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

Question

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

M36-40

Bunuel · Accepted Answer

Official Solution:

If  x  and  y  are positive integers, is  x  odd? 
 
(1)  \frac{x}{y}  is a prime number 
 
Can  x  be odd? Sure! Consider  x=3  and  y=1 .
 
Can  x  be even? Sure! Consider  x=2  and  y=1 .
 
Not sufficient.
 
(2)  x^y  is a prime number 
 
Can  x  be odd? Sure! Consider  x=3  and  y=1 .
 
Can  x  be even? Sure! Consider  x=2  and  y=1 .
 
Not sufficient.
 
(1)+(2)  x=3  and  y=1  AND  x=2  and  y=1  satisfy both statement, so  x  can be even as well as odd. Not sufficient.

Answer: E

EgmatQuantExpert · Answer

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.

Answer: E

AD2GMAT · Answer

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.

Answer E.

WizakoBaskar · Answer

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.

push12345 · Answer

Statement 2 in question says x^y not xy

Posted from my mobile device

EgmatQuantExpert · Answer

Hi,
The solution was provided considering  x^y  only - the absence of formatting made  x^y  as xy. It has been rectified now. 
Regards

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

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

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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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