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Problem Solving 1
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Source: Beat The GMAT — Problem Solving |
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AndreiGMAT
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First, this is not DS question, it is PS. Since the question only provides fractions, you should use a smart number. Choose for example x=20, which represents the number of day workers. And draw up a chart which will help you organize the logic.
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Day crew: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
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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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.
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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].
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Hi ezzeldin.khaled79,
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
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
