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Math Expert V
Joined: 02 Sep 2009
Posts: 58421
If x is an integer and y = 3x + 2, which of the following CANNOT be a  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 73% (01:34) correct 27% (01:38) wrong based on 1198 sessions

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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

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

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Math Expert V
Joined: 02 Sep 2009
Posts: 58421
Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a  [#permalink]

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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 CANNOT be a  [#permalink]

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1
Answer = C = 6

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 CANNOT be a  [#permalink]

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4
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 CANNOT be a  [#permalink]

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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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Senior Manager  S
Joined: 15 Jan 2017
Posts: 340
Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a  [#permalink]

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1
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 CANNOT be a  [#permalink]

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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

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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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GMAT 1: 670 Q49 V33 Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a  [#permalink]

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It took me a minute and 50 seconds to get this wrong, while Bunuel did it in about 10 seconds Intern  B
Joined: 28 Jul 2017
Posts: 3
Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a  [#permalink]

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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
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4017
Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a  [#permalink]

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Top Contributor
Baten80 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

A lotof integer properties questions can be answered by testing values. So, let's do that here.

KEY: x is an integer

So, if x = 1, then y = 3(1) + 2 = 5. Since 5 is a divisor of 5, we can ELIMINATE C
If x = 2, then y = 3(2) + 2 = 8. Since 4 and 8 are both divisors of 8, we can ELIMINATE A and E
If x = 3, then y = 3(3) + 2 = 11. Doesn't help us
If x = 4, then y = 3(4) + 2 = 14. Since 7 is a divisor of 14, we can ELIMINATE D

By the process of elimination, the correct answer is C

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

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_________________ Re: If x is an integer and y = 3x + 2, which of the following CA   [#permalink] 16 Sep 2019, 22:40
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