Bunuel wrote:

What is the value of positive integer x?

(1) x<45

(2) 45 is a factor of 4x^2

Given x>0 & Integer

Find Value of 'x'

Statement 1 x<45

=> So x=1,2,3,4....44

=> Many Values of 'x'. Therefore INSUFFICIENT

Statement 2 45 is a factor of \(4x^2\)

=> So \(4x^2\) is a multiple of 45

=> OR \(4x^2=45*k\) ----- 'k' some constant

=> OR \(x^2=\frac{(45*k)}{4}\)

=> For 'x' to be Positive Integer \(\frac{(45*k)}{4}\) should be a PERFECT SQUARE & Integer.

=> Now Prime Factorising 45 we have \(45=3^2*5\)

=> Therefore 'k' should be \((4*5)\) or \((4*5*2^2)\) or \((4*5*2^2*3^3)\) or \((4*5^3*2^2)\) and so on

=> Thus \(x^2\)=\(\frac{(45*4*5)}{4}\) or \(\frac{(45*4*5*2^2)}{4}\) or \(\frac{(45*4*5*2^2*3^2)}{4}\) or \(\frac{(45*4*5^3*2^2)}{4}\) and so on

=> OR x=15,30,90,150..... so on

=> Many Values of 'x'. Therefore INSUFFICIENT

BOTH Stat 1 & 2

=> x=15,30,90,150..... so on ---- from Stat 2

=> x=15,30 --------------- constraint of Stat 1

=> AGAIN 'x' has 2 values. Therefore INSUFFICIENT

Therefore 'E'

Thanks

Dinesh