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# How many positive integers can be expressed as a product of two or mor

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
How many positive integers can be expressed as a product of two or mor  [#permalink]

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06 Feb 2019, 02:46
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Difficulty:

55% (hard)

Question Stats:

49% (01:43) correct 51% (01:42) wrong based on 38 sessions

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How many positive integers can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once?

A. Eight
B. Nine
C. Ten
D. Eleven
E. Twelve

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Math Expert
Joined: 02 Aug 2009
Posts: 8006
How many positive integers can be expressed as a product of two or mor  [#permalink]

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06 Feb 2019, 04:44
Bunuel wrote:
How many positive integers can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once?

A. Eight
B. Nine
C. Ten
D. Eleven
E. Twelve

Two ways

1) combination..
Therefore, we have to add ways to pick 2 or 3 or all out of 4, so 4C2+4C3+4C4 = 6+4+1 = 11

2) there are two ways for each number - select or not select..
Therefore total ways is 2*2*2*2=16
Now this includes the 4 ways when each is taken alone, so subtract 4 from 16 = 16-4=12
It also includes the way when none is selected, so subtract 1..12-1=11

D
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Re: How many positive integers can be expressed as a product of two or mor  [#permalink]

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06 Feb 2019, 05:38
1
Bunuel wrote:
How many positive integers can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once?

A. Eight
B. Nine
C. Ten
D. Eleven
E. Twelve

Notice the word two or more factors.

Selecting 2 primes out of given 4= 4C2 ways= 6
Selecting 3 primes out of given 4= 4C3 ways =4
Selecting 4 primes out of given 4= 4C4 ways= 1
So total ways = 6+4+1 = Eleven
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Re: How many positive integers can be expressed as a product of two or mor  [#permalink]

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06 Feb 2019, 06:58
Bunuel wrote:
How many positive integers can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once?

A. Eight
B. Nine
C. Ten
D. Eleven
E. Twelve

total given prime no 5,7,11,13
no of different products which can be made using these 4 prime no and not including same prime factor >1 is
4c2+4c3+4c4
6+4+1 = 11
IMO D
Re: How many positive integers can be expressed as a product of two or mor   [#permalink] 06 Feb 2019, 06:58
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# How many positive integers can be expressed as a product of two or mor

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