Problem Solving

AAPL wrote:Official Guide

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

A. 15
B. 16
C. 17
D. 18
E. 19

When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, the values that have a remainder of 1 when divided by 3 are: 1, 4, 7, 10, 13, . . .

APPROACH #1: List the values.
The answer choices tell us that there are no more than 19 values, so this won't take long.
The value are: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46 ,49
There are 17 possible values
Answer: C

APPROACH #2: Find a pattern
Notice that we can list the possible values as follows:
1
3 + 1
2(3) + 1
3(3) + 1
4(3) + 1
etc

So, what's the BIGGEST possible value?
We know that 48 is a multiple of 3 (since 16 x 3 = 48)
So, our BIGGEST possible value is 49, which can be written as 16(3) + 1

So, the possible values can be written as follows:
0(3) + 1
1(3) + 1
2(3) + 1
3(3) + 1
4(3) + 1
.
.
.
16(3) + 1
There are 17 integers from 0 to 16 inclusive
Answer: C

Cheers,
Brent

AAPL wrote:Official Guide

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

A. 15
B. 16
C. 17
D. 18
E. 19

OA C

The first number that has a remainder of 1 when divided by 3 is 1, and the last number is 49.

Thus, the number of integers from 0 to 50 inclusive that have a remainder of 1 when divided by 3 is:

(49 - 1)/3 + 1 = 17

Answer: C