Last visit was: 22 Apr 2026, 22:00 It is currently 22 Apr 2026, 22:00
Home
Messages
Tests
Schools
Events
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
705-805 (Hard)|   Algebra|      
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 12 Mar 2026
Posts: 1,841
Own Kudos:
8,509
 [3]
Given Kudos: 707
Location: India
Posts: 1,841
Kudos: 8,509
 [3]
3*2^x+1=y^2, where x and y are non-negative integers. Find the sum of Updated on: 13 Sep 2019, 08:40
Originally posted by nick1816 on 13 Sep 2019, 08:24.
Last edited by chetan2u on 13 Sep 2019, 08:40, edited 1 time in total.
Corrected the OA
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

49% (02:22) correct 51% (02:14) wrong based on 91 sessions

History

Date
Time
Result
Not Attempted Yet
\(3*2^x+1=y^2\), where x and y are non-negative integers. Find the sum of x and y?

1) x is an even integer
2) y is an even integer.
ShowHide Answer
Official Answer
B
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
44,995
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 44,995
 [1]
3*2^x+1=y^2, where x and y are non-negative integers. Find the sum of 13 Sep 2019, 08:38
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
\(3*2^x+1=y^2\), where x and y are non-negative integers. Find the sum of x and y?
\(3*2^x\) will always be even for positive integers, and y will be ODD, and odd for x=0, and y will be EVEN..

1) x is an even integer
when x is 4, y is 7, x+y=11
when x=0, y=2 and x+y=2
Insuff

2) y is an even integer.
y will be EVEN only when x is 0..
\(3*2^x+1=y^2.....3*2^0+1=3+1=4=y^2...y=2\)
so x=0, y=2...x+y=0+2=2
Suff

B

nick1816, OA is wrong, please correct it..
User avatar
EncounterGMAT
User avatar
Joined: 10 Oct 2018
Last visit: 16 Oct 2019
Posts: 317
Own Kudos:
632
Given Kudos: 185
Status:Whatever it takes!
GPA: 4
Posts: 317
Kudos: 632
3*2^x+1=y^2, where x and y are non-negative integers. Find the sum of 13 Sep 2019, 09:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
\(3*2^x+1=y^2\), where x and y are non-negative integers. Find the sum of x and y?
\(3*2^x\) will always be even for positive integers, and y will be ODD, and odd for x=0, and y will be EVEN.

1) x is an even integer
y could be many odd numbers..
when x is 3, y is 5, x+y=8
when x=0, y=2 and x+y=2
Insuff

2) y is an even integer.
y will be EVEN only when x is 0..
so x=0, y=2...x+y=0+2=2
Suff

B

nick1816, OA is wrong, please correct it..
Show more
chetan2u I am getting the answer as A, and I have highlighted some of my confusion in your solution.
This is how I solved.
The question states \(3*2^x+1=y^2\) which means y^2, i.e, y has to be odd.

1) x is an even integer
since x=even, it is possible to find the value of x+y when x=4=> y=7.....for rest of the values of y, we get irrational numbers. however, when x=0, y=2->not possible since y has to be odd. SUFFICIENT

2) y is an even integer.
y=even. Not possible. since y has to be odd. INSUFFICIENT!

Sir, please advise and correct me if I am missing something.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
44,995
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 44,995
 [1]
3*2^x+1=y^2, where x and y are non-negative integers. Find the sum of 13 Sep 2019, 09:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EncounterGMAT
chetan2u
\(3*2^x+1=y^2\), where x and y are non-negative integers. Find the sum of x and y?
\(3*2^x\) will always be even for positive integers, and y will be ODD, and odd for x=0, and y will be EVEN.

1) x is an even integer
y could be many odd numbers..
when x is 3, y is 5, x+y=8
when x=0, y=2 and x+y=2
Insuff

2) y is an even integer.
y will be EVEN only when x is 0..
so x=0, y=2...x+y=0+2=2
Suff

B

nick1816, OA is wrong, please correct it..
chetan2u I am getting the answer as A, and I have highlighted some of my confusion in your solution.
This is how I solved.
The question states \(3*2^x+1=y^2\) which means y^2, i.e, y has to be odd.

1) x is an even integer
since x=even, it is possible to find the value of x+y when x=4=> y=7.....for rest of the values of y, we get irrational numbers. however, when x=0, y=2->not possible since y has to be odd. SUFFICIENT

2) y is an even integer.
y=even. Not possible. since y has to be odd. INSUFFICIENT!

Sir, please advise and correct me if I am missing something.
Show more

The question states \(3*2^x+1=y^2\) which means y^2, i.e, y has to be odd...
0 is non negative, so when x is 0...\(3*2^x+1=3*2^0+1=3*1+1=3+1=4=y^2...y=2\)..
Here y cannot be -2 as it is non negative
User avatar
EncounterGMAT
User avatar
Joined: 10 Oct 2018
Last visit: 16 Oct 2019
Posts: 317
Own Kudos:
632
Given Kudos: 185
Status:Whatever it takes!
GPA: 4
Posts: 317
Kudos: 632
3*2^x+1=y^2, where x and y are non-negative integers. Find the sum of 13 Sep 2019, 09:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u Thank-you sir for correcting me. I didn't infer the question stem and its possibilities fully.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,000
 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,000
 [1]
3*2^x+1=y^2, where x and y are non-negative integers. Find the sum of 13 Sep 2019, 10:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nick1816
\(3*2^x+1=y^2\), where x and y are non-negative integers. Find the sum of x and y?

1) x is an even integer
2) y is an even integer.
Show more

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have 2 variable (\(x\) and \(y\)) and 1 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
If \(x = 0\), then we have \(3 \cdot 2^x+1=3 \cdot 2^0+1=4=y^2\) or \(y=2\) and so \(x + y = 2\).
If \(x = 4\), then we have \(3 \cdot 2^x+1=3 \cdot 2^4+1=49=y^2\) or \(y=7\) and so \(x + y = 11\).
Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)
Since \(y\) is an even integer, \(3 \cdot 2^x\) must be an odd integer and the only possible non-negative integer of \(x\) is \(0\).
If \(x = 0\), then we have \(3 \cdot 2^x+1=3 \cdot 2^0+1=4=y^2\) or \(y=2\) and so \(x + y = 2\).
Since condition 2) yields a unique solution, it is sufficient.

Therefore, B is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
3*2^x+1=y^2, where x and y are non-negative integers. Find the sum of 01 Jul 2021, 22:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
109765 posts
kingbucky
498 posts
Gmat860sanskar
212 posts