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# If x is an integer and y = 3x + 2, which of the following

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Math Expert
Joined: 02 Sep 2009
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If x is an integer and y = 3x + 2, which of the following [#permalink]

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03 Mar 2014, 01:29
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Difficulty:

25% (medium)

Question Stats:

70% (01:15) correct 30% (01:15) wrong based on 730 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Problem Solving
Question: 125
Category: Arithmetic Properties of numbers
Page: 78
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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[Reveal] Spoiler: OA

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Math Expert
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Re: If x is an integer and y = 3x + 2, which of the following [#permalink]

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03 Mar 2014, 01:30
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SOLUTION

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

y is not a multiple of 3, actually it's 2 more than a multiple of 3. Therefore, since y is not a multiple of 3, it cannot be a multiple of 6 either.

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Re: If x is an integer and y = 3x + 2, which of the following [#permalink]

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03 Mar 2014, 02:41
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For any value of x as an integer, y = 3x+2 is not divisible by 6
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Re: If x is an integer and y = 3x + 2, which of the following [#permalink]

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04 Mar 2014, 03:30
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I hope there must be a better way to solve this question
But One method is :

Put different values of x : 0,1,2,3,4 ....
so y = 2, 5, 8, 11, 14, 17, 20, 23, 26 ...

Now checking for answer choices :
there is no multiple of 6 in the values of y

Hence Option C

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Re: If x is an integer and y = 3x + 2, which of the following [#permalink]

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04 Apr 2017, 16:16
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Expert's post
Bunuel wrote:

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

We are given the following:

y = 3x + 2

y - 2 = 3x

(y - 2)/3 = x

In order for y - 2 to be divisible by 3, y must be 2 greater than a multiple of 3. Since y is 2 greater than a multiple of 3, y cannot actually be a multiple of 3. Thus, 6 CANNOT be a divisor of y.

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Re: If x is an integer and y = 3x + 2, which of the following [#permalink]

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26 Jul 2017, 05:47
I applied a plug in technique and POE.
if x is 1; y is 5 (already present in options) so its a divisor of y
if x is 2 ; y is 8; again a divisor of y (basis options)
if x is 3; y is 11 - drop
if x is 4 ; y is 14 so 7 is a divisor
if x is 5; y is 17 drop
if x is 6; y is 20 so 4 and 5 are both divisors
if x is 7; y is 23
if x is 8; y is 26

thus 6 is only non divisor.

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Re: If x is an integer and y = 3x + 2, which of the following [#permalink]

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26 Jul 2017, 06:05
1
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Problem Solving
Question: 125
Category: Arithmetic Properties of numbers
Page: 78
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

y = 3x+2
To solve it faster , lets start putting values in sequence
x = 0, y = 2
x = 1, y = 5
x = 2 , y = 8
x = 3, y = 11
x = 4, y = 14

So, it is divisible by 4,5,7,8 . It is not divisible by 6.
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Re: If x is an integer and y = 3x + 2, which of the following [#permalink]

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21 Aug 2017, 21:39
It took me a minute and 50 seconds to get this wrong, while Bunuel did it in about 10 seconds

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Re: If x is an integer and y = 3x + 2, which of the following [#permalink]

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22 Aug 2017, 03:16
pretty straight forward... for divisibility by 6 we need last digit to be 6... and when we see the cyclical nature of multiple of 3 we find no match which when added to 2 gives 6.....so answer is 6

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Re: If x is an integer and y = 3x + 2, which of the following   [#permalink] 22 Aug 2017, 03:16
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