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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: 43850
If x is an integer with n distinct prime factors, is n greater than or [#permalink]

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13 Dec 2015, 04:37
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Difficulty:

55% (hard)

Question Stats:

58% (00:57) correct 42% (00:59) wrong based on 114 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.
[Reveal] Spoiler: OA

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Joined: 06 Oct 2013
Posts: 46
If x is an integer with n distinct prime factors, is n greater than or [#permalink]

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14 Dec 2015, 04:54
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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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Re: If x is an integer with n distinct prime factors, is n greater than or [#permalink]

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01 Mar 2017, 04:36
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Re: If x is an integer with n distinct prime factors, is n greater than or   [#permalink] 01 Mar 2017, 04:36
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