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

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Re: Inequality - Prime number [#permalink]
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.

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Re: Inequality - Prime number [#permalink]
Bunuel wrote:
saurabhgoel wrote:
35. If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.

(A) None

(B) I only

(C) II only

(D) III only

(E) I and II

My pick is (A)

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).

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

please enlighten me for this approach

Regards
Puneet
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Re: Inequality - Prime number [#permalink]
Bunuel wrote:
saurabhgoel wrote:
35. If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.

(A) None

(B) I only

(C) II only

(D) III only

(E) I and II

My pick is (A)

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).

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

please enlighten me for this approach

Regards
Puneet
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If y ≠ 3 and 2x/y is a prime integer greater than 2, which of th [#permalink]
1
Kudos
'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'.
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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which [#permalink]
1
Kudos
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.
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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which [#permalink]
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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Re: If y 3 and 2x/y is a prime integer greater than 2, which [#permalink]
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Re: If y 3 and 2x/y is a prime integer greater than 2, which [#permalink]
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