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anyone want to tackle not one but four problems. OA to be

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Manager
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anyone want to tackle not one but four problems. OA to be [#permalink]  29 May 2007, 20:36
anyone want to tackle not one but four problems. OA to be posted soon.

cheers dan

If r and s are positive integers, is r/s an inter?

1) Every factor of s is also a factor of r
2) Every prime factor of s is also a prime factor of r.

In the xy-plane, does the line with equation y = 3x + 2 contain the point (r, s)?

1) (3r + 2 – s )(4r + 9 – s) = 0
2) (4r – 6 – s)(3r + 2 – s) = 0

Linda put an amount of money into each of two new investments, A and B, they pay simple annual interest. If the annual interest rate of invest B is 1.5 times that of investment A, what amount did Linda put into investment A?

1) The interest for 1 year is $50 for investment A and$150 for investment B.
2) The amount that Linda put into investment B is twice the amount that she put into invest A

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
a) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100
Director
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Re: 4 challenging problems [#permalink]  29 May 2007, 20:49
dragonball20cal wrote:
anyone want to tackle not one but four problems. OA to be posted soon.

cheers dan

If r and s are positive integers, is r/s an inter?

1) Every factor of s is also a factor of r
2) Every prime factor of s is also a prime factor of r.

C

In the xy-plane, does the line with equation y = 3x + 2 contain the point (r, s)?

1) (3r + 2 – s )(4r + 9 – s) = 0
2) (4r – 6 – s)(3r + 2 – s) = 0

C

Linda put an amount of money into each of two new investments, A and B, they pay simple annual interest. If the annual interest rate of invest B is 1.5 times that of investment A, what amount did Linda put into investment A?

1) The interest for 1 year is $50 for investment A and$150 for investment B.
2) The amount that Linda put into investment B is twice the amount that she put into invest A

A

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
a) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100

okay got it.... C is the answer, 10,900

This one is tricky!!...Hmm need to give one more try! anyone with good explanation.

Other three were simple and straight

please tell the OA
Manager
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[#permalink]  30 May 2007, 11:17
I'm thinking D - 11,000 on the last one. 11,000x1.1 = 12,100
12,100x10 = 121,000 - 121,000+11,000 = 132,000

Not sure though, there might be a trick to it. OA please!!!
Manager
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OA [#permalink]  02 Jun 2007, 14:41
can anyone explain the answer solution?

If r and s are positive integers, is r/s an inter?

1) Every factor of s is also a factor of r
2) Every prime factor of s is also a prime factor of r.

OA: A

In the xy-plane, does the line with equation y = 3x + 2 contain the point (r, s)?

1) (3r + 2 – s )(4r + 9 – s) = 0
2) (4r – 6 – s)(3r + 2 – s) = 0

OA: C

Linda put an amount of money into each of two new investments, A and B, they pay simple annual interest. If the annual interest rate of invest B is 1.5 times that of investment A, what amount did Linda put into investment A?

1) The interest for 1 year is $50 for investment A and$150 for investment B.
2) The amount that Linda put into investment B is twice the amount that she put into invest A

OA: E

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
a) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100

OA: D
Manager
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[#permalink]  02 Jun 2007, 15:09
1. The answer is A

is r/s an inter is equivalent to asking if s is a factor of r because only if s is a factor of r can r/s be an integer.

Stmt 1 says that all factors of s (incl. itself) are factors of r which is what we are looking for. Hence Stmt 1 is sufficient and A is the answer.

2. The answer is C

does the line with equation y = 3x + 2 contain the point (r, s) is equivalent to asking if s=3r + 2 is true because (r,s) is a point on the line.
So we are looking for a Stmt which makes s=3r+2 true.

Both stmts are required to arrive at s=3r + 2 hence C

3. It seems I got this wrong since I was getting the answer as A but the OA says its E. Ofcourse I know where I went wrong. I assumed that the Principal amount for both investments is same which is not given in the question.

4. This solution is already explained by Hayabusa.
_________________

Regards

Subhen

Manager
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excellent!! [#permalink]  04 Jun 2007, 23:17
I'm all set now.

thanks

dan
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[#permalink]  05 Jun 2007, 08:50
Can someone explain C? By using both statements, I can get 4 equations...4 equations with 4 variables is supposed to be solvable, no?
[#permalink] 05 Jun 2007, 08:50
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