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

Question

I. y = 5x
II. y is a prime integer.
III. (x + 5)/y is odd.

(A) None
(B) I only
(C) II only
(D) I and II only
(E) II and III only

sashiim20 · Answer

Check each options;
(I) y = 5x
Let x = 1, y = 2 ; ===>  \frac{(x + 5)}{y}  =>  \frac{(1 + 5)}{2}  =  \frac{6}{2}  = 3 (Prime integer)

2 = 5 x 1 (y does not equal 5x) . Hence I must not be true.

(II) y is a prime integer.
Let x = 7, y = 4 ; ===>  \frac{(x + 5)}{y}  =>  \frac{(7 + 5)}{4}  =  \frac{12}{4}  = 3 (Prime integer)

y is not prime integer. Hence II must not be true.

(III)  \frac{(x + 5)}{y}  is odd.

Let x = 1 , y = 3 ; ===>  \frac{(x + 5)}{y}  =>  \frac{(1 + 5)}{3}  =  \frac{6}{3}  = 2 (Even and Prime integer)
Hence III must not be true.

Therefore None of the options must be true. Answer (A)...

gracie · Answer

let x=-3
let y=1
None
A

utkarshthapak · Answer

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.

BrentGMATPrepNow · Answer

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)/ 2.5 is odd.
NOT TRUE

Answer: A

Cheers,
Brent

arvind910619 · Answer

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

Leo8 · Answer

FullSizeRender (5).jpg Ans : A

JeffTargetTestPrep · Answer

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

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

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