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Euclid's Division Lemma

Two numbers a...

Question

Two numbers a and b, when divided by 7 and 6 respectively, leave remainders p and q respectively. What is the maximum value of p + q ?

A

11

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B

12

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C

6

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D

5

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Solution

The correct option is A
11

According to Euclid division lemma:
There exist integers m and n such that a = 7m + p and b = 6n + q.

For $0 \leq p < 7 \Rightarrow$ Maximum value of p will be 6.

For $0 \leq q < 6 \Rightarrow$ Maximum value of q will be 5.

Therefore, the maximum value of p + q will be 11.

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Two numbers a and b, when divided by 7 and 6 respectively, leave remainders p and q respectively. What is the maximum value of p + q ?

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