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# If p is divisible by 7 and q is divisible by 6, pq must have at least

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Joined: 02 Sep 2009
Posts: 59590
If p is divisible by 7 and q is divisible by 6, pq must have at least  [#permalink]

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13 Aug 2018, 04:56
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Difficulty:

35% (medium)

Question Stats:

49% (00:42) correct 51% (00:48) wrong based on 68 sessions

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If p is divisible by 7 and q is divisible by 6, pq must have at least how many factors greater than 1?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Eight

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Re: If p is divisible by 7 and q is divisible by 6, pq must have at least  [#permalink]

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13 Aug 2018, 05:02
Bunuel wrote:
If p is divisible by 7 and q is divisible by 6, pq must have at least how many factors greater than 1?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Eight
Option (B)
Actually pq has 5 factors greater than 1. Is that correct?
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Re: If p is divisible by 7 and q is divisible by 6, pq must have at least  [#permalink]

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13 Aug 2018, 07:30
kaushal25 wrote:
Bunuel wrote:
If p is divisible by 7 and q is divisible by 6, pq must have at least how many factors greater than 1?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Eight
Option (B)
Actually pq has 5 factors greater than 1. Is that correct?

No it can't be as

Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

So, least no of factors greater than 1 are 7 {2, 3, 6, 7, 14, 21, 42}, Answer must be (D)
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Re: If p is divisible by 7 and q is divisible by 6, pq must have at least  [#permalink]

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13 Aug 2018, 10:18
1
Bunuel wrote:
If p is divisible by 7 and q is divisible by 6, pq must have at least how many factors greater than 1?

(A) One
(B) Three
(C) Six
(D) Seven
(E) Eight

p is divisible by 7

q is divisible by 6

So, pq could be 42 and its multiples. We are looking for least number of factors GREATER than 1.

Let's factorize 42.

42 = 3*2*7

Total factor: (1+1 ) (1 + 1 ) (1 + 1) = 8

But we need to deduct 1 as we are looking for factors greater than 1.

So , there are at least 7 factors.

Re: If p is divisible by 7 and q is divisible by 6, pq must have at least   [#permalink] 13 Aug 2018, 10:18
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