number system

[vipulgoyal]

asked whether 30 is a factor of n?
(1) 30 is a factor of the square of n
(2) 30 is a factor of 2n

Ans given C my take A

[srcc25anu]

If stated that N is an INTEGER then we can say Statement 1 is sufficient.
St1: n^2 is divisible by 30
30 = 2 * 3 * 5
n^2 must contain ONLY even powers of any prime factors since its a perfect square
so n^2 could be (2 * 3 * 5)^2 and n would be 2 * 3 * 5. YES 30 is a factor

Lets try with n^2 = 2 * 3 * 5. Now n = sqrt (2 * 3 * 5) in not an integer
so n^2 cannot be 2 * 3 * 5

Any n^2 must have atleast 2nd powers of 2 , 3 and 5.
in any such case, n will be divisible by 30
SUFFICIENT

St2: 30 is factor of 2n
if n = 15, 2n = 30 and 2n divides 30 but 30 is NOT A FACTOR of N
if n = 30, 2n = 60 and 2n as well as n divides 30
Insufficient

Ans A

[srcc25anu]

asked whether 30 is a factor of n?
(1) 30 is a factor of the square of n
(2) 30 is a factor of 2n
Ans given C my take A

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