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# What is the value of positive integer x? (1) x is a factor of the prod

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Manager
Joined: 14 Sep 2015
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What is the value of positive integer x? (1) x is a factor of the prod  [#permalink]

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24 Jul 2017, 10:00
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Difficulty:

45% (medium)

Question Stats:

55% (01:06) correct 45% (00:25) wrong based on 20 sessions

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What is the value of positive integer x?

(1) x is a factor of the product of all integers from 1 to 5, inclusive
(2) x has 6 factors

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Joined: 05 Mar 2015
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Re: What is the value of positive integer x? (1) x is a factor of the prod  [#permalink]

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24 Jul 2017, 10:15
niteshwaghray wrote:
What is the value of positive integer x?

(1) x is a factor of the product of all integers from 1 to 5, inclusive
(2) x has 6 factors

(1) x = 1*2*3*4*5 * K
where K can be any +ve number

Not suff

(2) x = a^2*b
where a & b can be any +ve integer

not suff

combining
As x = a factor of the product of all integers from 1 to 5, in no way it can have 6 factors

Not suff

Ans E
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What is the value of positive integer x? (1) x is a factor of the prod  [#permalink]

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25 Jul 2017, 16:46
1) if x is a factor of product of all integers from 1 to 5.

it could be either 1,2,3,4,5, or any no. we get after multiplying these numbers.

so 1st is not sufficient

2) x has 6 factors-

6 can be written as (i) 2*3 or (ii) 6*1. no other combination is possible.

now x can be written in two ways in terms of primes

a) x= p^1*q^2 which will give the possibility of (i) having total factors (1+1)*(2+1) = 2*3
b) x= p^5*q^0 which will give the possibility of (ii) having total factors (5+1)*(0+1) = 6*1

we don't know the value of p,q (ii) too is not sufficient.

now after combining both-
from 1st the maximum possible values of x would be equal to 5!=120

120= 2*2*2*3*5
120= 2^3*3*5

now from (ii) we can ignore the possibility of p^5*q^0 as we don't have any prime raised to the power 5
only possibility is of (i) p^1*q^2

now q can only be equal to 2 because 2 is raised to the power 3, greater than the power of q.
but still p can be any of the number 2,3,5

so together too they are not sufficient

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What is the value of positive integer x? (1) x is a factor of the prod   [#permalink] 25 Jul 2017, 16:46
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