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A certain company assigns employees to offices in such a way

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A certain company assigns employees to offices in such a way [#permalink] New post 22 Jul 2008, 00:08
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1. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 5
B. 6
C. 7
D. 8
E. 9

2.Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month,2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

3. This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

a. 1/(r+2)
b. 1/(2r+2)
c. 1/(3r+2)
d. 1/(r+3)
e. 1/(2r+3)
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Re: PS - Math Hour (looking for explanation) [#permalink] New post 22 Jul 2008, 00:53
I have tried to solve the second task, and the answer is A:

Assumptions:
1. Let all the stereo produced be 1, then the company produced 2/3 of basic and 1/3 of deluxe stereos.
2. Let the number of hours to produce one basic stereo be X, then the number of hours to produce one deluxe stereo is 7/5*X.

So, the comoany spent 2/3*X hours to produce all basic stereos and 1/3*(7/5*X) to produce all deluxe stereos. Total number of hours spent for production of all stereos is:
2/3*X + 1/3*(7/5*X) = 17/15*X.

1/3*(7/5*X) = 7/15*X - the number of hours spent for deluxe stereos production.
Now we devide the number of hours spent for deluxe stereos production by the total number of hours spent for production of all stereos:

(7/15*X)/(17/15*X) = 7/17.
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Re: PS - Math Hour (looking for explanation) [#permalink] New post 22 Jul 2008, 01:01
priyankur_saha@ml.com wrote:
1. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 5
B. 6
C. 7
D. 8
E. 9

2.Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month,2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

3. This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

a. 1/(r+2)
b. 1/(2r+2)
c. 1/(3r+2)
d. 1/(r+3)
e. 1/(2r+3)


1. d)

The number of combinations are equal to

2*Combination with 3 in first office + Combination with 2 in first office + Combination with 1 in first office

= 2*1 + 3C2 + 3C2 = 8

2. a)

Total number of hours = x/3*7/5 + 2x/3 = 17x/15

Fraction for deluxe = (7x/15) / (17x/15) = 7/17

3. e)

Let '1' be total income this year and x be the saved money

Income spent = 1-x
Income saved = x

(r+1)x = (1-x)/2
2rx+2x = 1-x
x = 1/(2r+3)
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Re: PS - Math Hour (looking for explanation) [#permalink] New post 22 Jul 2008, 01:12
For the third task the answer is E:

Assumptions:
1. Let the income for this year be I.
2. Let saved income be x, then spent income is (I-x).
So, the fraction of income that Henry saved this year is x/I.

We know that next year Henry will have available for spent (1+r) for each dollar saved this year, so he will have x*(1+r), and this amount is twice more than he spent this year. Thus, we have an equation:
I-x = 2*x*(1+r), from which I=x*(3+2r).

Now we substitute I with x*(3+2r) in the equation x/I:
x/(x*(3+2r))=1/(3+2r).
Re: PS - Math Hour (looking for explanation)   [#permalink] 22 Jul 2008, 01:12
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