Last visit was: 27 Apr 2026, 02:17 It is currently 27 Apr 2026, 02:17
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
User avatar
DHAR
User avatar
Joined: 15 Dec 2015
Last visit: 13 Dec 2021
Posts: 92
Own Kudos:
949
 [13]
Given Kudos: 83
GMAT 1: 680 Q49 V34
GPA: 4
WE:Information Technology (Computer Software)
GMAT 1: 680 Q49 V34
Posts: 92
Kudos: 949
 [13]
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 12 Aug 2017, 02:27
1
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

57% (01:11) correct 43% (01:17) wrong based on 357 sessions

History

Date
Time
Result
Not Attempted Yet
If M and N are integers, what is the value of M + N?

(1) MN = 10
(2) \(M^2+N^2=29\)
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
AbdurRakib
User avatar
Joined: 11 May 2014
Last visit: 03 Mar 2026
Posts: 464
Own Kudos:
43,765
 [9]
Given Kudos: 220
Status:I don't stop when I'm Tired,I stop when I'm done
Location: Bangladesh
Concentration: Finance, Leadership
Schools: Wharton '20 Yale '20 Tepper '20
GPA: 2.81
WE:Business Development (Real Estate)
Schools: Wharton '20 Yale '20 Tepper '20
Posts: 464
Kudos: 43,765
 [9]
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 12 Aug 2017, 02:54
7
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
DH99
If M and N are integers, what is the value of M + N?

(1) MN = 10
(2) \(M^2+N^2=29\)
Show more

(1)
    If M=5 and N=2 ,then MN=10 and M+N=7
    if M=10 and N-=1,then MN=10 ,but M+N=11.. Not Sufficient

(2)
    If M=5 and N=2 ,then \(M^2+N^2=29\) and M+N=7

    if M=-5 and N=-2 then \(M^2+N^2=29\) ,but M+N=-7..Not Sufficient

Together,
    If M=5 and N=2,then MN=10 and \(M^2+N^2=29\).Hence ,M+N=7

    If M=-5 and N=-2,then MN=10 and \(M^2+N^2=29\).But M+N=-7...Not Sufficient

Therefore the Correct Answer is E
General Discussion
User avatar
DHAR
User avatar
Joined: 15 Dec 2015
Last visit: 13 Dec 2021
Posts: 92
Own Kudos:
949
Given Kudos: 83
GMAT 1: 680 Q49 V34
GPA: 4
WE:Information Technology (Computer Software)
GMAT 1: 680 Q49 V34
Posts: 92
Kudos: 949
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 12 Aug 2017, 02:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AbdurRakib: Good Explanation +1 kudos
User avatar
BijayKru
User avatar
Joined: 24 Sep 2018
Last visit: 04 Dec 2025
Posts: 60
Own Kudos:
25
Given Kudos: 27
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 700 Q50 V37
GMAT 1: 700 Q50 V37
Posts: 60
Kudos: 25
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 08 Apr 2020, 06:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think the answer will be C

(M+N)^2 = M^2 +N^2 +2MN

SO WE HAVE ALL THE VALUE IN I AND II. SO why not C is the answer.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,921
Own Kudos:
811,501
Given Kudos: 105,912
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,921
Kudos: 811,501
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 08 Apr 2020, 06:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
BijayKru
I think the answer will be C

(M+N)^2 = M^2 +N^2 +2MN

SO WE HAVE ALL THE VALUE IN I AND II. SO why not C is the answer.
Show more

There is a solution given HERE explaining why the answer is E and not C.

So basically, two sets satisfy mn = 10 and m^2 + n^2 = 29: m = 5 and n = 2 (or vise-versa) and m = - 5 and n = -2 (or vise-versa). The first set gives m + n = 7, while the second one gives m + n = -7.

The problem with your solution is that from (1)+(2) we can get that (m + n)^2 = m^2 + 2mn + m^2 = 29 + 20 = 49. But from this m + n could be both 7 and -7.

Hope it's clear.
User avatar
yashikaaggarwal
User avatar
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 29 Mar 2026
Posts: 3,088
Own Kudos:
3,158
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,088
Kudos: 3,158
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 08 Apr 2020, 06:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
BijayKru
I think the answer will be C

(M+N)^2 = M^2 +N^2 +2MN

SO WE HAVE ALL THE VALUE IN I AND II. SO why not C is the answer.

There is a solution given HERE explaining why the answer is E and not C.

So basically, two sets satisfy mn = 10 and m^2 + n^2 = 29: m = 5 and n = 2 (or vise-versa) and m = - 5 and n = -2 (or vise-versa). The first set gives m + n = 7, while the second one gives m + n = -7.

The problem with your solution is that from (1)+(2) we can get that (m + n)^2 = m^2 + 2mn + m^2 = 29 + 20 = 49. But from this m + n could be both 7 and -7.

Hope it's clear.
Show more

Can I conclude that DS need a particular answer and if we don't have that we can't select either of Above 4 options?

Posted from my mobile device
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,921
Own Kudos:
811,501
Given Kudos: 105,912
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,921
Kudos: 811,501
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 08 Apr 2020, 06:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
yashikaaggarwal
Bunuel
BijayKru
I think the answer will be C

(M+N)^2 = M^2 +N^2 +2MN

SO WE HAVE ALL THE VALUE IN I AND II. SO why not C is the answer.

There is a solution given HERE explaining why the answer is E and not C.

So basically, two sets satisfy mn = 10 and m^2 + n^2 = 29: m = 5 and n = 2 (or vise-versa) and m = - 5 and n = -2 (or vise-versa). The first set gives m + n = 7, while the second one gives m + n = -7.

The problem with your solution is that from (1)+(2) we can get that (m + n)^2 = m^2 + 2mn + m^2 = 29 + 20 = 49. But from this m + n could be both 7 and -7.

Hope it's clear.

Can I conclude that DS need a particular answer and if we don't have that we can't select either of Above 4 options?

Posted from my mobile device
Show more

There are two types of data sufficiency questions:

1. YES/NO DS Questions:

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".


2. VALUE DS QUESTIONS:

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

This question is a VALUE question, so a statement to be sufficient it should give the single numerical value of m + n.


Hope it's clear.
User avatar
MHIKER
User avatar
Joined: 14 Jul 2010
Last visit: 24 May 2021
Posts: 939
Own Kudos:
5,818
Given Kudos: 690
Status:No dream is too large, no dreamer is too small
Concentration: Accounting
Posts: 939
Kudos: 5,818
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 13 Jan 2021, 08:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DHAR
If M and N are integers, what is the value of M + N?

(1) MN = 10
(2) \(M^2+N^2=29\)
Show more

(1) \(1*10=10; 2*5=10\); Insufficient.

(2)\( (2)^2+(5)^2=29; (-2)^2+(-5)^2=25\);[/m] Insufficient.

Considering Both;

\((M+N)^2=M^2+N^2+2*MN=29+20=49\)

\((M+N)^2=49\)

M+N=+7 OR -7; Insufficient.

The answer is \(E\)
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 26 Apr 2026
Posts: 6,977
Own Kudos:
16,924
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,977
Kudos: 16,924
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 09 May 2021, 06:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DHAR
If M and N are integers, what is the value of M + N?

(1) MN = 10
(2) \(M^2+N^2=29\)
Show more

Answer: Option E

Video solution by GMATinsight

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,990
Own Kudos:
1,118
Posts: 38,990
Kudos: 1,118
If M and N are integers, what is the value of M + N? (1) (M)(N) = 10 06 Aug 2022, 05:28
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
109921 posts
kingbucky
498 posts
Gmat860sanskar
212 posts