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

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Difficulty:   35% (medium)

Question Stats: 75% (01:59) correct 25% (01:51) wrong based on 204 sessions

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

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

Source: Nova GMAT
Difficulty Level: 600

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Originally posted by Bunuel on 03 Jun 2017, 22:19.
Last edited by SajjadAhmad on 04 Jul 2019, 04:29, edited 1 time in total.
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Re: If (x + 5)/y is a prime integer, which of the following must be true?  [#permalink]

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

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

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)...
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Re: If (x + 5)/y is a prime integer, which of the following must be true?  [#permalink]

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

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

let x=-3
let y=1
None
A
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Re: If (x + 5)/y is a prime integer, which of the following must be true?  [#permalink]

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1
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.
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Joined: 12 Sep 2015
Posts: 4009
Re: If (x + 5)/y is a prime integer, which of the following must be true?  [#permalink]

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

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

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

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Re: If (x + 5)/y is a prime integer, which of the following must be true?  [#permalink]

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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

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Re: If (x + 5)/y is a prime integer, which of the following must be true?  [#permalink]

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Ans : A
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Re: If (x + 5)/y is a prime integer, which of the following must be true?  [#permalink]

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1
Bunuel wrote:
If (x + 5)/y is a prime integer, which of the following must be true?

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

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.

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Re: If (x + 5)/y is a prime integer, which of the following must be true?  [#permalink]

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_________________ Re: If (x + 5)/y is a prime integer, which of the following must be true?   [#permalink] 17 Oct 2018, 05:06
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