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n consecutive integers are selected from the integers

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n consecutive integers are selected from the integers [#permalink] New post  25 Apr 2012, 22:51
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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?

(1) n>4

(2) n is not divisible by 5
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Re: n consecutive integers are selected from the integers [#permalink] New post  25 Apr 2012, 22:59
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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.

Answer: A.

Similar questions to practice:
seven-different-numbers-are-selected-from-the-integers-1-to-99943.html#p770748
seven-integers-x1-x2-x3-x4-x5-x6-and-x7-are-picked-73611.html

Hope it helps.
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Re: n consecutive integers are selected from the integers [#permalink] New post  09 Jul 2023, 00:01
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Yojanalath wrote:
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.

Answer: A.

Similar questions to practice:
https://gmatclub.com/forum/seven-differ ... ml#p770748
https://gmatclub.com/forum/seven-intege ... 73611.html

Hope it helps.



One doubt - as per condition 1, are we supposed to select the consecutive integers from 1 onwards? Because if we select from 2,3,4,5,6, in this case, the remainders would be (3,2,1,0,1) and hence the range would be 3 as opposed to 4 if 1,2,3,4,5 are selected. This will make 1 insufficient. Please clarify.
Thanks!

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n consecutive integers do not necessarily start from 1. Yet, this is of no concern:

If we choose {1, 2, 3, 4, 5}, the remainders upon division by 5 will be {1, 2, 3, 4, 0}. The range of the remainders = 4 - 0 = 4.
If we choose {2, 3, 4, 5, 6}, the remainders upon division by 5 will be {2, 3, 4, 0, 1}. The range of the remainders = 4 - 0 = 4.

When choosing ANY n consecutive integers, where n > 4, the numbers will yield all five possible remainders (from 0 to 4, inclusive) upon division by 5.

Hope it helps.
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Re: n consecutive integers are selected from the integers [#permalink] New post  25 Apr 2012, 23:03
Awesome explanation. Thanks
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Re: n consecutive integers are selected from the integers [#permalink] New post  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] New post  14 Jul 2016, 06:37
hfbamafan 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?

(1) n>4

(2) n is not divisible by 5


Tricky part- Range of remainders.

if n > 4 then it will be = or >5.

When consecutive numbers are divided by 5, they leave a reminder of 0, 1, 2, 3, 4. And the range will always be 4

Statement 1 is sufficient.

n can be any value as per statement 2. And hence we can have any possible range from 1, 2 or 3. Not sufficient.
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Re: n consecutive integers are selected from the integers [#permalink] New post  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.

Answer: A.

Similar questions to practice:
seven-different-numbers-are-selected-from-the-integers-1-to-99943.html#p770748
seven-integers-x1-x2-x3-x4-x5-x6-and-x7-are-picked-73611.html

Hope it helps.


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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Re: n consecutive integers are selected from the integers [#permalink] New post  27 Nov 2018, 10:54
hfbamafan 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?

(1) n>4

(2) n is not divisible by 5



Thank you for posting the question, it is one of the simple questions which checks your mind alertness, specially for the beginners !
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n consecutive integers are selected from the integers [#permalink] New post  23 Dec 2018, 02:05
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.

Answer: A.

Similar questions to practice:
https://gmatclub.com/forum/seven-differe ... ml#p770748
https://gmatclub.com/forum/seven-integer ... 73611.html

Hope it helps.


I have a doubt and I seem to be making this same error in multiple questions now.

Statement (1) says that n>4. So if n = 5, remainder is 0, if n = 6, remainder 1...and so on till remainder is 4.
I get this but we haven't been given an upper limit of n. So can we assume that 4<n<10? Or rather can we assume that n is 'finite' if it isn't given explicitly mentioned in the question?
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Re: n consecutive integers are selected from the integers [#permalink] New post  08 Jul 2023, 20:32
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.

Answer: A.

Similar questions to practice:
https://gmatclub.com/forum/seven-differ ... ml#p770748
https://gmatclub.com/forum/seven-intege ... 73611.html

Hope it helps.



One doubt - as per condition 1, are we supposed to select the consecutive integers from 1 onwards? Because if we select from 2,3,4,5,6, in this case, the remainders would be (3,2,1,0,1) and hence the range would be 3 as opposed to 4 if 1,2,3,4,5 are selected. This will make 1 insufficient. Please clarify.
Thanks!

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Re: n consecutive integers are selected from the integers [#permalink]
08 Jul 2023, 20:32
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