Economist wrote:
If y ≠ 3 and 3x/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 III
Guys, I am sure this might have come earlier, but I am kind of confused about these MUST be true questions.
Here, if 3x/y is a prime number greater than 2 then x and y should always be equal so that they can cancel out. We cant have any other factor of 3x/y!!
Since this is a ‘Must be true’ kind of question, the best strategy to adopt would be that of trying to falsify each statement once and simultaneously eliminate the corresponding answer options.
Remember that any statement which is false ONCE, cannot be true ALWAYS. In a ‘Must be true’ question, the objective is to identify a statement/statements which is/are true ALWAYS/under all cases.
To make a statement false, we take a few simple cases i.e. simple values for the variables.
The question says that y≠3 and 3x/y is a prime number greater than 2. This means that the possible value for 3x/y can be 3,5,7 and so on.
If 3x/y = 3, then x and y can be any value, but both are equal, since x/y = 1. Statement I is true in this case, so we hold on to options containing statement I i.e. options B and E.
If 3x/y = 5, then x/y = 5/3. One possible value that satisfies this ratio is x = 10 and y = 6. Clearly, all 3 statements are false in this case.
This means that none of them are ALWAYS true. So, the correct answer options is A.
Hope this helps!
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Crackverbal Prep Team
www.crackverbal.com