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# If x is an integer with n distinct prime factors, is n greater than or

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Math Expert
Joined: 02 Sep 2009
Posts: 49300
If x is an integer with n distinct prime factors, is n greater than or  [#permalink]

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13 Dec 2015, 05:37
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Difficulty:

45% (medium)

Question Stats:

58% (01:02) correct 42% (00:56) wrong based on 175 sessions

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If x is an integer with n distinct prime factors, is n greater than or equal to 3?

(1) x is divisible by 6.
(2) x is divisible by 10.

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Intern
Joined: 06 Oct 2013
Posts: 45
If x is an integer with n distinct prime factors, is n greater than or  [#permalink]

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14 Dec 2015, 05:54
1
Bunuel wrote:
If x is an integer with n distinct prime factors, is n greater than or equal to 3?

(1) x is divisible by 6.
(2) x is divisible by 10.

Solution:

statement 1) x is divisible by 6.

x=6--> prime factors 2 and 3. n=2<3. NO

x=30-->prime factors 2,3 and 5. n=3=3.YES

x=210-->prime factors 2,3,5 and 7. n=4>3 YES.

Hence Not sufficient.

statement 2) x is divisible by 10.

x=10-->prime factors 2 and 5. n=2<3. NO

x=30-->prime factors 2,3 and 5. n=3=3 YES

x=210-->prime factors 2,3,5 and 7. n=4>3 YES

Hence Insufficient.

statement 1) and statement 2) together.

LCM of 10 and 6 is 30.

x=30--> prime factors are 2,3 and 5. n=3=3 YES.

x=210-->prime factors are 2,3,5,and 7. n=4>3 YES.

$$Always , n>=3$$

Hence together Sufficient.

ANS C.
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Joined: 31 Dec 2014
Posts: 1
Re: If x is an integer with n distinct prime factors, is n greater than or  [#permalink]

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07 Jun 2018, 10:38
Given, x is an integer and x has distinct prime factors.
so x = p1^a * p2^b * pn^z
Q is n>=3

(i)x is div by 6
6 = 2*3; x=2^a * 3^b * ..pn^z
X can have 2 or more than 2 prime factors.
Not sufficient

(ii)x is div. by 10
10 = 2*5; x=2^a * 5^b * ..pn^z
X can have 2 or more than 2 prime factors.
Not sufficient

(i)+(ii)
x = 2^a * 3^b * 5^c * ..pn^z
X definitely has 3 or more than 3 different prime factors.
Re: If x is an integer with n distinct prime factors, is n greater than or &nbs [#permalink] 07 Jun 2018, 10:38
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