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How many different positive factors does the integer n have?

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Joined: 02 Sep 2009
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How many different positive factors does the integer n have?  [#permalink]

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21 Sep 2018, 01:33
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Difficulty:

25% (medium)

Question Stats:

72% (00:38) correct 28% (00:56) wrong based on 39 sessions

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How many different positive factors does the integer n have?

(1) $$n = a^4b^3$$, where a and b are different positive prime numbers.
(2) The only positive prime numbers that are factors of n are 5 and 7.

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Re: How many different positive factors does the integer n have?  [#permalink]

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21 Sep 2018, 01:42
Bunuel wrote:
How many different positive factors does the integer n have?

(1) $$n = a^4b^3$$, where a and b are different positive prime numbers.
(2) The only positive prime numbers that are factors of n are 5 and 7.

Question: How many different positive factors does the integer n have?

Number of factors of a number $$= (p+1)*(q+1)*(r+1)...$$
if, Number $$= a^p*b^q*c^r$$... where a, b, c,... are distinct prine factors of number n

Statement 1:$$n = a^4b^3$$, where a and b are different positive prime numbers.

i.e. Number of factors of $$n = (4+1)*(3+1) = 12$$

SUFFICIENT

Statement 2:The only positive prime numbers that are factors of n are 5 and 7
But the exponents of 5 and 7 are unknown hence

NOT SUFFICIENT

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Re: How many different positive factors does the integer n have?  [#permalink]

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22 Sep 2018, 03:53

Solution

Given:
• The number n is an integer

To find:
• The number of different positive factors of n

Analysing Statement 1
From the information given in statement 1, $$n = a^4b^3$$, where a and b are different positive prime numbers.

• Therefore, number of factors of n = (4 + 1) x (3 + 1) = 5 x 4 = 20

Hence, statement 1 is sufficient

Analysing Statement 2
From the information given in statement 2, the only positive prime factors of n are 5 and 7.

• However, we don’t know the powers of each of those prime factors.

Hence, statement 2 is not sufficient.

The correct answer is option A.

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Re: How many different positive factors does the integer n have? &nbs [#permalink] 22 Sep 2018, 03:53
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