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If x and y are prime numbers, what is the smallest prime factor of \(xy^3\) ?
1) x=even
2) x+y=odd
1) x=even
2) x+y=odd
15 Dec 2016, 04:19
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MathRevolution
If x and y are prime numbers, what is the smallest prime factor of \(xy^3\) ?
1) x=even
2) x+y=odd
1) x=even
2) x+y=odd
1) We know that smallest prime factor is \(2\) which is the only even prime. Sufficient
2) We assume that x and y are different primes. In order for \(x + y\) to be odd, \(x\) and \(y\) should be of different parity, which gives us \(x = 2\) again. Sufficient.
Answer D
18 Dec 2016, 18:18
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==> In the original condition, there are only 2 variables (x, y), hence C is most likely to be the answer. For con 1), if x=even, an even number that is also a prime number is only “2”, so the smallest prime factor of \(xy^3\) becomes 2, and hence it is sufficient.
For con 2), in order to get x+y=odd, since it is even+odd=odd, x or y always becomes “2”, so the smallest prime factor of \(xy^3\) becomes “2”, and hence it is also sufficient.
This question is also related to mistake type 4(B), where con 1) is easy and con 2) is difficult. This type of question is a 5051-level question.
The answer is D.
Answer: D
For con 2), in order to get x+y=odd, since it is even+odd=odd, x or y always becomes “2”, so the smallest prime factor of \(xy^3\) becomes “2”, and hence it is also sufficient.
This question is also related to mistake type 4(B), where con 1) is easy and con 2) is difficult. This type of question is a 5051-level question.
The answer is D.
Answer: D
