The function g(x) is defined for integers x such that if x is even, g(x) = x/2 and if x is odd, g(x) = x + 5. Given that g(g(g(g(g(x))))) = 19, how many possible values for x would satisfy this equation? A. 1 B. 5 C. 7 D. 8 E. 11

2:42 sec method: if g(x) is odd, it means x was even. (because if x is odd, then g(x) will be x+5, odd+odd= even and thus not possible). and thus it was divided by 2. So multiply g(x) by 2 to get x. And if g(x) is even, either x is odd or even.. 2 options thus g(g(g(g(g(x)))))=19 odd thus, g(g(g(g(x)))) has only one value=38 as its even, g(g(g(x))) was either 74(=38*2) or 33(38-3) if 74, then again g(g(x)) can have 2 values. (148 or 69) and if 33, then only 1 value = 66 value of g(x) = 296,143,64,132,61 value of x = 296*2,291,286,128,59,264,127,122 IMO D While finding the answer i didn't calculate all values Just remember if odd, then we get even. and if even, then we get both even & odd as 19 is odd, 1st g() = even 2nd g()=even/odd 3rd g()=even/odd/even 4th g()=even/odd/even/even/odd 5th g()=even/odd/odd/even/odd/even/odd/even Total 8

2:42!!!! is a brilliant effort your A & E are exactly as OA & OE !! Except, the possible values of x will be 608, 299, 294, 284, 137, 264, 127, 122 And as 19 is odd, 1st g() = even 2nd g()=even/odd 3rd g()=even/odd/even 4th g()=even/odd/even/even/odd 5th g()=even/odd/odd/even/odd/even/odd/even the 5th g()=even/odd/even/even/odd/even/odd/even

sourabh33 wrote:2:42!!!! is a brilliant effort your A & E are exactly as OA & OE !! Except, the possible values of x will be 608, 299, 294, 284, 137, 264, 127, 122 And as 19 is odd, 1st g() = even 2nd g()=even/odd 3rd g()=even/odd/even 4th g()=even/odd/even/even/odd 5th g()=even/odd/odd/even/odd/even/odd/even the 5th g()=even/odd/even/even/odd/even/odd/even Thanks for the correction.