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What da integers !!!

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What da integers !!!

by ashish » Sun Jan 04, 2015 8:10 am
If y is not equal to 3, and 3x/y is 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.

Options:
A None
B I only
C II only
D III only
E I and III
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by [email protected] » Sun Jan 04, 2015 10:22 am
Hi ashish,

In Roman Numeral questions, usually the fastest way to get to the correct answer is to do the opposite of what the question asks. Here, we're asked what "MUST be true" so we'll try to prove the opposite (what is NOT always true and WHY). These questions are usually best solved by TESTing VALUES.

We're told that Y CANNOT be 3 and that 3X/Y is a PRIME number GREATER than 2...

I. X=Y

Many of the TESTs that you might come up with will involve making X and Y the same value (1 and 1, 2 and 2). In these situations, the fraction will always equal 3 (which IS a prime number greater than 2). The key to disproving THIS Roman Numeral is to try to make the prime number something OTHER than 3.

If X = 10 and Y = 6, then 3X/Y = 5 (which IS also a prime number greater than 2).
Roman Numeral I is NOT always true.

II. Y = 1

We can use the example that we used in Roman Numeral I to disprove this one too.
Roman Numeral II is NOT always true.

III. X and Y are prime numbers

Again, we can use the prior example to disprove this Roman Numeral
Roman Numeral III is NOT always true.

Final Answer: A

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by GMATinsight » Mon Jan 05, 2015 10:08 am
ashish wrote:If y is not equal to 3, and 3x/y is 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.

Options:
A None
B I only
C II only
D III only
E I and III
Such questions are very easy to attack by refuting the options and checking the validity of given information to be judged.

Question asks "MUST be true?"

Given: 3x/y is prime integer greater than 2 [Point to note is that they need not be Integers essentially]

I) x = y
If x=1/3, y=1/2 then 3x/y = 2(Prime) but x is not y so MAY BE FALSE

II) y=1
Use the information above in (I)
If x=1/3, y=1/2 then 3x/y = 2(Prime) but y is not 1 so MAY BE FALSE

III) x and y are Prime
Use the information above in (I)
If x=1/3, y=1/2 then 3x/y = 2(Prime) but x and y are not Prime so MAY BE FALSE
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by Matt@VeritasPrep » Mon Jan 05, 2015 10:20 am
Let's start with the equations.

3x/y = odd prime

3x = y * odd prime

At this point, let's look for a few easy solutions that satisfy the equation. You can be creative here, but the basic idea is to look for ways that I, II, and III are false.

One nice solution is x = 15, y = 9, and odd prime = 5. This shows that (I), (II), and (III) all need not be true, so the answer is A.
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