by: Yadnesh05
18 mins
|
|
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.
GMAT 1: 760 Q51 V42
Posts: 10,057
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:
66% (01:35) correct
34%
(01:57)
wrong
based on 305
sessions
History
Date
Time
Result
Not Attempted Yet
What is the reminder when \(n^2\) is divided by \(4\)?
1) When \(n\) is divided by \(2\), the reminder is \(1\).
2) When \(n\) is divided by \(3\), the reminder is \(1\).
1) When \(n\) is divided by \(2\), the reminder is \(1\).
2) When \(n\) is divided by \(3\), the reminder is \(1\).
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
MathRevolution
Statement 1: \(n=2k+1=>n^2=4k^2+4k+1\). Clearly if this number is divided by \(4\), then \(1\) will be the remainder. Sufficient
Statement 2: \(n=3k+1=>n^2=9k^2+6k+1=>8k^2+4k+k^2+2k+1=>n^2=4k(2k+1)+(k+1)^2\).
Hence the remainder will depend on the value of \((k+1)^2\) where \(k\) is unknown. if \(k=3\), then remainder will be \(0\) and if \(k=2\), remainder will be \(1\). Insufficient
Option A
GMAT 1: 760 Q51 V42
Posts: 10,057
=>
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.
Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
Plugging-in numbers is suggested for remainder questions.
The integers which have a remainder of 1 when divided by 2 are odd.
So,
\(n: 1, 3, 5, 7, 9, …\)
and
\(n^2: 1, 9, 25, 49, 81, …\)
Each value of \(n^2\) has a remainder of \(1\) when it is divided by \(4\).
So, condition 1) is sufficient.
Condition 2)
When \(n = 1, n^2= 1\) has a remainder of \(1\) when it is divided by \(4.\)
When \(n = 4, n^2=16\) has a remainder of \(0\) when it is divided by \(4\).
Since we don’t have a unique answer, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
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.
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.
Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
Plugging-in numbers is suggested for remainder questions.
The integers which have a remainder of 1 when divided by 2 are odd.
So,
\(n: 1, 3, 5, 7, 9, …\)
and
\(n^2: 1, 9, 25, 49, 81, …\)
Each value of \(n^2\) has a remainder of \(1\) when it is divided by \(4\).
So, condition 1) is sufficient.
Condition 2)
When \(n = 1, n^2= 1\) has a remainder of \(1\) when it is divided by \(4.\)
When \(n = 4, n^2=16\) has a remainder of \(0\) when it is divided by \(4\).
Since we don’t have a unique answer, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
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.
niks18
1) When \(n\) is divided by \(2\), the reminder is \(1\).
2) When \(n\) is divided by \(3\), the reminder is \(1\).
St 1: n = 1, 3, 5, 7 (Remainder = 1 when divided by 2)
n^2 = 1, 9, 25, 49 (Remainder = 1 when divided by 4) Sufficient
St 2: n = 1, 4, 7, 10 (Remainder = 1 when divided by 3)
n^2 = 1, 16, 49, 100 Remainder = 1, 0, 1, 0 when divided by 4) Insufficient
(A)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
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.
_________________
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.
_________________
Moderator:
Announcements
How to Tell If Your GMAT Prep Resources Are Actually Helping You
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.