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Property of Numbers Question

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Property of Numbers Question

by pierce22884 » Sat Feb 13, 2010 12:56 pm
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

OA: C
Source: GMAT Quant Review Book pg. 123.

Explanation: Although 3x is always divisible by 3, 3x+2 cannot be divisible by 3 since 2 is not divisible by 3. Thus, 3x+2 cannot be divisible by any multiple of 3, including 6.


I would appreciate it if someone could further explain this to me. What I don't understand is that if "X" is an integer, my approach would be to plug in numbers 2,3,4, etc., into x and begin crossing out choices. If x is 2, y=8, if x=4, y=7 and so on. If this is true, then why is 5 not a valid choice?

Thanks in advance for your time.
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by ajith » Sat Feb 13, 2010 1:16 pm
pierce22884 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

OA: C
Source: GMAT Quant Review Book pg. 123.

Explanation: Although 3x is always divisible by 3, 3x+2 cannot be divisible by 3 since 2 is not divisible by 3. Thus, 3x+2 cannot be divisible by any multiple of 3, including 6.


I would appreciate it if someone could further explain this to me. What I don't understand is that if "X" is an integer, my approach would be to plug in numbers 2,3,4, etc., into x and begin crossing out choices. If x is 2, y=8, if x=4, y=7 and so on. If this is true, then why is 5 not a valid choice?

Thanks in advance for your time.
say x =1; 1*3+2 =5 which is a multiple of 5
x=2; 2*3+2 = 8 which is a multiple of 4 and 8
x=4 4*3+2 =14 a multiple of 7
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by shashank.ism » Wed Feb 17, 2010 10:42 am
pierce22884 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

OA: C
Source: GMAT Quant Review Book pg. 123.

Explanation: Although 3x is always divisible by 3, 3x+2 cannot be divisible by 3 since 2 is not divisible by 3. Thus, 3x+2 cannot be divisible by any multiple of 3, including 6.


I would appreciate it if someone could further explain this to me. What I don't understand is that if "X" is an integer, my approach would be to plug in numbers 2,3,4, etc., into x and begin crossing out choices. If x is 2, y=8, if x=4, y=7 and so on. If this is true, then why is 5 not a valid choice?

Thanks in advance for your time.
Yeah plugin could be a good approach pierce22884...
Well 3x +2 could be even for even x, and hence divisible by 4 as half of the even numbers are divisible by 4
3x+2 is divisible by 5 eg 3+2 =5
3x+2 is surely not divisible by 3 as as addition of 3x,2 is surely not a multiple of 3 so it is not divisible by 6
3x+2 is divisible by 7 eg 3x4 +2 =14
3x +2 could be even for even x, and hence divisible by 8 as 1/3rdof the even numbers are divisible by 4

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by harsh.champ » Wed Feb 17, 2010 10:50 pm
pierce22884 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

OA: C
Source: GMAT Quant Review Book pg. 123.

Explanation: Although 3x is always divisible by 3, 3x+2 cannot be divisible by 3 since 2 is not divisible by 3. Thus, 3x+2 cannot be divisible by any multiple of 3, including 6.


I would appreciate it if someone could further explain this to me. What I don't understand is that if "X" is an integer, my approach would be to plug in numbers 2,3,4, etc., into x and begin crossing out choices. If x is 2, y=8, if x=4, y=7 and so on. If this is true, then why is 5 not a valid choice?

Thanks in advance for your time.
Hey pierce22884,
Well your approach of plugging no.s is right but it would be better if you also use the elimination technique.Now, in the soln. 6 is eliminated.
As to why lets see an example:-How do you test the divisibility by any number?Divide by that particular no. and if you get an integer as the quotient, the no. is divisible,else not.
Now, checking by 3:-(3x+2)/3 can be written as 3x/3 + 2/3 = x+ 2/3 .Now x is an integer but 2/3 is a fraction so the no. is not divisible.

If x is 2, y=8, if x=4, y=7 and so on. If this is true, then why is 5 not a valid choice?
Over here , if you put x=6,we get y=20 which is divisible by 5.In the question ,carefully see the "cannot".Thats why 5 is not a valid choice.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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