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