Operation on rational numbers

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 17
Joined: Mon Nov 23, 2015 6:19 am
Thanked: 1 times

Operation on rational numbers

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

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Tue Jan 12, 2016 9:19 pm

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.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Mon Sep 24, 2018 8:16 am

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