Last visit was: 18 Nov 2025, 14:08 It is currently 18 Nov 2025, 14:08
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Oct 2025
Posts: 3,380
Own Kudos:
2,141
 [5]
Given Kudos: 69
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,380
Kudos: 2,141
 [5]
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even Updated on: 08 Apr 2020, 00:11
Originally posted by GMATWhizTeam on 05 Apr 2020, 08:34.
Last edited by GMATWhizTeam on 08 Apr 2020, 00:11, edited 2 times in total.
1
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

27% (02:40) correct 73% (02:48) wrong based on 121 sessions

History

Date
Time
Result
Not Attempted Yet
If x and y are positive integers, is \((x+2)^{y+2}+x^y (y−2)^{x+2} \) even?

    (1) \(5x+8x^2+12x^3+9\) is odd.
    (2) \(3y+(11+y)+35(3y+2) \) is even.


GMATWhiz Quant Prepathon - Lesson 1 Question 1

Share your answers with explanations to participate in the Prepathon and win exciting prizes! Access the 1st lesson of the Prepathon using this link.

If you want to access the other posts of the Prepathon and participate in it, bookmark the Megathread of the Prepathon. Stay tuned and Enjoy learning!
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Oct 2025
Posts: 3,380
Own Kudos:
2,141
 [7]
Given Kudos: 69
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,380
Kudos: 2,141
 [7]
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even Updated on: 05 Apr 2020, 22:23
Originally posted by GMATWhizTeam on 05 Apr 2020, 08:37.
Last edited by GMATWhizTeam on 05 Apr 2020, 22:23, edited 2 times in total.
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
I hope you were able to internalize the first skill that we discussed in the Prepathon. Here's the detailed solution to the first question. Even if you got the question right make sure that you check out the method in the solution to ensure that you have solved it using the right method. All the best!



Feel free to post any doubts that you may have in the forum below. We will be happy to help you with your queries :)
General Discussion
User avatar
sauravleo123
User avatar
Joined: 27 Dec 2012
Last visit: 04 May 2020
Posts: 108
Own Kudos:
271
 [2]
Given Kudos: 23
Posts: 108
Kudos: 271
 [2]
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 05 Apr 2020, 08:56
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1: 5x+8x^2+12x^3= even
So 5x= even
So x=even
Now (x+2)^(y+2)+x^y(y-2)^(x+2)
= (even)^(y+2)+even^y(y-2)^(even+2)
= even
Sufficient
Statement 2: 3y+11+y+35(3y+2)=even
So 3y+y+35(3y+2)= odd
Case 1: y= odd
Odd+odd+odd= odd
Case 2: y=even
Even + even + even = odd
This case is not valid
Therefore y=odd
Back to question stem
(X+2)^odd+ x^odd(odd-2)^(x+2)
Now case 1: x=odd
odd^odd+ odd*odd= even
Case 2: x=even
Even+even=even
Both cases of x gives the same answer to the target question
Sufficient
D

Posted from my mobile device
User avatar
shameekv1989
User avatar
Joined: 14 Dec 2019
Last visit: 17 Jun 2021
Posts: 820
Own Kudos:
986
 [1]
Given Kudos: 354
Location: Poland
Concentration: Entrepreneurship, Strategy
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 1: 640 Q49 V27
GMAT 2: 660 Q49 V31
GMAT 3: 720 Q50 V38
GPA: 4
WE:Engineering (Consumer Electronics)
Products:
My Reviews
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 3: 720 Q50 V38
Posts: 820
Kudos: 986
 [1]
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 05 Apr 2020, 17:14
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x and y are positive integers, is \((x+2)^{y+2}+x^y (y−2)^{x+2} \) even?

