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If x and y are positive integers, is x even? (1) y^x is a prime number

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If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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New post 14 May 2018, 01:46
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Re: If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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New post 14 May 2018, 02:41
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Bunuel wrote:

GMAT CLUB'S FRESH QUESTION



If x and y are positive integers, is x even?

(1) y^x is a prime number
(2) x*y is a prime number


Solution:-

Statement 1 :- \(y^x\) is a prime number

If any number is raised to the power. The result will not be prime numbers.

For Statement 1 to be prime number. X has to be ONE.

Is X even. Ans is NO.

Hence it is sufficcient
.

Statement 2 :- x*y is a prime number

Product of two number is prime only if any one of X & Y is ONE.

But we cannot determine, If X = 1 or Y =1.

For example -
1) x =2 & y=1. X * Y = 2 * 1 = 2. is a prime number. And X is even.

2) x =1 & y=3. X * Y = 3 * 1 = 3. is a prime number. And X is odd.

No definite ans

Hence statement 2 is insufficient.

Ans - A
.
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Re: If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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New post 09 Aug 2018, 19:02
what if I assume that y=1 and vary x = 2,3,.... For all those options ST1 not sufficient as X can be odd or even. Please correct me.
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Re: If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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New post 10 Aug 2018, 07:43
ANGHOS82 wrote:
what if I assume that y=1 and vary x = 2,3,.... For all those options ST1 not sufficient as X can be odd or even. Please correct me.


Hi ANGHOS82,

Notes:-

1) An odd number can be prime. (Example 1, 3,7,11 etc)
2) An even number can be prime. (Example only 2)
3) 1 is not prime.
4) 1 is odd.
5) 1 raised to the power any positive integer is equal to 1.

As per your picked numbers,

y=1, x=2; so \(y^x=1^2=1\) , which is not a prime number, violating statement 1.

So, we can't pick y=1.

Hope it helps.
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Re: If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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New post 10 Aug 2018, 16:30
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION



If x and y are positive integers, is x even?

(1) y^x is a prime number
(2) x*y is a prime number



Hi, I tested x=0, to get that raising anything to 0 will result in a prime number, 1. Raising a prime number to 1, will result (obviously) to that same prime number. Hence, x could be either 0 or 1.

I made a silly mistake since it clearly stated that x and y are positive integers, so that would eliminate 0 as an option and make statement 1 sufficient (always odd). Just writing down my question helped to spot where I went wrong.
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Re: If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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New post 24 Dec 2018, 01:50
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Re: If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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New post 24 Dec 2018, 02:29
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION



If x and y are positive integers, is x even?

(1) y^x is a prime number
(2) x*y is a prime number


#1:
3^1 or 2^1 prime no so x has to be 1 only sufficient

#2: x*y= prime x can be either even or odd in case of 2*1 so in sufficient

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Re: If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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New post 26 Dec 2018, 01:20
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION



If x and y are positive integers, is x even?

(1) y^x is a prime number
(2) x*y is a prime number


Statement 1) a prime no has only 2 factors, 1 and itself. So, if y^x is prime. No of factors=x+1, x+1=2, x=1, x is odd. Sufficient.
Statement 2) x can 1 or the prime number. If xy=2, x can be 1 or 2. Either odd or even. Insufficient.
Hence, Option A is correct.
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Re: If x and y are positive integers, is x even? (1) y^x is a prime number   [#permalink] 26 Dec 2018, 01:20
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