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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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22 Jul 2016, 12:34
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55% (hard)

Question Stats:

55% (14:47) correct 45% (01:07) wrong based on 165 sessions

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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. $$x^y=y^x$$

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

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22 Jul 2016, 13:06
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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.

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

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23 Jul 2016, 23:51
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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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23 Aug 2016, 06:52
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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
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Re: If x and y are distinct prime numbers, which of the following could be [#permalink]

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22 Jan 2018, 18:16
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, 18:16
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