If y ≠ 3 and 2x/y is a prime integer greater than 2, which

Given 2x/y is prime >2

could be {3,5,7,11....}

I) x = y => 2x/y = 2 , 2 will never be prime >2 (Ruled out)
II)y=1 . Not necessarily. 2 (3)/2 = 3 which is prime and here y is 2 (Ruled out)
III)x and y are prime integers . not necessarily . (Ruled out)
2(3)/2 x and y prime
2(21)/6 x and y are not prime.

Answer is A (None)

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2).

I. x = y --> not necessarily true: x=3 and y=2 (2x/y=3=prime>2);

II. y=1 --> not necessarily true: x=3 and y=2 (2x/y=3=prime>2);

III. x and y are prime integers --> not necessarily true: x=10 and y=4 (2x/y=5=prime>2).

Answer: A.


Dear bunuel
can't we go have another approach
by considering the options from 1st to 3rd
and see if 2x/y is not a prime no >2
as below
I. x = y --> then 2x/y=2 which is not greater then 2 so can't be true
II. y=1 --> then 2x/y=2 which is also not greater then 2 so can't be true
III. x and y are prime integers --> then this value will be fractional only so cant be an INTEGER so can't be true

hence A is the answer

please enlighten me for this approach

Regards
Puneet

Dear bunuel
can't we go have another approach
by considering the options from 1st to 3rd
and see if 2x/y is not a prime no >2
as below
I. x = y --> then 2x/y=2 which is not greater then 2 so can't be true
II. y=1 --> then 2x/y=2x which is an even number always so can't be true
III. x and y are prime integers --> then this value will be fractional only so cant be an INTEGER so can't be true

hence A is the answer

please enlighten me for this approach

Regards
Puneet

'A' is the right option. Condition III is satisfied when y=2 and x= some prime integer, but for other primes, it negates the condition. Hence 'None'.

I think we can do it in a more simple way:
2x/y=prime
-->2x=prime * y ,that is, 2x=odd*odd which is never possible.
None of the options will satisfy dis...
Hence A.

This question seems to be transcribed incorrectly. I think it should be either y != 2 and 2x/y = prime > 2 or y != 3 and 3x/y = prime > 2.

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