Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 06 Jun 2020, 20:14

### 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

# If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

GMATWhiz Representative
Joined: 07 May 2019
Posts: 723
Location: India
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

Updated on: 07 Apr 2020, 23:11
1
3
00:00

Difficulty:

95% (hard)

Question Stats:

25% (02:50) correct 75% (02:58) wrong based on 64 sessions

### HideShow timer Statistics

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!

_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point

Originally posted by GMATWhizTeam on 05 Apr 2020, 07:34.
Last edited by GMATWhizTeam on 07 Apr 2020, 23:11, edited 2 times in total.
GMATWhiz Representative
Joined: 07 May 2019
Posts: 723
Location: India
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

Updated on: 05 Apr 2020, 21:23
3
1
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
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point

Originally posted by GMATWhizTeam on 05 Apr 2020, 07:37.
Last edited by GMATWhizTeam on 05 Apr 2020, 21:23, edited 2 times in total.
Manager
Joined: 27 Dec 2012
Posts: 127
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

05 Apr 2020, 07:56
1
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
Director
Joined: 14 Dec 2019
Posts: 668
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

05 Apr 2020, 16:14
1
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

GMATWhiz Representative
Joined: 07 May 2019
Posts: 723
Location: India
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

06 Apr 2020, 04:10
shameekv1989 wrote:
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

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
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
Director
Joined: 14 Dec 2019
Posts: 668
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

06 Apr 2020, 04:18
1
GMATWhizTeam wrote:
shameekv1989 wrote:
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

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.
GMATWhiz Representative
Joined: 07 May 2019
Posts: 723
Location: India
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

06 Apr 2020, 05:47
shameekv1989 wrote:
GMATWhizTeam wrote:
shameekv1989 wrote:
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

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.

It's my pleasure Shameek. Happy to know that the explanation helped
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
Manager
Joined: 21 Aug 2019
Posts: 132
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

09 Apr 2020, 02:08
GMATWhizTeam wrote:
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

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
_________________
I don't believe in giving up!
Director
Joined: 04 Aug 2010
Posts: 618
Schools: Dartmouth College
If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

09 Apr 2020, 04:43
GMATWhizTeam wrote:
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.

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.

_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance.
Senior Manager
Status: Student
Joined: 14 Jul 2019
Posts: 333
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

09 Apr 2020, 10:34
(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.
Director
Joined: 04 Aug 2010
Posts: 618
Schools: Dartmouth College
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even  [#permalink]

### Show Tags

09 Apr 2020, 10:52
minustark wrote:
2)so y is odd. We need the value of x. Not sufficient.

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.
_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance.
Re: If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even   [#permalink] 09 Apr 2020, 10:52

# If x and y are positive integers, is (x+2)^(y+2)+x^y(y−2)^(x+2) even

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne