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# How many odd factors does the integer n have?

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Intern
Joined: 08 Jul 2018
Posts: 39
How many odd factors does the integer n have?  [#permalink]

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15 Jul 2018, 10:23
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:28) correct 40% (01:06) wrong based on 15 sessions

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How many odd factors does the integer n have?

(1) 16 is the highest power of 2 that divides n

(2) n has a total of 68 factors and 3 prime factors.

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

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15 Jul 2018, 10:47
How many odd factors does the integer n have?

(1) 16 is the highest power of 2 that divides n
So 2^16 included but nothing about odd prime factors
Insufficient

(2) n has a total of 68 factors and 3 prime factors.
Now $$68=2*2*17=(1+1)(1+1)(16+1)$$
So the number is $$a*b*c^{16}$$
But we don't know what these a,b and c are..
Insufficient

Combined
We know that 2 has 16 to its power and $$a*b*c^{16}$$
So a and b are odd prime factors and the number of factors =(1+1)(1+1)=2*2=4
Sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: How many odd factors does the integer n have? &nbs [#permalink] 15 Jul 2018, 10:47
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