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# If the average of the consecutive even integers a, b, and c is less

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Joined: 02 Sep 2009
Posts: 53066
If the average of the consecutive even integers a, b, and c is less  [#permalink]

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03 Jun 2017, 21:19
2
9
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:59) correct 24% (01:54) wrong based on 226 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

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Schools: ISB '19, IIMA , IIMB, XLRI
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If the average of the consecutive even integers a, b, and c is less  [#permalink]

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03 Jun 2017, 22:10
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)...
VP
Joined: 07 Dec 2014
Posts: 1154
Re: If the average of the consecutive even integers a, b, and c is less  [#permalink]

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03 Jun 2017, 22:40
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 the average of the consecutive even integers a, b, and c is less  [#permalink]

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08 Jun 2017, 20:37
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: 11 Sep 2015
Posts: 3446
If the average of the consecutive even integers a, b, and c is less  [#permalink]

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09 Jun 2017, 06:38
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 the average of the consecutive even integers a, b, and c is less  [#permalink]

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09 Jun 2017, 10:15
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
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Re: If the average of the consecutive even integers a, b, and c is less  [#permalink]

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09 Jun 2017, 10:23
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Ans : A
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Re: If the average of the consecutive even integers a, b, and c is less  [#permalink]

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13 Jun 2017, 11:15
1
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 the average of the consecutive even integers a, b, and c is less  [#permalink]

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17 Oct 2018, 04:06
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Re: If the average of the consecutive even integers a, b, and c is less   [#permalink] 17 Oct 2018, 04:06
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