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Math Expert V
Joined: 02 Sep 2009
Posts: 59712
If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:13) correct 25% (01:32) wrong based on 134 sessions

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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

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Manager  P
Joined: 01 Aug 2017
Posts: 220
Location: India
GMAT 1: 500 Q47 V15 GPA: 3.4
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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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1
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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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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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.

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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PKN

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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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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 59712
Re: If x and y are positive integers, is x even? (1) y^x is a prime number  [#permalink]

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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

_________________
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5479
Location: India
Concentration: Sustainability, Marketing
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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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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

IMOA
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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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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. 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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