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by vaibhav101 » Thu May 31, 2018 8:20 am

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at a loading deck, 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 2 crews did the day crew load?

A 1/2
B 2/5
C 3/5
D 4/5
E 5/8
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by GMATGuruNY » Thu May 31, 2018 8:34 am
vaibhav101 wrote:at a loading deck, 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 2 crews did the day crew load?

A 1/2
B 2/5
C 3/5
D 4/5
E 5/8
Day crew:
Let the number of workers = 5.
Let the number of boxes loaded by each worker = 4.
Total number of boxes loaded = 5*4 = 20.

Night crew:
Since the night crew has 4/5 as many workers as the day crew, the number of workers on the night crew = (4/5)5 = 4.
Since each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew, the number of boxes loaded by each night crew worker = (3/4)4 = 3.
Total number of boxes loaded = 4*3 = 12.

(Boxes loaded by the day crew)/(Total number of boxes loaded by the two crews) = 20/(20+12) = 20/32 = 5/8.

The correct answer is E.
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by Brent@GMATPrepNow » Thu May 31, 2018 9:34 am
vaibhav101 wrote:at a loading deck, 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 2 crews did the day crew load?

A 1/2
B 2/5
C 3/5
D 4/5
E 5/8
I think the fast way is to plug in some nice numbers.
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 = [spoiler]5/8[/spoiler]

Answer: E

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by [email protected] » Thu May 31, 2018 6:16 pm
Hi vaibhav101,

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: E

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by Jeff@TargetTestPrep » Sun Jun 03, 2018 5:37 pm
vaibhav101 wrote:at a loading deck, 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 2 crews did the day crew load?

A 1/2
B 2/5
C 3/5
D 4/5
E 5/8
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.

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: E

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