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julia-pushkina [17]
2 years ago
12

Suppose that the division N/5 leaves a remainder of 4, and the division N/2 leaves a remainder of 1, what is the ones digit on N

?
Mathematics
1 answer:
Tju [1.3M]2 years ago
7 0

Since <em>N</em>/2 leaves a remainder, <em>N</em> must be odd and ends with 1, 3, 5, 7, or 9.

<em>N</em>/5 also leaves a remainder, so <em>N</em> is not divisible by 5, so it does not end in 5.

The only correct choice is then 9, since

1 = 0•5 + 1 and 1 = 0•2 + 1

3 = 0•5 + 3 and 3 = 1•2 + 1

7 = 1•5 + 2 and 7 = 3•2 + 1

9 = 1•5 + <u>4</u> and 9 = 4•2 + <u>1</u>

<u />

Alternatively, the given information is equivalent to saying

N\equiv 4\pmod5\\\\N\equiv1\pmod2

Then you can use the Chinese remainder theorem to find <em>N</em>.

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