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# 1) In n is a positive integer and the product of all the

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1) In n is a positive integer and the product of all the [#permalink]  26 Nov 2006, 15:41
1) In n is a positive integer and the product of all the integer from 1 to n, inclusive, is a multiple of 990, what is the least positive value of n?

a)10
b)11
c)12
d)13
e)14

2) A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?

a)0.5 <t< .075
b)1.75<t<2.0
c)2.0<t<2.5
d)2.5<t<3.0
e)3<t<3.5

3) At a constant rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously.

a)10
b)12
c)15
d)25
e)50

4) The total price of a basic computer and printer was \$2500. If the same printer had been purchased with an enhanced computer whose price was \$500 more than the price of the basic computer, then the price of printer would have been 1/5 of the that total. What was the price of the basic computer?

a)1500
b)1600
c)1750
d)1900
e)2000

5) Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours. How many hours would be needed if only 8 of the machines, working together, were used to complete the job?

a) 18
b)20
c)22
d)24
e)26

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For (1)

Yes... (B)

990 = 11*10*9. As 11 is prime, the list of factors from 1 to n must contain it.

Thus, the minimum value of n is 11 (n! = 11!).
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Fig and old_user thank you for your help!!!
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