    (1) \(5x+8x^2+12x^3+9\) is odd.
    (2) \(3y+(11+y)+35(3y+2) \) is even.

i) if \(5x+8x^2+12x^3+9\) = odd

9 = odd; 12*Term = even; 8*Term = even => O+E+E+unknown = odd => O+Unknown = odd => Unknown = even

Unknown = 5x = even => x = even

If x is even => \((x+2)^{y+2}+x^y (y−2)^{x+2} \) => \(Even^{anything}\) + (\(Even^{Anything}*(Anything)\)) = Even + Even = Even

Sufficient

ii) if \(3y+(11+y)+35(3y+2) \) = Even =>

Case i) y = odd => Odd*Odd + (Odd+Odd) + (Odd(Odd*Odd)+(Even)) => Odd+Even+(Odd+Even) => Odd+Even+Odd = Even

Case ii) y = even => Odd*Even+ (Odd+Even) + (Odd(Odd*Even)+(Even)) => Even+Odd+(Even+Even) => Even+Odd+Even = Odd

2 cases - 2 Answers - Insufficient

Answer - A
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Oct 2025
Posts: 3,380
Own Kudos:
2,141
Given Kudos: 69
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,380
Kudos: 2,141
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 06 Apr 2020, 05:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shameekv1989
If x and y are positive integers, is \((x+2)^{y+2}+x^y (y−2)^{x+2} \) even?

    (1) \(5x+8x^2+12x^3+9\) is odd.
    (2) \(3y+(11+y)+35(3y+2) \) is even.

i) if \(5x+8x^2+12x^3+9\) = odd

9 = odd; 12*Term = even; 8*Term = even => O+E+E+unknown = odd => O+Unknown = odd => Unknown = even

Unknown = 5x = even => x = even

If x is even => \((x+2)^{y+2}+x^y (y−2)^{x+2} \) => \(Even^{anything}\) + (\(Even^{Anything}*(Anything)\)) = Even + Even = Even

Sufficient

ii) if \(3y+(11+y)+35(3y+2) \) = Even =>

Case i) y = odd => Odd*Odd + (Odd+Odd) + (Odd(Odd*Odd)+(Even)) => Odd+Even+(Odd+Even) => Odd+Even+Odd = Even

Case ii) y = even => Odd*Even+ (Odd+Even) + (Odd(Odd*Even)+(Even)) => Even+Odd+(Even+Even) => Even+Odd+Even = Odd

2 cases - 2 Answers - Insufficient

Answer - A
Show more


Hey Shameev,

Thanks for posting your analysis.

As far as Statement 1 is concerned, your analysis is perfect. However, you made a small mistake in Statement 2.

Statement 2 clearly states that \(3y+(11+y)+35(3y+2) \) is even. This means that we need to find the even-odd nature of "y", that will make the given expression in statement 2 even.

Now, your calculation is perfect (highlighted in your solution). However, you did not realize that when y = even, statement 2 is not being satisfied. That means we need to discard this case and infer that "y" must be an odd number for statement 2 to be true.

Now, if y is odd, we need to check if the statement given in the question stem \((x+2)^{y+2}+x^y (y−2)^{x+2} \), is even or not.

I hope this explanation helped you in identifying your mistake. You can also watch the video solution of this question to gain more clarity. :)


Regards,
GMATWhiz Team
User avatar
shameekv1989
User avatar
Joined: 14 Dec 2019
Last visit: 17 Jun 2021
Posts: 820
Own Kudos:
986
 [1]
Given Kudos: 354
Location: Poland
Concentration: Entrepreneurship, Strategy
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 1: 640 Q49 V27
GMAT 2: 660 Q49 V31
GMAT 3: 720 Q50 V38
GPA: 4
WE:Engineering (Consumer Electronics)
Products:
My Reviews
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 3: 720 Q50 V38
Posts: 820
Kudos: 986
 [1]
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 06 Apr 2020, 05:18
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATWhizTeam
shameekv1989
If x and y are positive integers, is \((x+2)^{y+2}+x^y (y−2)^{x+2} \) even?

    (1) \(5x+8x^2+12x^3+9\) is odd.
    (2) \(3y+(11+y)+35(3y+2) \) is even.

i) if \(5x+8x^2+12x^3+9\) = odd

9 = odd; 12*Term = even; 8*Term = even => O+E+E+unknown = odd => O+Unknown = odd => Unknown = even

Unknown = 5x = even => x = even

If x is even => \((x+2)^{y+2}+x^y (y−2)^{x+2} \) => \(Even^{anything}\) + (\(Even^{Anything}*(Anything)\)) = Even + Even = Even

Sufficient

ii) if \(3y+(11+y)+35(3y+2) \) = Even =>

Case i) y = odd => Odd*Odd + (Odd+Odd) + (Odd(Odd*Odd)+(Even)) => Odd+Even+(Odd+Even) => Odd+Even+Odd = Even

Case ii) y = even => Odd*Even+ (Odd+Even) + (Odd(Odd*Even)+(Even)) => Even+Odd+(Even+Even) => Even+Odd+Even = Odd

2 cases - 2 Answers - Insufficient

Answer - A


Hey Shameev,

Thanks for posting your analysis.

