Boxes loaded by Day Crew Td

From whats provided in the q,
Bn = (3/4)*Bd
Cn = (4/5)*Cd

And we know,
(Td/Cd) = Bd
and (Tn/Cn) = Bn

What's required to find is Td/(Td+Tn)

Td + Tn = Bd*Cd + Bn*Cn

Plugging in the values from the equations determined above we arrive at
Td + Tn = (8/5)*Td

Hence, Td/(Td+Tn) = 5/8

I sometimes feel that actually plugging in values consumes "thinking" time and you rather follow the time-tested approach of forming equations from whats provided in the Q.

A rather simple approach would be as follows

Let's consider this:
1 person loading one box- Total boxes loaded is 1.
10 people loading 1 box each - Total boxes loaded is 10*1 = 10
20 people loaded 2 box each - Total boxes loaded is 20 * 2 = 40 boxes

The concept is boxes loaded is just the number of people times the boxes loaded by each.

Now, we are asked the ratio not the exact numbers. You can pick numbers and solve this problem similar to some other people but if you pay attention to the basic concept, you can do the following.

Night time workers: 4/5 people loaded 3/4 boxes so total boxes loaded is 4/5 * 3/4 = 3/5
Day time workers 1 person loaded 1 boxes so total boxes loaded 1*1 = 1

Now the total ratio asked is 1/ 1+3/5 = 5/8

GMAT tries to confuse you with fractions, but if you understand the concept, the answer should become obvious.

This is a great question

3 solutions and a take-away attached.

-Patrick

I just found this solution to the Official Guide 12ed problem solving question #138, he uses the table method to solve the problem. Very easy to understand; although, if people keep making the math look so easy we will probably start to see some Physics II questions on the exam. Physics II hurt my brain

https://www.youtube.com/watch?v=qwmMtKO3Rn4

I can't believe it was that easy. Even Khan Academy makes it too hard to solve quickly. Thank thank thank you for this post.