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# If F is a factor of 105, is F is a prime number?

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
If F is a factor of 105, is F is a prime number?  [#permalink]

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25 Jul 2018, 05:02
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Difficulty:

65% (hard)

Question Stats:

53% (01:21) correct 47% (01:29) wrong based on 128 sessions

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If F is a factor of 105, is F is a prime number?

(1) F is not divisible by 3

(2) F < 10

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: If F is a factor of 105, is F is a prime number?  [#permalink]

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25 Jul 2018, 05:07
If F is a factor of 105, is F is a prime number?
105=3*5*7.... Number of factors =2*2*2=8
Factors are 1,3,5,7,15,21,35,105

(1) F is not divisible by 3
So F can be 1,5,7,35...
If 5 or 7, yes
If 1 or 35, no
Insufficient

(2) F < 10
1,3,5,7..
If 3,5,7, yes
If 1, no
Insufficient

Combined
If 5 or 7, yes
If 1, no
Insufficient

E
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Re: If F is a factor of 105, is F is a prime number?  [#permalink]

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25 Jul 2018, 05:11
If F is a factor of 105, is F is a prime number?

(1) F is not divisible by 3

(2) F < 10

factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

(1) F is not divisible by 3 - Insufficient

F = 5 (prime)
F = 35 (not prime)

(2) F < 10 - Insufficient

F = 5 (prime)
F = 1 (not prime)

(1)+(2) - Insufficient

F = 5 (prime)
F = 1 (not prime)

Option E
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Re: If F is a factor of 105, is F is a prime number?  [#permalink]

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25 Jul 2018, 07:41
Bunuel wrote:
If F is a factor of 105, is F is a prime number?

(1) F is not divisible by 3

(2) F < 10

Note: F is a factor of 105. It means F mustn't be a prime factor. We are asked whether F is prime.

Before Dealing with statement , it's better to factorize 105.

1*105 = 105

15*7 = 105

35*3 = 105

21*5 = 105

All these probable factors are listed above.

Statement 1: F is not divisible by 3. Among the factors , 7 ,5 and 35 are not divisible by 3. 7 and 5 are prime but 35 and 1 are not. NOT sufficient.

Statement 2: F < 10 . Still 1 , 7 , 5 are not divisible by 3. Where 7 and 5 are prime 1 is not. Not Sufficient.

Combining both Statement : Still Not sufficient.

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Re: If F is a factor of 105, is F is a prime number?  [#permalink]

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07 Sep 2018, 08:29
Bunuel wrote:
If F is a factor of 105, is F is a prime number?

(1) F is not divisible by 3

(2) F < 10

$$\frac{{3 \cdot 5 \cdot 7}}{F} = \operatorname{int}$$

$$F\,\mathop = \limits^? \,\,{\text{prime}}$$

$$\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered} \,F = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ F = \,\,5\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \end{gathered} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Re: If F is a factor of 105, is F is a prime number?   [#permalink] 07 Sep 2018, 08:29
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