HOT Competition: A function g is defined, for all positive integers x

Question

A function g is defined, for all positive integers x > 3, as  g(x)= 4x-5  if x is even and  g(x) =5x-15  if x is odd, for all positive integers x > 3. What is the value of the positive integer, p?

(1)  g(g(p)) + g(p)= 195

(2)  g(g(g(g(p))))  is even.

Kinshook · Answer

Given: A function g is defined, for all positive integers x > 3, as g(x)= 4x-5 if x is even and g(x)=5x-15 if x is odd, for all positive integers x > 3. What is the value of the positive integer, p?

(1) g(g(p))+g(p)=195
Case1:p is even
g(4p-5)+4p-5=195
4p-5 is odd
5(4p-5)- 15+4p-5=195
24p=240
p = 10
Case 2:p is odd
g(5p-15)+5p-15=195
5p-15 is even
4(5p-15)-5+5p-15=195
25p=275
p=11
NOT SUFFICIENT

(2) g(g(g(g(p)))) is even.
p is even 
The value of p can not be found
NOT SUFFICIENT

(1) + (2) 
(1) g(g(p))+g(p)=195
(2) g(g(g(g(p)))) is even.
p is even
p = 10
SUFFICIENT

IMO C

Posted from my mobile device

binsnitin11 · Answer

A function g is defined, for all positive integers x > 3, as g(x)=4x−5 if x is even and g(x)=5x−15 if x is odd, for all positive integers x > 3. What is the value of the positive integer, p?

lets understand the given first:
g(x) = 4x-5 if x=even, so if we put even value we get g(x=even) = odd value and if we apply given function to the output of g(x=even) than we need to use g(g(x)) = 5(g(x) -15

same happens to if x= odd, it starts with g(x) = 5x-15 and than results even value and we need to use g(x) = 4x-5 function for the output

Now lets see the statement

(1) g(g(p))+g(p)=195g(g(p))+g(p)=195
St. 1 assume p = even above equation become:
5(4p-5)-15 + 4p-5 = 195
solve we get p = 10
if p =odd equation becomes
4(5p-15)-5 + 5p-15 = 195
solve for p we get p =11

so Not sufficient

(2) g(g(g(g(p)))) is even. 
st. 2 tell about the convoluted function results in even value, so if we consider p = even than only it is possible for an even resluts
 if p = even
g(p) = odd
g(g(p))=even
g(g(g(p)))=odd
g(g(g(g(p))))= even

so p can take any even value >3 Not Sufficient

Combining 1 &2 we get p = 10 sufficient

IMO C

Saupayan · Answer

We can't say if p is even or odd from this statement. 
If p is even, g(p) = odd, and g(g(p)) will be even. even + odd can give 195
similarly, if p is odd, g(p) = even and g(g(p)) will be odd. 195 can be the result still.

Now, can we say directly at this step that statement 1 is insufficient? In this case, it turns out the answer is yes. But, I am not so sure we can say that directly without solving for p.
Because we may run into one of the following cases:
1. What if the final equation comes out to be the same irrespective of us considering p EVEN or ODD
2. What if we consider p as EVEN, then solve for p, and it turns out to be odd (or vice versa).
In either of the above cases, A alone will suffice. In this particular case, however, it turns out p = 11 (if we consider it to be odd), or p = 10 (if we consider p even). So, statement 1 is not sufficient

All that this statement tells us is p is even. It doesn't tell us anything about the value of p. So clearly, multiple possibilities exist. In fact, for any even p, the statement 2 will hold true.

But combining statement 2 with 1, we get that p can only be 10 (and not 11). So, they are together sufficient to answer the above question.
Answer: C

ShankSouljaBoi · Answer

First , notice that g of g will be even if x is even and odd if x is odd

Statement one --- Lets say x is even that means g of g of of p will be even and g of p (which is 4p-5) will be odd… so we have a even and a odd number adding up to 195 which is odd as well. Cool so p can be any even value . We can that the statement is insufficient at this point, but analyze further.

Lets say x is odd that means g of g of of p will be odd and g of p (which is 5p-15) will be even… so again, we have a even and a odd number adding up to 195 which is odd as well.

So p can be any particular (stress on this) even integer or a particular(stress on this) odd integer. Hence Insufficient

Again lets say, p is even … then g of g of p will be even … again g of g of (anything even) will be even .

lets say, p is odd … then g of g of p will be odd … again g of g of (anything odd) will be odd . But, per the statement it has to be even so we'll disregard this case.
Statement 2 simply means that p is even. Insufficient by itself.

On combining , lets solve with p as even
we get 20p-40 + 4p-5 = 195 …. 24p = 240 p = 10.

C it is.

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

HOT Competition: A function g is defined, for all positive integers x

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

HOT Competition: A function g is defined, for all positive integers x

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards