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If x and y are positive prime numbers such that x does not equal....

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If x and y are positive prime numbers such that x does not equal....  [#permalink]

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New post 04 Aug 2019, 23:01
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If x and y are positive prime numbers such that x does not equal y and the product of xy is not even, which of the following CANNOT be true?

I) x + y = 85.
II) x – y is an even integer.
III) x/y is an integer.

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III

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Re: If x and y are positive prime numbers such that x does not equal....  [#permalink]

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New post 05 Aug 2019, 04:45
Let's decipher the question stem.
x NOT equal to y
x & y are odd primes.

I) x + y = 85. odd + odd = odd NOT POSSIBLE
II) x – y is an even integer. Odd - odd = even CORRECT
III) x/y is an integer. X is not equal to y and both are primes, hence x cannot be divisible by y.

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If x and y are positive prime numbers such that x does not equal....  [#permalink]

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New post 05 Aug 2019, 07:08
x and y are positive prime number.

Product of xy is not even, so xy is odd. Then, both x and y must be odd. Note that x is not equal to y

I) x + y = 85.
Odd + odd = even.
CANNOT be true

II) x – y is an even integer.
Odd - odd = even.
definitely true

III) x/y is an integer.
A is a prime number if A has only 2 factors: 1 and A itself. If x/y is an integer, then x is divisible by y or y is a factor of x. x is a prime number, so this can't be true at all.
CANNOT be true


Answer is (C) - I and III

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Re: If x and y are positive prime numbers such that x does not equal....  [#permalink]

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New post 11 Aug 2019, 19:16
CAMANISHPARMAR wrote:
If x and y are positive prime numbers such that x does not equal y and the product of xy is not even, which of the following CANNOT be true?

I) x + y = 85.
II) x – y is an even integer.
III) x/y is an integer.

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III



We see that x and y must both be odd prime numbers. Let’s test each Roman Numeral.

I) x + y = 85.

Since 2 odd numbers cannot sum to an odd number, I cannot be true.

II) x – y is an even integer.

Since the difference of two odd numbers is even, II is true.

III) x/y is an integer.

The division of two different prime numbers cannot be an integer. III cannot be true.

Answer: C
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Re: If x and y are positive prime numbers such that x does not equal....   [#permalink] 11 Aug 2019, 19:16
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