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# What is the probability that a randomly drawn positive factor of 60 is

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Joined: 02 Sep 2009
Posts: 59589
What is the probability that a randomly drawn positive factor of 60 is  [#permalink]

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19 Mar 2019, 02:10
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Difficulty:

35% (medium)

Question Stats:

68% (01:18) correct 32% (01:24) wrong based on 69 sessions

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What is the probability that a randomly drawn positive factor of 60 is less than 7?

(A) 1/10
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2

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Re: What is the probability that a randomly drawn positive factor of 60 is  [#permalink]

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19 Mar 2019, 06:14
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Bunuel wrote:
What is the probability that a randomly drawn positive factor of 60 is less than 7?

(A) 1/10
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2

total factors of 60 = 2^2 * 3*5 = 12 factors
i.e 1,2,3,4,5,6 = 6 factors<7
so P = 6/12 = 1/2
IMO E
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What is the probability that a randomly drawn positive factor of 60 is  [#permalink]

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19 Mar 2019, 07:39
Bunuel wrote:
What is the probability that a randomly drawn positive factor of 60 is less than 7?

(A) 1/10
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2

For a Number $$N=a^p*b^q*c^r*...$$where a, b, c etc are distinct prime factors of n and p, q r are their respective exponents

The number of factors of $$N = (p+1)*(q+1)*(r+1)*...$$ and so on

i.e. $$60 = 2^2*3^1*5^1$$

i.e. Number of factors of $$60 = (2+1)*(1+1)*(1+1) = 12$$

Factors of 60 which are less than 7 are $${1, 2, 3, 4, 5, 6}$$

i.e. Required Probability $$= 6/12 = 1/2$$

ALTERNATIVELY: One can find factors of a small number like 60 by simply writing all expressions in form of multiplication of two numbers
i.e. 60=
1*60
2*30
3*20
4*15
5*12
6*10

All the blue factors are less than 7 and total there are 12 factors hence required probability $$= 1/2$$
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Re: What is the probability that a randomly drawn positive factor of 60 is  [#permalink]

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21 Mar 2019, 18:02
Bunuel wrote:
What is the probability that a randomly drawn positive factor of 60 is less than 7?

(A) 1/10
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2

The factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60

So the probability of selecting a factor that is less than 7 is 6/12 = 1/2.

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Re: What is the probability that a randomly drawn positive factor of 60 is   [#permalink] 21 Mar 2019, 18:02
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