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

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Director
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If x is an integer and y = 3x + 2, which of the following [#permalink]  01 Oct 2007, 01:45
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

i'm struggling to find the best approach to do this in 2 minutes. I started plugging in numbers but there should be a better approach. Please help. Thanks
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Director
Joined: 09 Aug 2006
Posts: 766
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Re: Number Properties - Approach help!! [#permalink]  01 Oct 2007, 02:03
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

i'm struggling to find the best approach to do this in 2 minutes. I started plugging in numbers but there should be a better approach. Please help. Thanks

Answer C; plugged in values of x but after a little thought which cut down the time to solve. Basically, I looked for multiples of the answer choices and if after subtracting two from these multiples, they were divisible by 3, I eliminated them.

Eg: To check for choice D, 7, I thought of a multiple of 7, that is 56; subtracted 2 to get 54; Since 54 is a multiple of 3, we can eliminate D.

Plug in x = 2 to eliminate A & E
Plug in x = 11 to eliminate B
Plug in x = 18 to eliminate D

Manager
Joined: 10 Jan 2005
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Remember the basic formula to represent any integer as a product of a quotient, divisor and remainder:

Y = Xq + r, where 0 <= r < X

y = 3x + 2 follows this format so you see y cannot be divided by 3 because of the remainder 2.

Which of the answer choices are dependent on division by 3?
Only 6 (remember to be divisible by 6 an integer must be divisible both by 3 and by 2)
Manager
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Re: Number Properties - Approach help!! [#permalink]  13 Oct 2007, 14:52
X is an integer... This is important.

As such, you can re-write to

(y-2)/3 must not yield any remainder.

The set that works for this is {5, 8, 11, 14, 17, 20, 23, 26, 29, 32}
A eliminated by 32
B eliminated by 5
C not eliminated (note none of the numbers are divisible by 3...)
D eliminated by 14
E eliminated by 8
Director
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Re: Number Properties - Approach help!! [#permalink]  13 Oct 2007, 23:21
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

i'm struggling to find the best approach to do this in 2 minutes. I started plugging in numbers but there should be a better approach. Please help. Thanks

C,

(3x+2)/? is NEVER intenger.

(3x/?) + (2/?) is NEVER intenger

A) (3x/2) + (2/2)----------> out, cuz x can be 2
B) (3x/5) + (2/5)----------> not sure leave for now, move to the next
C) (3x/3*2) + (2/3*2)= x/2+1/3 for this to be an intenger x/2 must be +2/3 or -1/3, which is impossible given that x is an intenger.
Re: Number Properties - Approach help!!   [#permalink] 13 Oct 2007, 23:21
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