CAT Exam > CAT Questions > How many natural numbers less than 10 when sq...
Start Learning for Free
How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1?
Most Upvoted Answer
How many natural numbers less than 10 when squared and then divided by...
Understanding the Problem
We need to find the natural numbers less than 10 whose squares, when divided by 24, leave a remainder of 1. In other words, we are looking for numbers \( n \) such that:
n^2 mod 24 = 1
Natural Numbers to Consider
The natural numbers less than 10 are:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
Calculating Squares and Remainders
Now, let’s calculate the square of each number and find the remainder when divided by 24:
- 1^2 = 1; 1 mod 24 = 1
- 2^2 = 4; 4 mod 24 = 4
- 3^2 = 9; 9 mod 24 = 9
- 4^2 = 16; 16 mod 24 = 16
- 5^2 = 25; 25 mod 24 = 1
- 6^2 = 36; 36 mod 24 = 12
- 7^2 = 49; 49 mod 24 = 1
- 8^2 = 64; 64 mod 24 = 16
- 9^2 = 81; 81 mod 24 = 9
Numbers that Meet the Condition
From the calculations above, the numbers that satisfy the condition n^2 mod 24 = 1 are:
- 1 (1 mod 24 = 1)
- 5 (25 mod 24 = 1)
- 7 (49 mod 24 = 1)
Total Count
Thus, there are three natural numbers less than 10 that, when squared and divided by 24, leave a remainder of 1:
- 1
- 5
- 7
Conclusion
The final answer is 3.
We need to find the natural numbers less than 10 whose squares, when divided by 24, leave a remainder of 1. In other words, we are looking for numbers \( n \) such that:
n^2 mod 24 = 1
Natural Numbers to Consider
The natural numbers less than 10 are:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
Calculating Squares and Remainders
Now, let’s calculate the square of each number and find the remainder when divided by 24:
- 1^2 = 1; 1 mod 24 = 1
- 2^2 = 4; 4 mod 24 = 4
- 3^2 = 9; 9 mod 24 = 9
- 4^2 = 16; 16 mod 24 = 16
- 5^2 = 25; 25 mod 24 = 1
- 6^2 = 36; 36 mod 24 = 12
- 7^2 = 49; 49 mod 24 = 1
- 8^2 = 64; 64 mod 24 = 16
- 9^2 = 81; 81 mod 24 = 9
Numbers that Meet the Condition
From the calculations above, the numbers that satisfy the condition n^2 mod 24 = 1 are:
- 1 (1 mod 24 = 1)
- 5 (25 mod 24 = 1)
- 7 (49 mod 24 = 1)
Total Count
Thus, there are three natural numbers less than 10 that, when squared and divided by 24, leave a remainder of 1:
- 1
- 5
- 7
Conclusion
The final answer is 3.
Community Answer
How many natural numbers less than 10 when squared and then divided by...
3
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1?
Question Description
How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1?.
How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1?.
Solutions for How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? defined & explained in the simplest way possible. Besides giving the explanation of
How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1?, a detailed solution for How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? has been provided alongside types of How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? theory, EduRev gives you an
ample number of questions to practice How many natural numbers less than 10 when squared and then divided by 24 leaves a remainder of 1? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup