How many integers between 10 and 20, inclusive, have a remainder of 1 : Problem Solving (PS)

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

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Math Expert

Joined: 02 Sep 2009

Posts: 65241

How many integers between 10 and 20, inclusive, have a remainder of 1 [#permalink]

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22 May 2020, 07:33

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Question Stats:

79% (01:02) correct

21% (00:52) wrong

based on 46 sessions

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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

Spoiler: OA

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Re: How many integers between 10 and 20, inclusive, have a remainder of 1 [#permalink]

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22 May 2020, 07:39

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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Re: How many integers between 10 and 20, inclusive, have a remainder of 1 [#permalink]

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22 May 2020, 07:40

Bunuel wrote:

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

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
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Re: How many integers between 10 and 20, inclusive, have a remainder of 1 [#permalink]

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22 May 2020, 07:43

Top Contributor

Bunuel wrote:

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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Re: How many integers between 10 and 20, inclusive, have a remainder of 1 [#permalink] 22 May 2020, 07:43

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

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