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I am a little unsure about the rule for which denominator to

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Manager
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I am a little unsure about the rule for which denominator to [#permalink] New post 13 Dec 2005, 06:43
I am a little unsure about the rule for which denominator to use in some % problems. Try the following question for example and let me know if you have the rule:

At Company X senior sales representatives visit the home office once every 30 days, and junior sales representatives visit the home office once every 20 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?

A. 10%
B. 25%
C. 33%
D. 50%
E. 67%
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 [#permalink] New post 13 Dec 2005, 07:12
2 years is approximately 720 days (24*30).

For senior: 720/30=24
For junior: 720/20=36

36/24=1.5

Therefore 50% more.

(D)
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 [#permalink] New post 13 Dec 2005, 07:18
I get D - Approximately 50%

Set up as follows:
Junior Rep visits the office 1/20 days.
Senior rep visits the office 1/30 days

(1 visit/20 days)*(365 days/year)*(2 years)= ~36 days visiting the office in a 2 year time span.
(1 visit/30 days)*(365 days/year)*(2 years)= ~24 days visiting the office in a 2 year time span.

36-24 = 12
12/24(100) = 50%

If you notice, when I set up the equation to get the number of days each rep visited in the two years, the "labels" canceled each other out. I remember learning about this technique in science class to make conversions (for example from hours to minutes to seconds). Essentially, you want the solution you're looking for (in this case the # of visits), to end up on top and alone. You'll notice that there is a "day" label on top and bottom - they cancel each other out. Also, you'll notice there's a "years" label on top and bottom as well, and they cancel each other out. This leaves "visits" alone and on top.

I hope that makes sense...and I hope that's what you were looking for...
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 [#permalink] New post 13 Dec 2005, 11:09
If the question states "x is what percent greater/smaller than y?", y will always be the denominator. (x-y)/y
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 [#permalink] New post 13 Dec 2005, 13:42
Juinor repr.=360/20=18
Sen repr.=360/30=12

18/12==3/2= 1 1/2 or 50%

It does't matter what period you are considering, this ratio 3/2 will always stay the same.

D stands
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 [#permalink] New post 13 Dec 2005, 17:26
yb wrote:
If the question states "x is what percent greater/smaller than y?", y will always be the denominator. (x-y)/y


C

I agree with you "yb" ....it should be 12/36*100= 33%
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 [#permalink] New post 14 Dec 2005, 04:00
No need to calculate by years. The ratio of visiting frequency of S to J is 2:3.How much percentage 3 is greater than 2. Simply and exactly (no approximate) 50%. It will be 33% if asked how much percentage lesser is Senior's visit form Junior's.
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  [#permalink] 14 Dec 2005, 04:00
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