At a loading dock, each worker on the night crew loaded

Just take the Box Loaded by each Night crew is Bn and Box Loaded by each Day Crew is Bd.Then
According to question (Bn)=(3/4)(Bd) i.e (Bn)/(Bd)=3/4

Now again let Night Crew Has Nn number of crew members and Day crew has Nd members.Then according to question (Nn)=(4/5)(Nd) i.e (Nn)/(Nd)=4/5

As number of box carried by the group will be the product of Number of crew multiplied by the number of boxes carried by each member,
According to question we need to find out { (Nd)(Bd) } / { (Nn)(Bn)+(Nd)(Bd) }

Dividing the Nominator and denominator by (Nd)(Bd),

We get, 1 / { (Nn)(Bn)/(Nd)(Bd) + 1 } i.e 1 / { (Nn)/(Nd)*(Bn)/(Bd) + 1 }

i.e 1 / { (3/4)*(4/5) + 1} =5/8

So answer is E.
Thanks for a valued Question.

Consider KUDOS if you like the Solution.

its 5/8,
Work done by day crew will be 4x (let x=1), the count of day crew = 5x
Work done by day crew will be 3x (let x=1), the count of day crew = 4x
Total amount work done by both is 5*4+4*3 = 20+12 = 32
Ratio of amount of work done by day crew to total amount of work done is = 20/32 =5/8.

Say,
Day crew = 5 people
Night crew = (4/5)*5 = 4 people

Each person in day crew loaded = 4 boxes.
Each person in night crew loaded = (3/4)*4= 3 boxes.

Total boxes loaded by day crew = 5*4 = 20
Total boxes loaded by night crew = 4*3 = 12

Fraction of boxes loaded by day crew = 20/(20+12) = 20/32 = 5/8

Ans: "E"

Workers at night crew loaded 3/4 as many boxes as did day crew so they loaded fewer boxes. Night crew has 4/5 as many workers as the day crew so night crew has fewer workers too. Overall, night crew loaded 3/4 * 4/5 = 3/5 as many boxes as did day crew. So out of a total of 8 boxes, Night Crew loaded 3 and Day Crew loaded 5 so Day Crew loaded 5/8 of total boxes. Or
Boxes loaded by Night Crew: Boxes loaded by Day Crew = 3/5 : 1 = 3:5
So day crew loaded 5/8 of total boxes.


*Didn't see fluke's response there! The concept used is pretty similar.

Hi,
I'm trying to plug in for Question # 138 in OG 12. Could anyone point out where i'm going wrong in my reasoning? I understand the solutions posted in the earlier posts but would like to know where i went wrong.
No. of Boxes loaded by Night workers = 3/4 of Day workers
No. of Night workers = 4/5 of Day workers.

Let the number of Day workers = 100 and they load a total of 100 boxes.
No. of boxes loaded by Night workers = 3/4 x 100 = 75
No. of Night workers = 4/5 x 100 = 80

total no. of boxes loaded by both workers = 175
total no. of boxes loaded by day workers = 100

fraction of boxes loaded by day workers out of the total = 100/175 = 4/7
The closest answer is 4/5 which is D.

But the correct answer is 5/8 which is E.

Here is the problem in your solution:
It is given that EACH night worker loads 3/4 of the boxes loaded by EACH day worker. (not that total number of boxes loaded by night workers is 3/4 of the boxes loaded by day workers)

If I want to take values and I say, each day worker loads 100 boxes, then each night worker loads 75 boxes.
Total no of boxes loaded by day workers = 100*100 = 10,000
Total no of boxes loaded by night workers = 80*75 = 6000

Fraction of total boxes loaded by day workers = 10,000/16,000 = 5/8

Though, if I want to take numbers and plug in, I would take easier numbers.
Say, there are 5 day workers. Then there are 4 night workers.
Say, each day worker loads 4 boxes in a day. Each night worker then loads 3 boxes in a day.
Total no of boxes loaded by day workers = 5*4 = 20
Total no of boxes loaded by night workers = 4*3 = 12
Fraction of boxes loaded by day workers = 20/32 = 5/8

I think that the biggest problem for solving this kind of questions is the language understanding (i.e. misunderstanding).
I've had a lot of trouble with this one until I figured out that the night crew did 3/4 and the day crew did 4/4 of the work. And that the night crew had 4/5 workers and the day crew 5/5 workers.
It can become quite messy for a non-native person.

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?
a. 1/2
b. 2/5
c. 3/5
d. 4/5
e. 5/8

SEE IT THIS WAY:

day crew loads=x boxes/ member
night crew loads = 3x/4 boxes/ member

day crew workers= y
night crew workers= 4y/5

total boxes loaded/ day= xy+ (3x/4)*(4y/5)= xy+3xy/5= 8xy/5

required fraction= xy/(8xy/5) = 5/8

Hence E

Hope this clarifies..!!

I picked some smart numbers and used a table to organize the given information. Just another way to visualize the problem for me...
So, let's say we have 5 day workers. That would give us 4 night workers (4/5 of day). Say the day workers load 12 boxes (I picked a smart-ish number), then the night workers would load 9 boxes (3/4 of what the Day workers load). Put it all in a table and see what you have.

