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Bunuel
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
PS21168

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

Now, any number when divided by 3 will give us 0, 1 or 2 remainder
Only those numbers which are multiples of 3 will give us 0 remainder, others will give us 1 or 2 remainder

=> Between 10 and 20 we can exclude all the multiples of 3 to get the answer

=> Exclude 12, 15, 18 => 3 numbers

=> Numbers which will give a remainder of 1 or 2 when divided by 3 = (20 - 10 + 1) - 3 = 8

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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­Fun little remainder problem. Just build off of the nearby multiples of 3 in the range:

­
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