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A number when divided by 462 gives the remainder as 25. When same number is divided by 14, the remainder will be?
- a)9
- b)5
- c)12
- d)11
- e)15
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A number when divided by 462 gives the remainder as 25. When same numb...
Let x be the quotient, then that number becomes 462*x + 25
Which = (22x * 14) + (14*1)+11
Which = 14 (22x + 1) + 11
Which = (22x * 14) + (14*1)+11
Which = 14 (22x + 1) + 11
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
A number when divided by 462 gives the remainder as 25. When same numb...
Given information:
- A number when divided by 462 gives the remainder as 25.
- We need to find the remainder when the same number is divided by 14.
Solution:
Let the number be N.
1. N divided by 462 gives the remainder as 25
We can write this as an equation:
N = 462a + 25, where a is some integer.
2. Find the remainder when N is divided by 14
We can write this as:
N = 14b + r, where b is some integer and r is the remainder we need to find.
We can substitute the first equation into the second equation:
462a + 25 = 14b + r
We want to solve for r, the remainder when N is divided by 14. To do this, we can simplify the equation by dividing both sides by 14 and looking at the remainder:
33a + 1 = 2b + (r/14)
Since the left-hand side is an integer, the right-hand side must also be an integer. The only way for this to happen is if r/14 is an integer, which means that r must be a multiple of 14 plus some integer between 0 and 13.
We can simplify the equation further by taking both sides modulo 2:
33a + 1 ≡ r/14 (mod 2)
Since 33 is odd and 1 is odd, the left-hand side is odd. This means that the right-hand side must also be odd, which implies that r/14 is odd. Therefore, r must be an odd multiple of 14 plus some integer between 0 and 13.
The only answer choice that satisfies this condition is (D) 11. Therefore, the remainder when N is divided by 14 is 11.
- A number when divided by 462 gives the remainder as 25.
- We need to find the remainder when the same number is divided by 14.
Solution:
Let the number be N.
1. N divided by 462 gives the remainder as 25
We can write this as an equation:
N = 462a + 25, where a is some integer.
2. Find the remainder when N is divided by 14
We can write this as:
N = 14b + r, where b is some integer and r is the remainder we need to find.
We can substitute the first equation into the second equation:
462a + 25 = 14b + r
We want to solve for r, the remainder when N is divided by 14. To do this, we can simplify the equation by dividing both sides by 14 and looking at the remainder:
33a + 1 = 2b + (r/14)
Since the left-hand side is an integer, the right-hand side must also be an integer. The only way for this to happen is if r/14 is an integer, which means that r must be a multiple of 14 plus some integer between 0 and 13.
We can simplify the equation further by taking both sides modulo 2:
33a + 1 ≡ r/14 (mod 2)
Since 33 is odd and 1 is odd, the left-hand side is odd. This means that the right-hand side must also be odd, which implies that r/14 is odd. Therefore, r must be an odd multiple of 14 plus some integer between 0 and 13.
The only answer choice that satisfies this condition is (D) 11. Therefore, the remainder when N is divided by 14 is 11.
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A number when divided by 462 gives the remainder as 25. When same number is divided by 14, the remainder will be?a)9b)5c)12d)11e)15Correct answer is option 'D'. Can you explain this answer?
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A number when divided by 462 gives the remainder as 25. When same number is divided by 14, the remainder will be?a)9b)5c)12d)11e)15Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A number when divided by 462 gives the remainder as 25. When same number is divided by 14, the remainder will be?a)9b)5c)12d)11e)15Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 462 gives the remainder as 25. When same number is divided by 14, the remainder will be?a)9b)5c)12d)11e)15Correct answer is option 'D'. Can you explain this answer?.
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