How many integers between 10 and 20, inclusive, have a remainder of 1 or 2 when divided by 3 ?

BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:35 am

How many integers between 10 and 20, inclusive, have a remainder of 1 or 2 when divided by 3 ?

A. 9
B. 8
C. 7
D. 4
E. 3

Answer: A
Source: official guide

Key concept: When we divide an integer by 3, the remainder must be 0, 1 or 2
There are 11 integers from 10 to 20, inclusive
Among those 11 integers, the numbers that leaves a remainder of 0 are: 12, 15, and 18
In other words, 3 numbers leave a remainder of 0 when divided by 3

11 - 3 = 8
So it must be the case that the remaining 8 integers leave a remainder of 1 or 2.

Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:35 am

How many integers between 10 and 20, inclusive, have a remainder of 1 or 2 when divided by 3 ?

A. 9
B. 8
C. 7
D. 4
E. 3

Answer: A
Source: official guide

Solution:

Recall that the only possible remainders that we can obtain when we perform division by 3 are 0, 1, and 2. Thus, we want to exclude those integers between 10 and 20, inclusive, that give us a remainder of 0. The remaining integers will be those that yield a remainder of either 1 or 2 when we divide them by 3.

Since the only integers between 10 and 20, inclusive, that have a remainder of 0 when divided by 3 are the multiples of 3, we see that we can exclude integers 12, 15, and 18 from the list if we want only integers that have a remainder of 1 or 2 when divided by 3. Since there are 11 integers from 10 to 20 and we are excluding 3 of them, 11 - 3 = 8 integers will have a remainder of 1 or 2 when divided by 3.

Answer: B