As far as Statement 1 is concerned, your analysis is perfect. However, you made a small mistake in Statement 2.

Statement 2 clearly states that \(3y+(11+y)+35(3y+2) \) is even. This means that we need to find the even-odd nature of "y", that will make the given expression in statement 2 even.

Now, your calculation is perfect (highlighted in your solution). However, you did not realize that when y = even, statement 2 is not being satisfied. That means we need to discard this case and infer that "y" must be an odd number for statement 2 to be true.

Now, if y is odd, we need to check if the statement given in the question stem \((x+2)^{y+2}+x^y (y−2)^{x+2} \), is even or not.

I hope this explanation helped you in identifying your mistake. You can also watch the video solution of this question to gain more clarity. :)


Regards,
GMATWhiz Team
Show more

GMATWhizTeam :- Thank you so much for pointing out my mistake and providing a detailed analysis. Really appreciate your time.
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Oct 2025
Posts: 3,380
Own Kudos:
2,141
Given Kudos: 69
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,380
Kudos: 2,141
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 06 Apr 2020, 06:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shameekv1989
GMATWhizTeam
shameekv1989
If x and y are positive integers, is \((x+2)^{y+2}+x^y (y−2)^{x+2} \) even?

    (1) \(5x+8x^2+12x^3+9\) is odd.
    (2) \(3y+(11+y)+35(3y+2) \) is even.

i) if \(5x+8x^2+12x^3+9\) = odd

9 = odd; 12*Term = even; 8*Term = even => O+E+E+unknown = odd => O+Unknown = odd => Unknown = even

Unknown = 5x = even => x = even

If x is even => \((x+2)^{y+2}+x^y (y−2)^{x+2} \) => \(Even^{anything}\) + (\(Even^{Anything}*(Anything)\)) = Even + Even = Even

Sufficient

ii) if \(3y+(11+y)+35(3y+2) \) = Even =>

Case i) y = odd => Odd*Odd + (Odd+Odd) + (Odd(Odd*Odd)+(Even)) => Odd+Even+(Odd+Even) => Odd+Even+Odd = Even

Case ii) y = even => Odd*Even+ (Odd+Even) + (Odd(Odd*Even)+(Even)) => Even+Odd+(Even+Even) => Even+Odd+Even = Odd

2 cases - 2 Answers - Insufficient

Answer - A


Hey Shameev,

Thanks for posting your analysis.

As far as Statement 1 is concerned, your analysis is perfect. However, you made a small mistake in Statement 2.

Statement 2 clearly states that \(3y+(11+y)+35(3y+2) \) is even. This means that we need to find the even-odd nature of "y", that will make the given expression in statement 2 even.

Now, your calculation is perfect (highlighted in your solution). However, you did not realize that when y = even, statement 2 is not being satisfied. That means we need to discard this case and infer that "y" must be an odd number for statement 2 to be true.

Now, if y is odd, we need to check if the statement given in the question stem \((x+2)^{y+2}+x^y (y−2)^{x+2} \), is even or not.

I hope this explanation helped you in identifying your mistake. You can also watch the video solution of this question to gain more clarity. :)


Regards,
GMATWhiz Team

GMATWhizTeam :- Thank you so much for pointing out my mistake and providing a detailed analysis. Really appreciate your time.
Show more

It's my pleasure Shameek. Happy to know that the explanation helped :)
User avatar
Farina
User avatar
Joined: 21 Aug 2019
Last visit: 13 Oct 2020
Posts: 100
Own Kudos:
43
Given Kudos: 352
Posts: 100
Kudos: 43
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 09 Apr 2020, 03:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATWhizTeam
I hope you were able to internalize the first skill that we discussed in the Prepathon. Here's the detailed solution to the first question. Even if you got the question right make sure that you check out the method in the solution to ensure that you have solved it using the right method. All the best!



