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17 Jul 2017, 23:07
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C
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Difficulty:
55%
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Question Stats:
64% (01:50) correct
36%
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wrong
based on 245
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What is the probability that an integer chosen from a set P, which contains consecutive positive integers, when divided by 5, leaves a prime remainder?
(1) The value of the range of the integers in set P is 10.
(2) The largest integer in set P is 35.
(1) The value of the range of the integers in set P is 10.
(2) The largest integer in set P is 35.
Bunuel
It should be C
Statement 1: Insufficient
Range gives us the number of sets which is 11. However, the number of prime remainders depends on where the sequence starts.
Say our set P contains 11 integers starting from 1 i.e. set P has elements 1,2,3,4,5,6,7,8,9,10,11. Remainder when divided by 5 would be 1,2,3,4,0,1,2,3,4,0,1 where we have 2,3 (primes) appearing twice.
If we have a set starting with 2 i.e. set P has elements 2,3,4,5,6,7,8,9,10,11,12. Remainder when divided by 5 would be 2,3,4,0,1,2,3,4,0,1,2 so we have 1 extra prime remainder in the form of last 2. This changes probability.
Statement 2: Insufficient
Largest integer is 35, but again applying the same rule, without knowing how many elements are in the range, we cannot be sure of the remainder and its probability of being prime.
Combining, we know the set is 25-35 so we can calculate the total number of primes easily.
21 Oct 2025, 09:00
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