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A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves a reminder 6 if the same number when divided by 11 leaves a reminder m and the resulting quotient when divided by 7 leaves a reminder n what are the value of m and n respectively?
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A number when divided by 7 leaves a remainder 3 and the resulting quot...
The given information can be represented in the form of congruences:
x ≡ 3 (mod 7) and (x/7) ≡ 6 (mod 11)
The first congruence states that when the number x is divided by 7, the remainder is 3. This can be written as x = 7k + 3 for some integer k.
Substituting this value of x in the second congruence, we get:
(7k + 3) / 7 ≡ 6 (mod 11)
Simplifying the above congruence we get
k + 3/7 ≡ 6 (mod 11)
Now the question is asking for the remainder when the number is divided by 11 and the quotient when divided by 7.
so when the same number x = 7k + 3 is divided by 11 we get:
x ≡ 3 (mod 11)
and the quotient when divided by 7 is k, so we have:
x/7 = k (mod 7)
Therefore, m = 3 and n = k.
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A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves a reminder 6 if the same number when divided by 11 leaves a reminder m and the resulting quotient when divided by 7 leaves a reminder n what are the value of m and n respectively?
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A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves a reminder 6 if the same number when divided by 11 leaves a reminder m and the resulting quotient when divided by 7 leaves a reminder n what are the value of m and n respectively? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves a reminder 6 if the same number when divided by 11 leaves a reminder m and the resulting quotient when divided by 7 leaves a reminder n what are the value of m and n respectively? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves a reminder 6 if the same number when divided by 11 leaves a reminder m and the resulting quotient when divided by 7 leaves a reminder n what are the value of m and n respectively?.
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