If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
(1) n is even.
(2) The cube root of n is an integer.Sol: Given n= I^2 where I some integer and 2<n<100 or 2<I^2<100
St 1: n is even and only possible squares in the given range are for 4,6,8 which are 16,36,
64 respectively...So n can be 4,6 or 8.
A and D ruled out
St2: Cube root of n= a where " a " is an integer So Taking cube we get
n=a^3.So n is a cube of an integer "a" but " a^3" should be between 2 and 100 so a^3=27 or
64. Since 2 (n=3 or 4) answers are there so not possible.
Combining we get,
n is even and cube root of n is an integer so only possible value of n=64
Ans is C
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