GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 09 Apr 2020, 22:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The function g(x) is defined for integers x such that if x

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Apr 2010
Posts: 114
The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

14 Feb 2011, 17:22
15
76
00:00

Difficulty:

95% (hard)

Question Stats:

25% (02:58) correct 75% (02:50) wrong based on 824 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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10264
Location: Pune, India
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

16 Jan 2013, 05:36
17
12
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

Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 552
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, 00:50
12
9
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 Even
g2: 1*(Even,Odd ) = 1 Even 1 Odd
g3: 1*(Even,Odd) + 1 Even = 2 Even 1 Odd
g4: 2*(Even, Odd) + 1 Even = 3 Even 2 Odd
g5: 3*(Even, Odd) + 2 Even = 5 Even 3 Odd = Total 8

Ans D it is!
##### General Discussion
Retired Moderator
Joined: 16 Nov 2010
Posts: 1193
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, 18:18
6
6
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, 15:46
5
1
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
e-GMAT Representative
Joined: 02 Nov 2011
Posts: 2986
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

16 Jan 2013, 00:58
10
2
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: 165
Location: India
GMAT 1: 440 Q33 V13
GPA: 3
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

16 Jan 2013, 01:18
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 Even
g2: 1*(Even,Odd ) = 1 Even 1 Odd
g3: 1*(Even,Odd) + 1 Even = 2 Even 1 Odd
g4: 2*(Even, Odd) + 1 Even = 3 Even 2 Odd
g5: 3*(Even, Odd) + 2 Even = 5 Even 3 Odd = Total 8

Ans 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?
Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 552
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, 01:42
6
2
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 Even
g2: 1*(Even,Odd ) = 1 Even 1 Odd
g3: 1*(Even,Odd) + 1 Even = 2 Even 1 Odd
g4: 2*(Even, Odd) + 1 Even = 3 Even 2 Odd
g5: 3*(Even, Odd) + 2 Even = 5 Even 3 Odd = Total 8

Ans 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?

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 g2
Lets 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
GMAT 1: 760 Q50 V41
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, 22:25
1
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: 10264
Location: Pune, India
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

12 Mar 2014, 02:38
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

Manager
Joined: 11 Mar 2014
Posts: 118
Location: India
Concentration: Strategy, Technology
GMAT 1: 760 Q50 V41
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, 04:44
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: 10264
Location: Pune, India
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

13 Mar 2014, 05:21
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

Manager
Joined: 22 Feb 2009
Posts: 149
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

06 Aug 2014, 21:15
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 Even
g2: 1*(Even,Odd ) = 1 Even 1 Odd
g3: 1*(Even,Odd) + 1 Even = 2 Even 1 Odd
g4: 2*(Even, Odd) + 1 Even = 3 Even 2 Odd
g5: 3*(Even, Odd) + 2 Even = 5 Even 3 Odd = Total 8

Ans 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
Intern
Joined: 11 Apr 2016
Posts: 38
Location: India
Concentration: Marketing, Technology
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

10 Nov 2016, 00:56
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: 22
Location: India
Schools: IIMB (D), Bocconi '21
GMAT 1: 680 Q49 V33
GRE 1: Q162 V167
GPA: 3.7
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

19 Jan 2019, 02:10
Even G can generate 1 Odd and One Even Inner expression (x)
and Odd G can only generate 1 Even Inner Expression (x)

Intern
Joined: 19 Jul 2018
Posts: 22
Location: India
Schools: IIMB (D), Bocconi '21
GMAT 1: 680 Q49 V33
GRE 1: Q162 V167
GPA: 3.7
The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

19 Jan 2019, 02:10
https://photos.app.goo.gl/L4gEV8RtxvVWqi9T9
Even G can generate 1 Odd and One Even Inner expression (x)
and Odd G can only generate 1 Even Inner Expression (x)

Non-Human User
Joined: 09 Sep 2013
Posts: 14506
Re: The function g(x) is defined for integers x such that if x  [#permalink]

### Show Tags

09 Feb 2020, 01:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The function g(x) is defined for integers x such that if x   [#permalink] 09 Feb 2020, 01:03
Display posts from previous: Sort by