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Number - should 1 be included

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Number - should 1 be included

by gmatrant » Wed Jan 04, 2012 11:16 am
How many integers from 0 to 50 inclusive have a remainder of 1 when divided by 3?

My only doubt is should 1 also be treated as a number, which means 1 divided by 3 is zero.

If one is included the answer is 17 else 16.
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by rijul007 » Wed Jan 04, 2012 11:30 am
Yes, 1 is also included.

3(0)+1 = 1
When 1 is divided by 3, remainder is 1.
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by chieftang » Wed Jan 04, 2012 2:14 pm
gmatrant wrote:How many integers from 0 to 50 inclusive have a remainder of 1 when divided by 3?

My only doubt is should 1 also be treated as a number, which means 1 divided by 3 is zero.

If one is included the answer is 17 else 16.

Well, what is the answer when 1 is divided by 3? 0, remainder 1. So........
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by Anurag@Gurome » Wed Jan 04, 2012 6:44 pm
gmatrant wrote:How many integers from 0 to 50 inclusive have a remainder of 1 when divided by 3?

My only doubt is should 1 also be treated as a number, which means 1 divided by 3 is zero.

If one is included the answer is 17 else 16.
1 divided by 3 has a remainder of 1. When an integer a is divided by integer b, and if a is the smaller out of the two, then a will also be the remainder.

Example: 7/15 has remainder 7.

Now, 1 = 3 * 0 + 1
49 = 3 * 16 + 1
This is an AP with common difference = 3. So, 49 = 1 + 3(n - 1) or n = 17
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