Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Oct 27 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 04 Apr 2010
Posts: 117

The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
14 Feb 2011, 18:22
Question Stats:
26% (03:00) correct 74% (02:50) wrong based on 1160 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Consider me giving KUDOS, if you find my post helpful. If at first you don't succeed, you're running about average. ~Anonymous




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
16 Jan 2013, 06:36
MOKSH wrote: 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 Notice that when x is odd, g(x) = x + 5 (Recall that Odd + Odd = Even) This means g(x) becomes even when x is odd. So if g(x) is odd, x MUST have been even. Since g(g(g(g(g(x))))) = 19, we can say that g(g(g(g(x)))) must be even i.e. 19*2 = 38 Since g(g(g(g(x)))) = 38, g(g(g(x))) can be either even or odd so it can take 2 values: 38*2 = 76 or 38  5 = 33 If g(g(g(x))) = 76 g(g(x)) can again take two values  one even and one odd If g(g(g(x))) = 33, g(g(x)) MUST be even 33*2 = 66. So g(g(x)) can take 3 values: 2 even and one odd. Notice that every even value gives you 2 values of the inner expression  one even and one odd  and every odd value gives you only one even value of the inner expression. Then g(x) can take 5 different values  3 even and 2 odd Then x can take 8 different values  5 even and 3 odd An example of pattern recognition.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 563
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
16 Jan 2013, 01:50
MOKSH wrote: 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 Wow, more like a mathmatical puzzle than a gmat question. I love it! Let me define terms: in g(x) = R x is argument, R is result, g() is function, in g(g(g(g(g(x))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1: 1 Eveng2: 1*(Even,Odd ) = 1 Even 1 Oddg3: 1*(Even,Odd) + 1 Even = 2 Even 1 Oddg4: 2*(Even, Odd) + 1 Even = 3 Even 2 Oddg5: 3*(Even, Odd) + 2 Even = 5 Even 3 Odd = Total 8Ans D it is!
_________________




Retired Moderator
Joined: 16 Nov 2010
Posts: 1252
Location: United States (IN)
Concentration: Strategy, Technology

The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
14 Feb 2011, 19:18
g(g(g(g(g(x))))) = 19 => g(g(g(g(x)))) is even = 38 (if it were odd, the output is even) now g(g(g(x))) can be 76 or 33 g(g(x)) can be 152, 71 or 66 g(x) can be 304, 147, 142, 132 or 61 x can be 608,299,294,284,137, 127, 264, 132 So total 8 values, hence the answer is D
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 01 Dec 2012
Posts: 30
Concentration: Finance, Operations
GPA: 2.9

The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
15 Jan 2013, 16:46
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



eGMAT Representative
Joined: 02 Nov 2011
Posts: 2867

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
16 Jan 2013, 01:58
MOKSH wrote: 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 Hope this image helps you clarify these possible 8 set of values of x. Shalabh Jain
_________________



Manager
Joined: 04 Oct 2011
Posts: 168
Location: India
Concentration: Entrepreneurship, International Business
GPA: 3

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
16 Jan 2013, 02:18
Vips0000 wrote: MOKSH wrote: 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 Wow, more like a mathmatical puzzle than a gmat question. I love it! Let me define terms: in g(x) = R x is argument, R is result, g() is function, in g(g(g(g(g(x))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1: 1 Eveng2: 1*(Even,Odd ) = 1 Even 1 Oddg3: 1*(Even,Odd) + 1 Even = 2 Even 1 Oddg4: 2*(Even, Odd) + 1 Even = 3 Even 2 Oddg5: 3*(Even, Odd) + 2 Even = 5 Even 3 Odd = Total 8Ans D it is! Vips im totally lost in this... can u explain!!! how u started g1 with even? based on answer choices? if so how come u calculated g2?
_________________
GMAT  Practice, Patience, Persistence Kudos if u like



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 563
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
16 Jan 2013, 02:42
shanmugamgsn wrote: Vips0000 wrote: MOKSH wrote: 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 Wow, more like a mathmatical puzzle than a gmat question. I love it! Let me define terms: in g(x) = R x is argument, R is result, g() is function, in g(g(g(g(g(x))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1: 1 Eveng2: 1*(Even,Odd ) = 1 Even 1 Oddg3: 1*(Even,Odd) + 1 Even = 2 Even 1 Oddg4: 2*(Even, Odd) + 1 Even = 3 Even 2 Oddg5: 3*(Even, Odd) + 2 Even = 5 Even 3 Odd = Total 8Ans D it is! Vips im totally lost in this... can u explain!!! how u started g1 with even? based on answer choices? if so how come u calculated g2? ha ha.. the explanation was this: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Anyway, to start from scratch: how u started g1 with even? based on answer choices? question says, g(x) = x/2 , if x is even=> Observation: if x is even, result is even/2 which could be odd or even. g(x) = x+5, if x is odd => Observation: if x is odd, result is always even. (odd number+5= even number) Another way to get there : We know final result is 19. that is: g(something) =19 Now what is this something? it could be 38 giving 19 when divided by 2. Or it could be 14 when 5 is added. However, it can not be 14 because 14 is even and g(14) will be 7 not 19 by the definition of g(x). So there is only possiblity 38. So if result is odd, then argument must have been even. Therefore for argument of g1, you start with Even since the result is odd (19). if so how come u calculated g2Lets again see, we found out that argument of g1 was even. Now this even could have been result of another even number or an odd number. Let see the example: taking forward previous values. We found above that argument for g1 is 38. now, argument for g2? we know that g2(something) =38 What is this something? it could be 76, which gives 38 when divided by 2. Or it could be 33 which gives 38 when 5 is added. Both of these values are possible as per g(x) definition. It can not be a gmat question. but its good fun. to summarize, try to understand these lines: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even
_________________



Manager
Joined: 11 Mar 2014
Posts: 118
Location: India
Concentration: Strategy, Technology
GPA: 3.3
WE: Engineering (Other)

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
11 Mar 2014, 23:25
VeritasPrepKarishma wrote: MOKSH wrote: 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 Notice that when x is odd, g(x) = x + 5 (Recall that Odd + Odd = Even) This means g(x) becomes even when x is odd. So if g(x) is odd, x MUST have been even. Since g(g(g(g(g(x))))) = 19, we can say that g(g(g(g(x)))) must be even i.e. 19*2 = 38 Since g(g(g(g(x)))) = 38, g(g(g(x))) can be either even or odd so it can take 2 values: 38*2 = 76 or 38  5 = 33 If g(g(g(x))) = 76 g(g(x)) can again take two values  one even and one odd If g(g(g(x))) = 33, g(g(x)) MUST be even 33*2 = 66. So g(g(x)) can take 3 values: 2 even and one odd. Notice that every even value gives you 2 values of the inner expression  one even and one odd  and every odd value gives you only one even value of the inner expression. Then g(x) can take 5 different values  3 even and 2 odd Then x can take 8 different values  5 even and 3 odd An example of pattern recognition. Karishma, Your method is incorrect (though the answer is correct). You forgot that in such questions, there may be overlapping answers. The only way to solve this is to find all possible values of x. Solving step by step gives x = 122 or 127 or 264 or 294 or 608 or 299 or 284 or 137. Hence (D).



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
12 Mar 2014, 03:38
RG800 wrote: VeritasPrepKarishma wrote: MOKSH wrote: 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 Notice that when x is odd, g(x) = x + 5 (Recall that Odd + Odd = Even) This means g(x) becomes even when x is odd. So if g(x) is odd, x MUST have been even. Since g(g(g(g(g(x))))) = 19, we can say that g(g(g(g(x)))) must be even i.e. 19*2 = 38 Since g(g(g(g(x)))) = 38, g(g(g(x))) can be either even or odd so it can take 2 values: 38*2 = 76 or 38  5 = 33 If g(g(g(x))) = 76 g(g(x)) can again take two values  one even and one odd If g(g(g(x))) = 33, g(g(x)) MUST be even 33*2 = 66. So g(g(x)) can take 3 values: 2 even and one odd. Notice that every even value gives you 2 values of the inner expression  one even and one odd  and every odd value gives you only one even value of the inner expression. Then g(x) can take 5 different values  3 even and 2 odd Then x can take 8 different values  5 even and 3 odd An example of pattern recognition. Karishma, Your method is incorrect (though the answer is correct). You forgot that in such questions, there may be overlapping answers. The only way to solve this is to find all possible values of x. Solving step by step gives x = 122 or 127 or 264 or 294 or 608 or 299 or 284 or 137. Hence (D). You are starting with 19 and performing 2 operations on it (*2 or 5) in different number and different order. Each chain of operations will give you a different result. You don't have to do it to find that out.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 11 Mar 2014
Posts: 118
Location: India
Concentration: Strategy, Technology
GPA: 3.3
WE: Engineering (Other)