Feel free to post any doubts that you may have in the forum below. We will be happy to help you with your queries :)
Show more

I am having tough time in doing pre-analysis, your videos will surely help me. Surprisingly I marked the correct answer here and checked the video later, my approach was correct. Thank you so much
User avatar
GMATGuruNY
User avatar
Joined: 04 Aug 2010
Last visit: 08 Nov 2025
Posts: 1,344
Own Kudos:
3,795
Given Kudos: 9
Schools:Dartmouth College
Expert
Expert reply
Posts: 1,344
Kudos: 3,795
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 09 Apr 2020, 05:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATWhizTeam
If x and y are positive integers, is \((x+2)^{y+2}+x^y (y−2)^{x+2} \) even?

    (1) \(5x+8x^2+12x^3+9\) is odd.
    (2) \(3y+(11+y)+35(3y+2) \) is even.
Show more

The problem is about EVEN vs ODD.
If x=0 and y>0, none of the expressions in the problem will yield a fraction.
Implication:
We can ignore the condition that x must be positive and test x=0 in each statement.

Statement 1:
Case 1: x=0, with result that \(5x+8x^2+12x^3+9 = 9\)
If y=2, then \((x+2)^{y+2}+x^y (y−2)^{x+2} = 16\)
Here, the answer to the question stem is YES.
If y=1, then \((x+2)^{y+2}+x^y (y−2)^{x+2} = 8\)
Here, the answer to the question stem is YES.

Case 2: x=1, with result that \(5x+8x^2+12x^3+9 = 34\)
Not viable, since the sum must be ODD.

Since only Case 1 is viable -- and the answer is YES in Case 1 whether y is even or odd -- SUFFICIENT.

Statement 2:
For the sole purpose of determining whether y can be even in Statement 2, we can test y=0.
If y=0, then \(3y+(11+y)+35(3y+2) = 81\) -- not viable, since the sum must be EVEN.
Implication:
In Statement 2, y must be ODD.

If y=1 and x=0, then the answer to the question stem is YES, as shown in Statement 1.
If y=1 and x=1, then \((x+2)^{y+2}+x^y (y−2)^{x+2} = 26\), so the answer to the question stem is YES.
Since the answer is YES whether x is even or odd, SUFFICIENT.

Show Spoiler
D
User avatar
minustark
User avatar
Joined: 14 Jul 2019
Last visit: 01 Apr 2021
Posts: 469
Own Kudos:
398
Given Kudos: 52
Status:Student
Location: United States
Concentration: Accounting, Finance
Schools: Zicklin Baruch "22
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Products:
My Reviews
Schools: Zicklin Baruch "22
GMAT 1: 650 Q45 V35
Posts: 469
Kudos: 398
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 09 Apr 2020, 11:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(x + 2)^(y +2) + x^y (y-2)^(x +2) will be even when each of them are either odd or even. Since x is a base here, if x is even, the value will be even regardless the value of y except y =0.

1) 5x +8x^2+12x^3 +9 is odd. 8x^2 +12x^3 is even as even * (odd/even) =even . So 5x + 9 will have to odd as Odd + odd =even and even + odd =odd. That means 5x is even and for this x has to be even. The powers of x in the question stem cannot be 0. Sufficient.
2) 3y+(11+y)+35(3y+2) is even. WE can rewrite it as : 3y +11+y+105y +70 . 109y +81 is even. As Odd +odd =even and odd * odd =odd, so y is odd. We need the value of x. Not sufficient.
A is the answer.
User avatar
GMATGuruNY
User avatar
Joined: 04 Aug 2010
Last visit: 08 Nov 2025
Posts: 1,344
Own Kudos:
3,795
Given Kudos: 9
Schools:Dartmouth College
Expert
Expert reply
Posts: 1,344
Kudos: 3,795
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 09 Apr 2020, 11:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
minustark
2)so y is odd. We need the value of x. Not sufficient.
Show more

The assumption in red is incorrect.
If y=odd and x=odd, then \((x+2)^{y+2}+x^y (y−2)^{x+2} = \) ODD + ODD = EVEN
If y=odd and x=even, then \((x+2)^{y+2}+x^y (y−2)^{x+2} = \) EVEN + EVEN = EVEN
Regardless of the value of x, the answer to the question stem is YES.
Thus, statement 2 is SUFFICIENT.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,586
Own Kudos:
1,079
Posts: 38,586
Kudos: 1,079
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even 14 Oct 2024, 07:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts