Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
19 Aug 2021, 08:00
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (02:19) correct
47%
(02:48)
wrong
based on 329
sessions
History
Date
Time
Result
Not Attempted Yet
If \(m ≠ n\), \(m^2 = 17m + n\) and \(n^2 = 17n + m\), then what is the value of \(\sqrt{m^2 + n^2 + 1}\)
A. 16
B. 17
C. 18
D. 19
E. 289
M37-36
A. 16
B. 17
C. 18
D. 19
E. 289
|
M37-36
Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
23 Nov 2021, 07:14
Kudos
Bookmarks
Official Solution:
If \(m ≠ n\), \(m^2 = 17m + n\) and \(n^2 = 17n + m\), then what is the value of \(\sqrt{m^2 + n^2 + 1}\)?
A. \(16\)
B. \(17\)
C. \(18\)
D. \(19\)
E. \(289\)
Subtract one equation from another:
\(m^2 -n^2= (17m + n) -(17n + m)\);
\((m -n)(m+n)= 16(m-n)\);
Reduce by \(m-n\) (we can safely do that because \(m ≠ n\) and thus \(m -n≠ 0\)): \(m+n= 16\).
\(\sqrt{m^2 + n^2 + 1}=\sqrt{(17m + n) + (17n + m)+ 1}=\sqrt{18(m + n) + 1}=\sqrt{18*16+1}=\sqrt{289}=17\).
Answer: B
If \(m ≠ n\), \(m^2 = 17m + n\) and \(n^2 = 17n + m\), then what is the value of \(\sqrt{m^2 + n^2 + 1}\)?
A. \(16\)
B. \(17\)
C. \(18\)
D. \(19\)
E. \(289\)
Subtract one equation from another:
\(m^2 -n^2= (17m + n) -(17n + m)\);
\((m -n)(m+n)= 16(m-n)\);
Reduce by \(m-n\) (we can safely do that because \(m ≠ n\) and thus \(m -n≠ 0\)): \(m+n= 16\).
\(\sqrt{m^2 + n^2 + 1}=\sqrt{(17m + n) + (17n + m)+ 1}=\sqrt{18(m + n) + 1}=\sqrt{18*16+1}=\sqrt{289}=17\).
Answer: B
General Discussion
19 Aug 2021, 08:18
Kudos
Bookmarks
Asked: If \(m ≠ n\), \(m^2 = 17m + n\) and \(n^2 = 17n + m\), then what is the value of \(\sqrt{m^2 + n^2 + 1}\)
m^2 + n^2 + 1 = 17m + n + 17n + m + 1 = 18(m+n) + 1
\(n = m^2 - 17m\)
\(m = n^2 - 17n \)
\(n - m = m^2 - n^2 - 17(m-n) = (m-n)(m+n) - 17(m-n)\)
-1 = m + n - 17 ; Since m ≠ n
m + n = 16
\(m^2 + n^2 + 1 = 18*16 + 1 = 289 = 17^2\)
\(\sqrt{m^2 + n^2 + 1} = 17\)
IMO B
m^2 + n^2 + 1 = 17m + n + 17n + m + 1 = 18(m+n) + 1
\(n = m^2 - 17m\)
\(m = n^2 - 17n \)
\(n - m = m^2 - n^2 - 17(m-n) = (m-n)(m+n) - 17(m-n)\)
-1 = m + n - 17 ; Since m ≠ n
m + n = 16
\(m^2 + n^2 + 1 = 18*16 + 1 = 289 = 17^2\)
\(\sqrt{m^2 + n^2 + 1} = 17\)
IMO B
