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

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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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For any value of x as an integer, y = 3x+2 is not divisible by 6
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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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Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a [#permalink]
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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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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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Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a [#permalink]
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 CANNOT be a [#permalink]
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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If x is an integer and y = 3x + 2, which of the following CANNOT be a [#permalink]
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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 B
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

CONVENIONAL APPROACH:
Since 3x represents a multiple of 3 for all integer values of x, it must then be the case that (3x + 2) represents a value that’s 2 greater than some multiple of 3.
Since y = 3x + 2, we now know that y is 2 greater than some multiple of 3, which means y is NOT a multiple of 3.
In other words, 3 is NOT a divisor of y.

Key divisibility Rule: 6 is a divisor of y if and only if 3 and 2 are both divisors of y.
Since 3 is NOT a divisor of y, 6 cannot be a divisor of y.

Originally posted by BrentGMATPrepNow on 14 Mar 2018, 08:17.
Last edited by BrentGMATPrepNow on 18 Apr 2022, 09:12, edited 2 times in total.
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Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a [#permalink]
If a number is divisible by 6 then it is divisible by both 2 and 3. However, adding 2 to multiple of 3 makes it non-divisible by 3 and hence 6 is the correct answer.
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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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Given that x is an integer and y = 3x + 2 and we need to find which of the following CANNOT be a divisor of y

(A) 4
x = 2 we get, y = 3*2 + 2 = 6 + 2 = 8 => 4 IS A DIVISOR of y

(B) 5
x = 6 we get, y = 3*6 + 2 = 18 + 2 = 20 => 5 IS A DIVISOR of y

(C) 6
This wont be possible as 3 is a factor of 6 so 3x + 2 can never be a multiple of 3 or cannot be any multiple of a multiple of 3 => 6 IS NOT A DIVISOR of y

In exam, we don't need to solve further but I am solving to complete the solution.

(D) 7
x = 4 we get, y = 3*4 + 2 = 12 + 2 = 14 => 7 IS A DIVISOR of y

(E) 8
x = 2 we get, y = 3*2 + 2 = 6 + 2 = 8 => 8 IS A DIVISOR of y

Hope it helps!

Watch the following video to learn the Basics of Divisibility Rules

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Re: If x is an integer and y = 3x + 2, which of the following CANNOT be a [#permalink]
Since y = 3x + 2 that means whatever value we put for X(integer), we won't get the value of Y in multiple of 3. So, in any option in which 3 is a factor, that number will not be a divisor of Y.

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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

What does y = 3x + 2 mean? It means that y when divided by 3 gives x as quotient and 2 as remainder. So y is not completely divisible by 3 i.e. 3 is not a factor of y.
Since 6 has a 3 too, 6 cannot be a factor of y either.