How many integers from 0 to 53, inclusive, have a remainder of 1 when divided by 3 ? Pick
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,..... 52, 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,52 = 1+(n-1)3   or, (n-1)3 = 51   or, n-1 = 17   or, n = 18   18
<result>D</result>
How many integers from 0 to 53, inclusive, have a remainder of 1 when divided by 3 ?