How many integers from 0 to 48, inclusive, have a remainder of 1 when divided by 3 ? Choose the most appropriate option
A) 15
B) 16
C) 17
D) 18
E) 19
My ans is also C.17.   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,..... 46, 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, 46 = 1+(n-1)3   or, (n-1)3 = 45   or, n-1 = 15   or, n = 16   16
<result>B</result>
How many integers from 0 to 48, inclusive, have a remainder of 1 when divided by 3 ?