EgmatQuantExpert wrote:
Question:
\(x\) is a positive integer less than \(30\), which of the following option correctly indicates the number of values of \(x\) for which \(x^2/18\) has \(2\) factors?
A) 0
B) 1
C) 4
D) 5
E) 7
1=< x < 30
for \(x^2/18\) to have 2 factors x^2 greater than 18
5<= x < 30
now x can't be odd as 18 = even x odd and x can't be only even i.e 16,8 etc
so from 5 to 30 remove odd values and purely even value( powers of 2 )
6 10 12 14 18 20 22 24 26 28
here numbers must be multiple of 3 as 18 = 9x2 and if x has 3 x^2 will have 9
so
6 12 18 24 left
6^2 = 36 and 36/18 = 2 ( factors 2)
12^2 = 144 and 144/18 = 8 factors 4
18^2/18 = 18 factors 6
24^2/18 = 4/3x24 = 32 2^5 factors 6
x can only be 6
(B) imo