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16 Aug 2023, 01:30
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B
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Difficulty:
35%
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Question Stats:
72% (01:38) correct
28%
(00:59)
wrong
based on 43
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What is the value of positive integer x?
(1) The units digit of x is 5.
(2) x, x - 3 and x + 2 are all prime numbers
(1) The units digit of x is 5.
(2) x, x - 3 and x + 2 are all prime numbers
16 Aug 2023, 03:43
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The question deals with prime numbers. So we write down all the prime numbers between 1 and 200.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.
For an one time analysis we could see that except 2,5,7 we can't find such combination when the difference between two prime numbers is 3.
Statement I
The units digit of x is 5.
Insufficient information.
Statement II
x, x - 3 and x + 2 are all prime numbers
We could see the only combination is 2,5,7
Sufficient
IMO B
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.
For an one time analysis we could see that except 2,5,7 we can't find such combination when the difference between two prime numbers is 3.
Statement I
The units digit of x is 5.
Insufficient information.
Statement II
x, x - 3 and x + 2 are all prime numbers
We could see the only combination is 2,5,7
Sufficient
IMO B
16 Aug 2023, 14:55
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AryaSwagat
I agree with this approach, though no need to write out the prime number from 1-200. Once we find the 2,5, and 7 combination, we know that 2, 5, 7 is the only combination that fits the sequence regarding prime numbers. If we try X=7, we would get 4, 7, 9. Plugging in other numbers for X would result in an even number on the lower end (thus non-prime). 2, 5, and 7 being the only combination, B IMO
