gmatyro wrote:
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
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Karishma
Veritas Prep GMAT Instructor
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