If (x + 5)/y is a prime integer, which of the following must be true?

All the given conditions can be proved wrong.

Ques says (x+5)/y is prime number.

Statement 1 - y = 5x: Let x = 5, y = 2.So the expression will have a value 5 which is a prime number and satisfies the original condition and here, y is not equal to 5x. False
Statement 2 - y is prime: Let x = 23, y = 4. So the expression will have a value 7 which is a prime number and satisfies the original condition but y is not prime. False
Statement 3 - (x+5)/y is odd: Let x = -3, y = 1. So the expression will have a value 2 which is a prime number and satisfies the original condition but (x+5)/y is not odd, it is even. False

None of the condition is always true. Option A is correct.

Great question, Bunuel!!!

IMPORTANT: Many test-takers will automatically assume that x and y are integers.
However, there's nothing in the question that states this.

Also, when it comes to "What MUST be true" questions, we can eliminate any answer choice that we can show to be false.

Given this, let's see what happens when x = 0, and y = 2.5
Notice that this meets the condition that (x + 5)/y is a prime integer, since (0 + 5)/2.5 = 2, and 2 IS a prime integer.

Now let's test the three statements...

I. 2.5 = 5(0)
NOT TRUE

II. 2.5 is a prime integer.
NOT TRUE

At this point, we need not even check statement III, since there is no answer choice that says "III only"
That said, let's test III for "fun"

III. (0 + 5)/2.5is odd.
NOT TRUE

Answer: A

Cheers,
Brent

Imo A
Let's take one statement at a time
1 y=5x can not be true
2 y prime number not true always 30 /10 =3
3 last statement can be even as well if take x=-3 and Y =1
Then the result is even 2

Sent from my ONE E1003 using GMAT Club Forum mobile app

Ans : A

We are given that (x + 5)/y is a prime integer. Let’s analyze each Roman numeral.

I. y = 5x

If x = 5 and y = 2, we have (x + 5)/y = (5 + 5)/2 = 10/2 = 5, which is a prime integer. However, y ≠ 5x, since 2 ≠ 5(5). Roman numeral I is not correct.

II. y is a prime integer.

If x = 15 and y = 4, we have (x + 5)/y = (15 + 5)/4 = 20/4 = 5, which is a prime integer. However, y = 4 is not a prime integer. Roman numeral II is not correct.

III. (x + 5)/y is odd.

If x = 1 and y = 3, we have (x + 5)/y = (1 + 5)/3 = 6/3 = 2, which is a prime integer. However, (x + 5)/y = 2 is not odd. Roman numeral III is not correct.

Answer: A

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