Let n = a^p * b^q* ....
Statement 1:
n^3 has total 7 divisors
The number of factors is given by (p+1)(q+1)...
If the number of factors = 7
Only possibility is: (6+1)(1) = 7
=> n = a^2p
But, there can be multiple values of n depending on values of 'a' and 'p'
Statement 1 is insufficient.
Statement 2:
3*n^2 has 10 total divisors
n^2 = a^2p * b^2q...
And 3*n^2 = 3 * a^2p * b^2q...
Multiple possibilities can arise depending on values of 'a', 'b', 'p', and 'q'
Statement 2 is insufficient
Statement 1 and Statement 2:
n = a^2p
=> n^2 = a^4p
Number of factors = (4+1) = 5
But, number of factors of 3* a^4p = 8
=> a and p can be found out
Statement 1 and 2 together are sufficient.
Answer : C
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MBA - IB, IIFT | Class of 2018 - 20
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