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n consecutive integers are selected from the integers [#permalink]
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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]
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25 Apr 2012, 22:59
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 40=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 40=0 but if 2 integers selected are 6 and 7 then the remainders will be 1 and 2 and the range will be 21=1. not sufficient. Answer: A. Similar questions to practice: sevendifferentnumbersareselectedfromtheintegers1to99943.html#p770748sevenintegersx1x2x3x4x5x6andx7arepicked73611.htmlHope it helps.
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Re: n consecutive integers are selected from the integers [#permalink]
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25 Apr 2012, 23:03
Awesome explanation. Thanks
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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 (n1) 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 = 40 = 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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Re: n consecutive integers are selected from the integers [#permalink]
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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]
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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 40=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 40=0 but if 2 integers selected are 6 and 7 then the remainders will be 1 and 2 and the range will be 21=1. not sufficient. Answer: A. Similar questions to practice: sevendifferentnumbersareselectedfromtheintegers1to99943.html#p770748sevenintegersx1x2x3x4x5x6andx7arepicked73611.htmlHope 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
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