How many integers from 0 to 44, inclusive, have a remainder of 1 when divided by 3 ?
Options.
A) 13
B) 16
C) 17
D) 18
E) 19
Explanation:   1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.   Hence we have an arithmetic progression: 1, 4, 7, 10,..... 43, which are in the form 3n+1.   Now we have to find out number of terms.   tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.   so, 43 = 1+(n-1)3   or, (n-1)3 = 42   or, n-1 = 12   or, n = 13   13
<result>A</result>
How many integers from 0 to 44, inclusive, have a remainder of 1 when divided by 3 ?