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#p770748https://gmatclub.com/forum/seven-intege ... 73611.htmlHope 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!
Posted from my mobile devicen 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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