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
13 Mar 2014, 05:44
VeritasPrepKarishma wrote: You are starting with 19 and performing 2 operations on it (*2 or 5) in different number and different order. Each chain of operations will give you a different result. You don't have to do it to find that out. Why can't the *2 of one number be equal to the 5 of another? I don't get it



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
13 Mar 2014, 06:21
RG800 wrote: VeritasPrepKarishma wrote: You are starting with 19 and performing 2 operations on it (*2 or 5) in different number and different order. Each chain of operations will give you a different result. You don't have to do it to find that out. Why can't the *2 of one number be equal to the 5 of another? I don't get it You are starting with the same number 19. Think about it: if you multiply 19 by 2 four times and subtract 5 once, can it be equal to if you multiply by 2 three times and subtract 5 twice? Similarly, if you multiply by 2 four times and then subtract 5 once, can it be equal to if you subtract 5 once and then multiply by 2 four times. The sequence in which operations are applied on a number change the number.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 22 Feb 2009
Posts: 156

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
06 Aug 2014, 22:15
Vips0000 wrote: MOKSH wrote: 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 Wow, more like a mathmatical puzzle than a gmat question. I love it! Let me define terms: in g(x) = R x is argument, R is result, g() is function, in g(g(g(g(g(x))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1: 1 Eveng2: 1*(Even,Odd ) = 1 Even 1 Oddg3: 1*(Even,Odd) + 1 Even = 2 Even 1 Oddg4: 2*(Even, Odd) + 1 Even = 3 Even 2 Oddg5: 3*(Even, Odd) + 2 Even = 5 Even 3 Odd = Total 8Ans D it is! I like your answer, but g1 should be g5, g2 should be g4, .... g5 should g1 in the possibilities section. Let me know If I am wrong
_________________
......................................................................... +1 Kudos please, if you like my post



Intern
Joined: 11 Apr 2016
Posts: 39
Location: India
Concentration: Marketing, Technology
WE: Business Development (Computer Software)

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
10 Nov 2016, 01:56
Best approach is to start with 19 and create a tree of possible values till 5 layers and eliminate options between even and odd.
Layer 1 19 38 or 24
Layer 2 38  76 or 33 24  48 or 19
Layer 3 76  152 or 71 33  66 or 28 48  28 or 43 19  38 or 14(Eliminate 14 since it cannot be even number)
Layer 4 & Layer 5 keep on solving and eliminate based on even or odd number possibility. Final answer is 8 possible values



Intern
Joined: 19 Jul 2018
Posts: 16
Location: India
GPA: 3.9

Re: The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
19 Jan 2019, 03:10
Even G can generate 1 Odd and One Even Inner expression (x) and Odd G can only generate 1 Even Inner Expression (x)
My Answer: 8



Intern
Joined: 19 Jul 2018
Posts: 16
Location: India
GPA: 3.9

The function g(x) is defined for integers x such that if x
[#permalink]
Show Tags
19 Jan 2019, 03:10
https://photos.app.goo.gl/L4gEV8RtxvVWqi9T9Even G can generate 1 Odd and One Even Inner expression (x) and Odd G can only generate 1 Even Inner Expression (x) My Answer: 8




The function g(x) is defined for integers x such that if x
[#permalink]
19 Jan 2019, 03:10