--------- Day ---- Night ----- Total
People---- 5-------- 4------------
Boxes ---- 12 -------9 -----------
Total -----60-------36--------96

I arrived at the Totals on the bottom by multiplying the people and boxes (5x12, 4x9).

So if you want to figure out what fraction of the total the day workers loaded, use:

\(\frac{60}{96}\)

This is (number of boxes the day crew loaded) divided by (total number of boxes)

This simplifies to \(\frac{5}{8}\). Thus, E is the answer.

Hope this method helps.

Refer diagram below



Let boxes in day per worker = 1

Let workers in day = 1

Total boxes loaded in day = 1*1 = 1

Similarly, total boxes loaded in night \(= \frac{3}{4} * \frac{4}{5} = \frac{3}{5}\)

Total boxes loaded \(= 1+\frac{3}{5} = \frac{8}{5}\)

Fraction \(= \frac{1}{\frac{8}{5}} = \frac{5}{8}\)

Answer = E

The easiest way to solve this question is to choose convenient values for the number of day workers and for the number of boxes loaded by each day worker.

We are given that the night crew loaded 3/4 as many boxes as each worker on the day crew and that the night crew has 4/5 as many workers as the day crew. We can set up an equation relating the number of day workers and the number of night workers:

4/5(number of day workers) = number of night workers

Let's choose the convenient value of 20 for the number of day workers and substitute it into the equation above:

4/5 x 20 = number of night workers

16 = number of night workers

Next, we set up the equation for the number of boxes loaded by each worker.

(¾) x (number of boxes loaded by each day worker) = number of boxes loaded by each night worker

Now let's choose the convenient value of 8 for the number of boxes loaded by each day worker and substitute it into the above equation:

¾ x 8 = number of boxes loaded by each night worker

6 = number of boxes loaded by each night worker

Thus, the total number of boxes loaded by each type of worker is as follows:

Day workers = 20 x 8 = 160

Night workers = 16 x 6 = 96

Total boxes loaded = 160 + 96 = 256

The question asks us to determine the fraction of all the boxes loaded by the day crew, and that is:

(Total boxes loaded by day crew)/(Total boxes loaded)

160/256

40/64

5/8

Answer is E.

Hi Manonamission,

This question can be solved by TESTing VALUES.

We're told that the night crew consists of 4/5 as many workers as the day crew:

Night crew = 4 workers
Day crew = 5 workers

We're also told that each member of the night crew loaded 3/4 as many crates as each member of the day crew:

Each Night crew member = 3 crates/each
Each Day crew member = 4 crates/each

We're asked to find the fraction of the TOTAL CRATES loaded by the Day crew...

Day crew total = (5)(4) = 20 crates
Night crew total = (4)(3) = 12 crates

(Day crew total)/(All crates) = 20/(20+12) = 20/32 = 5/8

Final Answer:

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

Hi,
Let the number of workers in day be x and each loads y boxes, so total is x*y....

While in night, the workers are 4/5*x and each loads 3/4*y, so total = 4x/5 * 3y/4= 3xy/5....

TOTAL= xy + 3/5* xy =8/5*xy..

Fraction day workers loads xy/(8/5)xy=5/8..
E..

The other way is of course take some numeric value for each, but these values should be multiples of the denominator to avoid confusion....
So day worker should be 4 or its multiple and # of day workers be 5...
Day workers load 4*5=20..
Ni workers load 3/4*4*4/5*5=3*4=12..
So TOTAL=12+20=32..
Fraction of day work=20/32=5/8

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart
To solve this question, we're just going to divide the "total box loaded by day crew" by "all the boxes loaded by the two crews". That means: \(\frac{4×5}{(12+20)}=5/8\). But the question did not specify the "total" job loaded by day crew; it simply said "did the day crew load".
Am I missing anything to comprehend whole the scenario?
Thanks__

Hi Asad,

The phrase "all the boxes loaded by the two crews" can be reasonably broken down into two "pieces":

"ALL of the boxes loaded by the DAY CREW" + "ALL of the boxes loaded by the NIGHT CREW"

There's nothing in the prompt that's asking us to consider anything other than the TOTAL number of boxes loaded by the Day Crew vs. the TOTAL of ALL BOXES loaded by both crews, so in the absence of that extra information (which again, is NOT there), we have to assume that the question is referring to ALL of the boxes loaded by the Day Crew.

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

The question doesn't need to say "total boxes loaded by day crew". It is obvious.

Think about it - you have two types of toys - red toys and green toys.
Say, there are 4 red toys and 6 green toys.

what fraction of all the toys you have are the red toys?
You will say 4/10 right?

Do you need to say "total red toys"? No. When you want the red toys out of total, you are automatically considering all red toys.
Same is the case here:
what fraction of all the boxes loaded by the two crews did the day crew load?
Since you are considering ALL boxes, some were loaded by day crew (whenever and by whichever day crew member) and others by night crew. You need the fraction loaded by day crew. You will need all boxes loaded by day crew.

Since the two pieces of information regarding the night shift are related to the information regarding the day shift, let's assign some nice values to the day shift.

Number of workers
Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)

Boxes loaded per worker
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)

Total boxes loaded
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes

Combined total boxes for both shifts = 20 + 12 = 32

Of the 32 boxes, the day shift loaded 20 of them.
20/32 = 5/8

Answer: E

Cheers,
Brent