Number system

[nikhilagrawal]

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

Shlould Answer be A or D ??

[pepeprepa]

If D
x and y are prime number. Prime numbers are odd if >2
We know that odd/odd=odd
So x/y=odd
And (x/y)*2=even because odd*even=even
However 2x/y is a prime integer so there is a problem.

If I.
2x/y=2
It's impossible

If II.
2x/y=2x
It's impossible

I say A

[parallel_chase]

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

Shlould Answer be A or D ??

I think answer should be A.

CASE I - if x=y then 2x/y can not be a prime integer greater than 2

CASE II if y=1 then 2x/y can not be a prime integer or if x =1 then it can not be greater than 2.

CASE III if x and y both are prime integers. Lets plug in values to find out.

if x=13, y=2 then 2x/y= 13
if x=5 , y=7 then 2x/y is not even an integer.

Hence answer is A. None.

Let me know if you think otherwise.

[sudhir3127]

My answer is A.

Plug in values ..

for option A. plug in 1 as value..it fails.
For option B , y is given as 1 plug in X as 1 as well.. it fails...

for Option 3 . plug in X as 5 and Y as 7.. it fails..

hence the option is A . None..

[Ian Stewart]

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.

CASE III if x and y both are prime integers. Lets plug in values to find out.

if x=13, y=2 then 2x/y= 13
if x=5 , y=7 then 2x/y is not even an integer.

You've done this backwards, logically (and so has another post above). We know that 2x/y is a prime. That's a fact, provided in the question. It's absolutely impossible for x to be 5, and y to be 7, because then 2x/y is not a prime. You can't just assume x and y are any primes; you can only assume they are primes that make 2x/y an integer. Still, if we want to know whether III) must be true, we want to see if it's possible that it's false: that is, we want to see if we can find examples for x and y which are *not* prime, that still make 2x/y a prime.

What do we know: 2x/y is an odd prime- let's call it p. So:

2x/y = p
2x = py

The primes that divide the left side must divide the right side. So y is divisible by 2, and x is divisible by p. That's all we know, though. It could be that p is 5, y is 10, and x is 25, for example. So III) does not need to be true. (I'm assuming x and y need to be positive integers- I'd guess this should have been mentioned in the question).

[devesh99]

Why can't the answer be C i.e. Y=1

For ex. if we have Y=1, and x= 3/2 then 2x/y = 3

Since the problem does not put any restriction on x, we can assume x to be fractions.

any suggestions

[cheryl3007]

devesh99, I think the answer to your question is the term "MUST BE TRUE" in the question stem.

y = 1 could be true, not MUST BE TRUE.

E.g y can be 2
If x = 5, y = 2 --> (2 x 5 )/2 = 5: prime number greater than 2

I vote for A.

HTH.

[navdeepbajwa]

Y cannot be 1 as 2x/y holds for y=2 and it must prove false for any value of y except y=1

Answer must be A