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If x and y are distinct prime numbers, which of the following could be

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If x and y are distinct prime numbers, which of the following could be [#permalink]

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If x and y are distinct prime numbers, which of the following could be true?

A. \(\frac{x^y}{y}\) is an odd integer

B. \(x^2y^3=x^2\)

C. \(\frac{y^x}{4}\) is an even integer

D. \(\frac{xy}{2}\) is an even integer

E. \(x^y=y^x\)
[Reveal] Spoiler: OA

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Re: If x and y are distinct prime numbers, which of the following could be [#permalink]

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AbdurRakib wrote:
If x and y are distinct prime numbers, which of the following COULD be true?

A. \(\frac{x^y}{y}\) is an odd integer
B. \(x^2y^3\)=\(x^2\)
C. \(\frac{y^x}{4}\) is an even integer
D. \(\frac{xy}{2}\) is an even integer
E. \(x^y\)=\(y^x\)


The keyword here is COULD.

Scanning the answer choices, I see that C could be true.
If x = 2 and y = 3, then (x^y)/4 = (2³)/4 = 2, and 2 IS an even integer.

Answer:
[Reveal] Spoiler:
C

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Re: If x and y are distinct prime numbers, which of the following could be [#permalink]

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AbdurRakib wrote:
If x and y are distinct prime numbers, which of the following could be true?

A. \(\frac{x^y}{y}\) is an odd integer
B. \(x^2y^3\)=\(x^2\)
C. \(\frac{y^x}{4}\) is an even integer
D. \(\frac{xy}{2}\) is an even integer
E. \(x^y\)=\(y^x\)


Given, x and y are distinct Prime numbers.

A. \(\frac{x^y}{y}\) is an odd integer --> x and y doesn't have anything in common. So, the division would never be an Integer.Incorrect
B. \(x^2y^3\)=\(x^2\) --> it means y is 1 but i is not a prime number. Incorrect
C. \(\frac{y^x}{4}\) is an even integer --> For y=2 and X=3, we will have 8/4=2. An even Integer. Hence Correct Answer
D. \(\frac{xy}{2}\) is an even integer --> if xy/2 is integer, then one of x or y must be 2. which would mean it will cancel with the 2 at the denominator , hence it can never be Even. Incorrect
E. \(x^y\)=\(y^x\)[/quote] for two distinct primes, this property will never be true. Check for any set of pair. Incorrect
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Re: If x and y are distinct prime numbers, which of the following could be [#permalink]

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Here ley x be 2 and y be 3 and smash that C
Also D is incorrect as 2 is the only even prime and even if we take x as 2 => 2*odd/2=> 1*odd=Odd
hence C is the answer.
Note => Don't stress too much on E :o
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Re: If x and y are distinct prime numbers, which of the following could be [#permalink]

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New post 22 Jan 2018, 17:16
AbdurRakib wrote:
If x and y are distinct prime numbers, which of the following could be true?

A. \(\frac{x^y}{y}\) is an odd integer
B. \(x^2y^3\)=\(x^2\)
C. \(\frac{y^x}{4}\) is an even integer
D. \(\frac{xy}{2}\) is an even integer
E. \(x^y\)=\(y^x\)


We can try with \((x,y) = (3,2) & (5,2)\).. Option C.
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Re: If x and y are distinct prime numbers, which of the following could be   [#permalink] 22 Jan 2018, 17:16
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