Saturday, September 12, 2015

Data sufficiency - factors

Data sufficiency

If N = 3x x 5y, where x and y are positive integers, and N has 12 positive factors, what is the value of N?
(1) 9 is NOT a factor of N
(2) 125 is a factor of N


The number of factors  is given by formula (x+1)(y+1) where x,y are the powers of the prime numbers after prime factorization.

12 = (x+1)(y+1)
The product of (6,2) (4,3) give 12.

Hence the pair combinations of x and y can be (5,1)(11,0),(3,2) { x =5 and y=1 or x=1 and y=5)

Hence N = 3x 5y

As per statement 1. If 9 is not a factor of N. It means the values of x and y should be (1,5) 
sufficient.

As per statement 2. if 125 is a factor of N, it means the values of x and y can be any combination.

Hence A



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