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
