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22 Feb 2021, 06:20
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If the sum of the positive factors of a Positive integer N is P and the product of all positive factors of N is Q. Then how many values of N exist from 1 to 50 (both inclusive) such that P*Q = ODD?
A) 5
B) 6
C) 7
D) 8
E) 9
A) 5
B) 6
C) 7
D) 8
E) 9
Source: https://www.GMATinsight.com
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22 Feb 2021, 08:57
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GMATinsight
P*Q = Odd. => So both P and Q should be odd.
Q is the product of factors and Q is odd. It is possible only when all factors are odd : Odd*odd*odd....=odd
If the factors are odd, the number itself has to be ODD.
Now sum of the positive factors, all of which are odd, is odd.
That is odd+odd+odd+...=odd.
This will be the case only when the number of factors are odd.
If the number of factors are odd, the number N will be a square.
So N is odd and a perfect square.
Squares of odd integers from 1 to 50 : Till 7^2 or 49
So 1, 3, 5 and 7.
4 is the answer.
23 Feb 2021, 00:20
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question here is testing + factors of numbers from 1 to 50 inclusive
such that the result of factors P*Q is odd ; which is possible only when the value of both P & Q is odd
we can eliminate option which are even i.e. B, D
also we can see that the square of the numbers from 1 to 7 falls into range 1 to 50 i.e. the square of integer always has odd set of integers.
so total values of N would be 7
option C
such that the result of factors P*Q is odd ; which is possible only when the value of both P & Q is odd
we can eliminate option which are even i.e. B, D
also we can see that the square of the numbers from 1 to 7 falls into range 1 to 50 i.e. the square of integer always has odd set of integers.
so total values of N would be 7
option C
GMATinsight
