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After the division of a number successively by 3,4 and 7, the remainders obtained are 2,1 and 4 respectively. What will be the remainder if 84 divides the same number?
- a)41
- b)80
- c)75
- d)53
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
After the division of a number successively by 3,4 and 7, the remainde...
Since after division of a number successively by 3,4 and 7, the
remainders obtained are 2,1 and 4 respectively, the number is
of form ((((4×4)+1)×3)+2)k=53K
Let k=1; the number becomes 53
If it is divided by 84, the remainder is 53.
Option d) is the correct answer.
remainders obtained are 2,1 and 4 respectively, the number is
of form ((((4×4)+1)×3)+2)k=53K
Let k=1; the number becomes 53
If it is divided by 84, the remainder is 53.
Option d) is the correct answer.
Most Upvoted Answer
After the division of a number successively by 3,4 and 7, the remainde...
Understanding the Problem:
Given remainders after dividing the number successively by 3, 4, and 7, we need to find the remainder when the number is divided by 84.
Key Points to Consider:
- Remainder after dividing by 3 is 2
- Remainder after dividing by 4 is 1
- Remainder after dividing by 7 is 4
Calculating the Number:
Let the number be x. According to the given information:
- x = 3a + 2 (where 'a' is a quotient)
- x = 4b + 1 (where 'b' is a quotient)
- x = 7c + 4 (where 'c' is a quotient)
Finding the Number:
To find the number, we can solve these congruences simultaneously:
- x ≡ 2 (mod 3)
- x ≡ 1 (mod 4)
- x ≡ 4 (mod 7)
Solving these congruences, we get x = 53 as the number.
Finding the Remainder when 84 Divides the Number:
Now, we need to find the remainder when 53 is divided by 84.
Dividing 53 by 84, we get the remainder as 53.
Therefore, the remainder when 84 divides the number is 53 (option D).
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After the division of a number successively by 3,4 and 7, the remainders obtained are 2,1 and 4 respectively. What will be the remainder if 84 divides the same number?a)41b)80c)75d)53Correct answer is option 'D'. Can you explain this answer?
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