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# If x and y are positive integers, is x odd? (1) x*y is a prime number

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Math Expert
Joined: 02 Sep 2009
Posts: 64216
If x and y are positive integers, is x odd? (1) x*y is a prime number  [#permalink]

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14 May 2018, 00:43
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Difficulty:

15% (low)

Question Stats:

82% (01:30) correct 18% (01:37) wrong based on 193 sessions

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GMAT CLUB'S FRESH QUESTION

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

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

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Joined: 04 Jan 2015
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If x and y are positive integers, is x odd? (1) x*y is a prime number  [#permalink]

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Updated on: 28 May 2018, 21:37

Solution

Given:
• x and y are positive integers

To find:
• whether the value of x is odd or not

Analysing Statement 1
• As per the information provided in Statement 1, $$\frac{x}{y}$$ is a prime number
• There can be multiple cases when this statement is true:
o If x = 4 and y = 2, then $$\frac{x}{y}$$ = 2, an even prime number
o If x = 9 and y = 3, then $$\frac{x}{y}$$ = 3, an odd prime number
• We can see whether x is even or odd cannot be specified
Hence, Statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information provided in Statement 2, $$x^y$$ is a prime number
o This is only possible when y = 1 and x is any prime number
o As x can be both even prime or odd prime, we cannot specify
Hence, Statement 2 is not sufficient to answer

Combining Both Statements
• Combining both the statements, we can say y = 1, x = prime number
o Even considering both, x can be both even prime or odd prime
Therefore, we cannot specify whether x is even or odd

Hence, the correct answer is option E.

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Originally posted by EgmatQuantExpert on 14 May 2018, 02:11.
Last edited by EgmatQuantExpert on 28 May 2018, 21:37, edited 1 time in total.
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Joined: 30 Jul 2014
Posts: 103
GPA: 3.72
Re: If x and y are positive integers, is x odd? (1) x*y is a prime number  [#permalink]

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15 May 2018, 07:54
If x and y are positive integers, is x odd?

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

From 1) (x,y) pairs would be - (2,1) (4,2) (5,1) etc.. hence no conclusion
From 2) y could only be 1, but x could be - 2,3,5... etc.. hence no conclusion

Combining 1) and 2) (x.y) could be - (2,1)(5,1) etc... hence no conclusion.

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

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15 May 2018, 23:43
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION

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

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

The data is sufficient if we can determine conclusively whether x is odd or even.

Statement 1: x/y is a prime number
Approach - Counter example
Example: x = 100 and y = 20. x/y = 5, is prime. x is even.
Counter Example: x = 85 and y = 17. x/y = 5, is prime. x is odd.

Because both possibilities exist, statement 1 ALONE is NOT sufficient.

Statement 2: x^y is a prime number
Because the question stem clearly states that x and y are positive integers, we can deduce that x is prime and y is 1.
Example: x = 5 and y = 1. x^y = 5, is prime. x is odd.
Counter Example: x = 2 and y = 1. x^y = 2, is prime. x is even.

Because both possibilities exist, statement 2 ALONE is NOT sufficient.

Combine the two statements.
Let us use the deduction from statement 2 as the starting point.
It narrows down our choice for y to just one value. y = 1.

Example: x = 5 and y = 1. x/y = 5 and x^y = 5, is prime. Satisfies both statements. x is odd.
Counter Example: x = 2 and y = 1. x/y = 2 and x^y = 2, is prime. This example also satisfies both statements. x is even.

Despite combining the two statements, we are not able to deduce whether x is odd, choice E is the answer.
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Re: If x and y are positive integers, is x odd? (1) x*y is a prime number  [#permalink]

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28 May 2018, 20:05
1
EgmatQuantExpert wrote:

Solution

Given:
• x and y are positive integers

To find:
• whether the value of x is odd or not

Analysing Statement 1
• As per the information provided in Statement 1, $$\frac{x}{y}$$ is a prime number
• There can be multiple cases when this statement is true:
o If x = 4 and y = 2, then $$\frac{x}{y}$$ = 2, an even prime number
o If x = 9 and y = 3, then $$\frac{x}{y}$$ = 3, an odd prime number
• We can see whether x is even or odd cannot be specified
Hence, Statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information provided in Statement 2, xy is a prime number
o This is only possible when y = 1 and x is any prime number
o As x can be both even prime or odd prime, we cannot specify
Hence, Statement 2 is not sufficient to answer

Combining Both Statements
• Combining both the statements, we can say y = 1, x = prime number
o Even considering both, x can be both even prime or odd prime
Therefore, we cannot specify whether x is even or odd

Hence, the correct answer is option E.

Statement 2 in question says x^y not xy

Posted from my mobile device
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Joined: 04 Jan 2015
Posts: 3367
Re: If x and y are positive integers, is x odd? (1) x*y is a prime number  [#permalink]

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28 May 2018, 21:37
push12345 wrote:

Statement 2 in question says x^y not xy

Posted from my mobile device

Hi,
The solution was provided considering $$x^y$$ only - the absence of formatting made $$x^y$$ as xy. It has been rectified now.
Regards
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Math Expert
Joined: 02 Sep 2009
Posts: 64216
Re: If x and y are positive integers, is x odd? (1) x*y is a prime number  [#permalink]

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24 Dec 2018, 01:17
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION

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

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

_________________
Re: If x and y are positive integers, is x odd? (1) x*y is a prime number   [#permalink] 24 Dec 2018, 01:17