Numberest
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The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m>n. What is the remainder when m–n is divided by 6?
The answer is 5.
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1 solution
We are given that the numbers m and n, when divided by 6, leave remainders of 2 and 3, respectively.
Hence, we can represent the numbers m and n as 6p+2 and 6q+3, respectively, where p and q are suitable integers.
Now, m–n=(6p+2)–(6q+3)=6p–6q–1=6(p–q)–1.
A remainder must be positive, so let’s add 6 to this expression and compensate by subtracting 6: 6(p–q)–1=6(p–q)–6+6–1=6(p–q)–6+5=6(p–q–1)+5 Thus, the remainder is 5