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

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by guerrero » Sat Jul 27, 2013 1:42 pm
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
â… . x = y
â…¡. y = 1
â…¢. x and y are prime integers.
(A) None
(B) â…  only
(C) â…¡only
(D) â…¢only
(E) â… and â…¢

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by [email protected] » Sat Jul 27, 2013 2:16 pm
Hi guerrero,

This is an example of a Roman Numeral question; a rather effective way to crush them is to prove the "opposite" of what the question asks for and then eliminate answer choices.

In this case, we know that y cannot be 3 and that 3x/y is a prime > 2

The questions asks for what MUST be true....so I'm going to prove what's NOT NECESSARILY TRUE...

I. x = y
Does x HAVE TO = y?
Can you come up with ANY situation in which that's not true?
How about...
x = 5/3
y = 1
We've satisfied all of the conditions and proven that x doesn't have to equal y.
Eliminate B and E

II y = 1
Does y HAVE TO = 1?
How about...
x = 2
y = 2
We've satisfied all of the conditions and proven that y doesn't have to = 1.
Eliminate C

III x and y are prime integers
How about...the example we used in Roman numeral 1
x = 5/3
y = 1
Eliminate D (we eliminated E earlier)

Final Answer is A

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by Matt@VeritasPrep » Sat Jul 27, 2013 2:19 pm
Let's explore some options:

Say x = 5/3, y = 1, p = 5: then (i) and (iii) need not be true.

Say x = 1, y = 3/5, p = 5: then (ii) need not be true.
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