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Operation on rational numbers

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Operation on rational numbers

by saadishah » Thu Dec 03, 2015 1:15 am

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An OG question

Q. 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

Don't really follow the explanation given in the OG.
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by GMATGuruNY » Thu Dec 03, 2015 3:11 am
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
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 loads 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 [email protected] » Thu Dec 03, 2015 10:12 am
HI saadishah,

TESTing VALUES (the approach that Mitch used) is a fairly easy way to work through this question. If you want to use an Algebraic approach, then that's fine, but you have to be very careful about what your variables represent.

The number of night workers is related to the number of day workers...

IF...
N = number of night workers
D = number of day workers

N = (4/5)D

Next, you have to create a variable and an equation for the number of boxes loaded per employee.

B = number loaded per day worker
(3/4)B = number loaded per night worker

Now we can set up a ratio of boxes loaded by the Day workers to TOTAL boxes loaded by all workers:

(D)(B) / [ (D)(B) + (N)(3/4)(B) ]

Since N = (4/5)D, we can substitute in that value...

DB / [DB + (4/5)(D)(3/4)(B)]

Next, we can multiply and simplify...

DB / [DB + (12/20)DB]
DB / (32/20)DB]
1 / [32/20]

20/32 = 5/8

Final Answer: E

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by Brent@GMATPrepNow » Thu Dec 03, 2015 10:14 am
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
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 vishnujthattil » Wed Jan 13, 2016 10:02 am
saadishah wrote:An OG question

Q. 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

Don't really follow the explanation given in the OG.
As given in the problem night crew loaded 3/4 boxes and there are 4/5 workers as compared to day crew, so in effect their work is 3/4 * 4/5= 3/5 times the day crew's work, which means the ratio of night crew's work to day crew's work is 3:5. That easily gives the fraction of work by day crew, i.e 5/(3+5) = 5/8.
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by Jeff@TargetTestPrep » Sun Jun 24, 2018 5:05 pm
saadishah wrote:An OG question

Q. 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
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 x (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.

3/4 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:

3/4 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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by kapstone1996 » Sat Nov 10, 2018 9:11 am
Day workers (20)
Night workers (20) * (4/5) = 16

Number of boxes per day worker = 1 per worker so (20 ) total
Number of boxes per night worker = (3/4)*(16) = 12 total for night worker

combined day and night = 20 + 12 = 32
Day / combined = 20/32, simplified, divided the top and bottom by (4)

Number of Workers for day
20/32 divided by 4/4 = 5/8
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