How many integers between 10 and 20, inclusive, have a remainder of 1

Question

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

yashikaaggarwal · Answer

Every no. Other than the multiple of 3 leaves remainder 1&2.

For the no. Between 10 to 20
There are only 3 multiples that comes in between 10-20 (inclusive) , I.e., 12,15,18 
The no. Between 10 to 20 = 
Total no. = extreme no. - first no. + 1
20-10+1
11 no. Are In total between 10 to 20
Total - 3 multiples
11-3 = 8
Answer is B

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GMATinsight · Answer

Number of integers between 10 and 20 inclusive = (20-10)+1 = 9 {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Remove all numbers which are divisible by 3 i.e. {12, 15, 18}

Remaining numbers = 11-3 = 8

Answer: Option B

BrentGMATPrepNow · Answer

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

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=P0S6j2uTaj4

DanTheGMATMan · Answer

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

https://www.youtube.com/watch?v=utYg6N0So9Q

bumpbot · Answer

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How many integers between 10 and 20, inclusive, have a remainder of 1

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GMAT Problem Solving (PS) Questions

How many integers between 10 and 20, inclusive, have a remainder of 1

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