SSC CGL Exam > SSC CGL Questions > Let x be the least number, which when divided...
Start Learning for Free
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x is
- a)24
- b)21
- c)22
- d)18
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves ...
Solution:
Let's understand the given information:
- The number leaves a remainder of 3 when divided by 5, 6, 7 and 8.
- The number leaves a remainder of 0 when divided by 9.
To find the least number that satisfies these conditions, we need to find the LCM of 5, 6, 7, and 8, and then add 3 to get the smallest number with the required remainders. Let's do this step by step.
Finding LCM of 5, 6, 7, and 8:
- Prime factorization of 5: 5
- Prime factorization of 6: 2 x 3
- Prime factorization of 7: 7
- Prime factorization of 8: 2 x 2 x 2
We need to take the highest power of each prime factor that appears in the factorization of any of the numbers. Therefore, the LCM of 5, 6, 7, and 8 is:
LCM = 2 x 2 x 2 x 3 x 5 x 7 = 840
Finding the smallest number with remainders of 3 when divided by 5, 6, 7, and 8:
We need to add 3 to the LCM to get the smallest number that satisfies the given conditions:
Number = LCM + 3 = 840 + 3 = 843
Now, we need to check if this number leaves a remainder of 0 when divided by 9:
843 ÷ 9 = 93 with a remainder of 0
Therefore, the smallest number that satisfies the given conditions is 843.
Sum of digits of 843:
Sum of digits of 843 = 8 + 4 + 3 = 15
Therefore, the correct answer is option (D) 18.
Let's understand the given information:
- The number leaves a remainder of 3 when divided by 5, 6, 7 and 8.
- The number leaves a remainder of 0 when divided by 9.
To find the least number that satisfies these conditions, we need to find the LCM of 5, 6, 7, and 8, and then add 3 to get the smallest number with the required remainders. Let's do this step by step.
Finding LCM of 5, 6, 7, and 8:
- Prime factorization of 5: 5
- Prime factorization of 6: 2 x 3
- Prime factorization of 7: 7
- Prime factorization of 8: 2 x 2 x 2
We need to take the highest power of each prime factor that appears in the factorization of any of the numbers. Therefore, the LCM of 5, 6, 7, and 8 is:
LCM = 2 x 2 x 2 x 3 x 5 x 7 = 840
Finding the smallest number with remainders of 3 when divided by 5, 6, 7, and 8:
We need to add 3 to the LCM to get the smallest number that satisfies the given conditions:
Number = LCM + 3 = 840 + 3 = 843
Now, we need to check if this number leaves a remainder of 0 when divided by 9:
843 ÷ 9 = 93 with a remainder of 0
Therefore, the smallest number that satisfies the given conditions is 843.
Sum of digits of 843:
Sum of digits of 843 = 8 + 4 + 3 = 15
Therefore, the correct answer is option (D) 18.
Free Test
FREE
| Start Free Test |
Community Answer
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves ...
See the question says , the sum of the digits, the number is Divided by 9=0, as 9x2=18,9x3=27,
8+1=9,3+6=9
8+1=9,3+6=9
Attention SSC CGL Students!
To make sure you are not studying endlessly, EduRev has designed SSC CGL study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in SSC CGL.
|
Explore Courses for SSC CGL exam
|
|
Similar SSC CGL Doubts
Top Courses for SSC CGLView all
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer?
Question Description
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer?.
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer?.
Solutions for Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.
Here you can find the meaning of Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0. the sum of digits of x isa)24b)21c)22d)18Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice SSC CGL tests.
|
|
Explore Courses for SSC CGL exam
|
|
Suggested Free Tests
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