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# S is a set of natural numbers from 1 to 100 whose smallest

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Manager
Joined: 22 Feb 2007
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S is a set of natural numbers from 1 to 100 whose smallest [#permalink]  20 Mar 2007, 21:31
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S is a set of natural numbers from 1 to 100 whose smallest prime factor is 5. What is the maximum number of elements of the set S?

(A) 7
(B) 9
(C) 30
(D) 32
(E) None of these
Senior Manager
Joined: 11 Feb 2007
Posts: 356
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5 is one of the factors. So it's a multiple of 5.

So the numbers would be 5, 10, 15, 20, ...etc

Since 2 is also prime that is smaller than 5, exclude all even number from the list of numbers (10, 20, 30, etc)

Since 3 is also prime that is smaller than 5, exclude all those that are multiples of 3 (15, 45, 75, etc.)

You're left with 7 numbers (5, 25, 35, 55, 65, 85, 95).

Manager
Joined: 12 Feb 2007
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Is there a good book, or a huge set of numerical number property questions?
Manager
Joined: 28 Feb 2007
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Location: California
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Re: PS - number properties [#permalink]  21 Mar 2007, 10:11
GMAThopeful wrote:
S is a set of natural numbers from 1 to 100 whose smallest prime factor is 5. What is the maximum number of elements of the set S?

(A) 7
(B) 9
(C) 30
(D) 32
(E) None of these

A
There are 20 numbers (ending in 5 and 0) who have a prime factor of 5. Out of these all numbers ending in 0 have 2 as the smallest prime factor so we discard them. Among remaining only 5, 25, 35, 55, 65, 85, 95 have 5 as smallest prime factor
Senior Manager
Joined: 29 Jan 2007
Posts: 450
Location: Earth
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if you observe all the possible numbers are product of 5 and prime numbers that are equal to or greater than 5.

It has to be that way for 2 and 3 to not figure out as one of the factors.
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