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21 Mar 2023, 07:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (02:17) correct
27%
(02:17)
wrong
based on 41
sessions
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If n is a positive integer, how many positive odd factors does it have ?
(1) The highest integer power of 2, that divides n is 16.
(2) n has a total of 68 factors and 3 prime factors.
(1) The highest integer power of 2, that divides n is 16.
(2) n has a total of 68 factors and 3 prime factors.
How many odd positive integers divide the positive integer n completely?
(1) 16 is the highest power of 2 that divides n
(2) n has a total of 68 factors and 3 prime factors.
(1) 16 is the highest power of 2 that divides n
(2) n has a total of 68 factors and 3 prime factors.
20 May 2023, 20:10
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Bunuel
Statement 1
This tells us that n will have 2 as one of the factors, but does not tell us anything about other factors (whether are any or not, let alone how many)
Not sufficient.
Statement 2
This just tells us that n has a total of 68 factors and only 3 prime factors.
If we factorize 68, we get : 68 = \(2^2 . 17^1\)
Using this -
If n has all 3 odd prime factors : 3, 7, and 11
We can get 68 prime factors : 3^16 . \(7^1 . 11^1\)
If n has one even prime factor and 2 odd prime factors
We can get 68 prime factors : 2^16 . \(7^1 . 11^1\)
Not sufficient.
Combined together
We know one of the factors is 2 using statement 1, and statement 2 tells us that n has 3 prime factors.
Only 2 is an even prime number, all the other prime numbers are odd.
Using this property we can say that n has 2 odd prime factors.
Sufficient.
Therefore, C.
21 May 2023, 11:30
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Bunuel
Understanding Statement 1 alone:
2^16 is a factor of n, but there is no information about the odd factors of n.
Insufficient
Understanding Statement 2 alone:
When n has a total of 68 factors and 3 prime factors, it means that the three distinct prime factors p, q and r must have powers as 1, 1, and 16. There is no information about the factors a, b and c.
Insufficient
Understanding Statement 1 and 2 together:
Prime number 2 has a power of 16 and other two prime numbers must be odd with power of 1 and 1 respectively. Hence, we can find number of odd factors of n.
Sufficient
