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

Question

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

Bunuel · Accepted Answer

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.

Answer: C.

niyantg · Answer

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

PareshGmat · Answer

Answer = C = 6

For any value of x as an integer, y = 3x+2 is not divisible by 6

JeffTargetTestPrep · Answer

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.

Answer: C

Madhavi1990 · Answer

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.

shashankism · Answer

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.
 Answer C

NamVu1990 · Answer

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

Boundtohappen · Answer

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

BrentGMATPrepNow · Answer

A  lot of 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.

Answer: C

akshaysraje · Answer

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.

BrushMyQuant · Answer

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

So,  Answer will be C 
Hope it helps!

Watch the following video to learn the Basics of Divisibility Rules

https://www.youtube.com/watch?v=D9ZWVUyvFvM

Sourav8888 · Answer

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.

So, answer is B.

KarishmaB · Answer

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. Answer (C) Check this video for more on factors: https://www.youtube.com/watch?v=DxIH8rjhpKY and these posts: https://anaprep.com/number-properties-f ... -a-number/ https://anaprep.com/number-properties-r ... e-factors/ https://anaprep.com/number-properties-f ... ct-square/

chandy123 · Answer

Step 1: Analyze $ y = 3x + 2 $. 
For $ y $ to be divisible by a given number $ k $, $ 3x + 2 $ must be divisible by $ k $. This means:
\ 
We will check the divisibility for each option.

Step 2: Check divisibility by 4. 
If $ 3x + 2 $ is divisible by 4:
\ 
Simplify:
\ 
Since $ 3 \equiv -1 \, (\text{mod} \, 4) $, we have:
\ 
Thus, $ x $ can take values that make $ y $ divisible by 4. **4 is a possible divisor.**

Step 3: Check divisibility by 5. 
If $ 3x + 2 $ is divisible by 5:
\ 
Simplify:
\ 
Since $ 3 $ is coprime to 5, $ x $ can take values that make $ y $ divisible by 5. **5 is a possible divisor.**

Step 4: Check divisibility by 6. 
If $ 3x + 2 $ is divisible by 6, it must be divisible by both 2 and 3. 
- Divisibility by 2: $ 3x + 2 \equiv 0 \, (\text{mod} \, 2) $, which is always true because $ 3x \equiv 0 \, (\text{mod} \, 2) $.
- Divisibility by 3: $ 3x + 2 \equiv 0 \, (\text{mod} \, 3) $, but $ 3x \equiv 0 \, (\text{mod} \, 3) $, so $ 3x + 2 \equiv 2 \, (\text{mod} \, 3) $, which is not divisible by 3. 
Thus, **6 cannot be a divisor.**

Step 5: Check divisibility by 7. 
If $ 3x + 2 $ is divisible by 7:
\ 
Simplify:
\ 
Since $ 3 $ is coprime to 7, $ x $ can take values that make $ y $ divisible by 7. **7 is a possible divisor.**

Step 6: Check divisibility by 8. 
If $ 3x + 2 $ is divisible by 8:
\ 
Simplify:
\ 
Since $ 3 $ is coprime to 8, $ x $ can take values that make $ y $ divisible by 8. **8 is a possible divisor.**

Final Answer:

C. 6

EnriqueDandolo · Answer

Hey  KarishmaB  thanks so much for your answer, it helped me understand how to solve this question. Just to make sure I understood right, what you mean here is that since we know that "y" is not divisible by 3, we can conclude that if we were to divide (3x+2)/(2*3) we don't know if the 2 will cancel out but we know for sure that the 3 wont, therefore any number with a 3 in it's prime box in this question, will definitely not be a divisor of 3x+2. Does this sound right to you?

Many thanks in advance for your help.

Sa800 · Answer

i dont get it....nowhere does it say that x is a POSITIVE integer so why is everyone just plugging in POSITIVE values for x?

Sa800 · Answer

i think the way you worded it doesnt really make sense....

'Since y is 2 greater than a multiple of 3, y cannot actually be a multiple of 3'

but the previous sentence states '

In order for y - 2 to be divisible by 3, y must be 2 greater than a multiple of 3.'

DanTheGMATMan · Answer

https://www.youtube.com/watch?v=Zal4NgHhm2Q

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

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

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