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If x and y are prime integers and x < y, which of the following cannot be true?
- a)x is even
- b)x + y is odd
- c)xy is even
- d)y + xy is even
- e)2x + y is even
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
If x and y are prime integers and x < y, which of the following can...
Let's look at each answer choice:
(A) UNCERTAIN: x could be the prime number 2.
(B) UNCERTAIN: x could be the prime number 2, which when added to another prime number (odd) would yield an odd result. Ex: 2 + 3 = 5
(C) UNCERTAIN: Since x could be the prime number 2, the product xy could be even.
(D) UNCERTAIN: y > x and they are both prime so y must be odd. If x is another odd prime number, the expression will be: (odd) + (odd)(odd), which equals an even (O + O = E).
(E) FALSE: 2x must be even and y must be odd (since it cannot be the smallest prime number 2, which is also the only even prime). The result is even + odd, which must be odd.
The correct answer is E.
(A) UNCERTAIN: x could be the prime number 2.
(B) UNCERTAIN: x could be the prime number 2, which when added to another prime number (odd) would yield an odd result. Ex: 2 + 3 = 5
(C) UNCERTAIN: Since x could be the prime number 2, the product xy could be even.
(D) UNCERTAIN: y > x and they are both prime so y must be odd. If x is another odd prime number, the expression will be: (odd) + (odd)(odd), which equals an even (O + O = E).
(E) FALSE: 2x must be even and y must be odd (since it cannot be the smallest prime number 2, which is also the only even prime). The result is even + odd, which must be odd.
The correct answer is E.
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If x and y are prime integers and x < y, which of the following can...
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If x and y are prime integers and x < y, which of the following cannot be true?a)x is evenb)x + y is oddc)xy is evend)y + xy is evene)2x + y is evenCorrect answer is option 'E'. Can you explain this answer?
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