The Odd Factor Sum of a positive integer is the sum of all its Odd Fac

Question

The Odd Factor Sum of a positive integer is the sum of all its Odd Factors. If positive integer P is divisible by 8 numbers in total, one of which is 42, what is the Odd Factor Sum of P?

A. 20
B. 21
C. 31
D. 32
E. Cannot be determined

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chetan2u · Answer

P must be divisible by all the factors of 42.
42= 2*3*7, so the number of positive factors = (1+1)(1+1)(1+1) = 8

This tells us that P is 42 itself.
Thus, the sum of all its Odd Factors = 1+3+7+21 = 32

D

Crytiocanalyst · Answer

The factors of P are 7,3,2 as 42 is a divisor then

then the prime factorization yield 7,3,2and the no of factors as (1+1)*(1+1)*(1+1) =8

The sum becomes 1+7 +3+21 = 32

THerefore IMO D

TCHRL · Answer

The factors can be listed based on the initial factor, 42: 42; 21; 7; 4 ;3; 2 ; 1 This list gives all odd factors of 42. 21+7+3+1 = 32 .

Note that we are missing one factor to reach the 8 menitonned.

We can assume that the last factor would be x itself, and given that 42 is a factor of x, x=42 * ( 1;2;3... ;42) = even, thus all odd factors have already been found.

(Note that I score 47-48 in Quant FE, my reasoning is probably not optimal).

The Odd Factor Sum of a positive integer is the sum of all its Odd Fac

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The Odd Factor Sum of a positive integer is the sum of all its Odd Fac

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