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n consecutive integers are selected from the integers 1 through k, and each number is divided by 5. What is the range of the remainders?

A positive integer can give only 5 remainders upon division by 5: 0, 1, 2, 3, or 4.

(1) n>4. If we select 5 (or more) consecutive integers then they will give all five possible remainders (from 0 to 4, inclusive), so the range will be 4-0=4. Sufficient.

(2) n is not divisible by 5 --> if 2 integers are selected which are for example 9 and 10 then the remainders will be 4 and 0 and the range will be 4-0=0 but if 2 integers selected are 6 and 7 then the remainders will be 1 and 2 and the range will be 2-1=1. not sufficient.

Re: n consecutive integers are selected from the integers [#permalink]

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11 Aug 2013, 09:09

When n is the divisor, remainder ranges from 0 to (n-1)

Hence

(1).

n>4 means 1 through k would be

1,2,3,4,5 or 1,2,3,4,5,6... and so on and so forth.

So we know from above that the highest remainder when divided by 5 would be "4" and the lowest would be "0". Hence Sufficient as range = highest remainder - lowest remainder = 4-0 = 4

(2).

1,2 1,2,3

Both the above have different ranges of remainder Hence Insufficent

(A) It is !!
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Re: n consecutive integers are selected from the integers [#permalink]

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06 Oct 2014, 13:36

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Re: n consecutive integers are selected from the integers [#permalink]

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14 Jul 2016, 03:10

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Re: n consecutive integers are selected from the integers [#permalink]

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24 Jan 2017, 11:11

Bunuel wrote:

n consecutive integers are selected from the integers 1 through k, and each number is divided by 5. What is the range of the remainders?

A positive integer can give only 5 remainders upon division by 5: 0, 1, 2, 3, or 4.

(1) n>4. If we select 5 (or more) consecutive integers then they will give all five possible remainders (from 0 to 4, inclusive), so the range will be 4-0=4. Sufficient.

(2) n is not divisible by 5 --> if 2 integers are selected which are for example 9 and 10 then the remainders will be 4 and 0 and the range will be 4-0=0 but if 2 integers selected are 6 and 7 then the remainders will be 1 and 2 and the range will be 2-1=1. not sufficient.

Bunuel how you determined that they are positive ?If I am not wrong integer can be negative too. If we say N>4 and choose -2,-1,0,1,2 then range will be between {0,2}

Any help
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