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sourabh33: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Mar 22, 2011 12:01 pm; Thanked: 21 times; Followed by:3 members; GMAT Score:720

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by sourabh33 » Thu Jun 02, 2011 4:12 am

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

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Source: Beat The GMAT — Problem Solving | Thu Jun 02, 2011 4:12 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Thu Jun 02, 2011 4:40 am

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

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sourabh33: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Mar 22, 2011 12:01 pm; Thanked: 21 times; Followed by:3 members; GMAT Score:720

by sourabh33 » Thu Jun 02, 2011 5:57 am

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

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vikram4689: Legendary Member; Posts: 1325; Joined: Sun Nov 01, 2009 6:24 am; Thanked: 105 times; Followed by:14 members

by vikram4689 » Thu Jun 02, 2011 7:14 am

Nice Method Canes....thanks

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Thu Jun 02, 2011 7:36 am

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