OG # Properties Question

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Canman: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Fri Jul 11, 2008 5:00 am; Thanked: 4 times

by Canman » Mon Jul 14, 2008 3:05 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

Even though this seems to be a simple problem, I'm a little hung up on the logic. I feel there may be a bigger, more important number properties lesson burried in here that is just on the verge of coming together for me, so I can let this problem go! Thanks for your help.

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Source: Beat The GMAT — Problem Solving | Mon Jul 14, 2008 3:05 pm

BlueRain: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Sun Jul 13, 2008 10:36 pm; Thanked: 1 times; GMAT Score:770

by BlueRain » Mon Jul 14, 2008 3:31 pm

Easy solving steps (process of elimination)
if x = 1, y = 5, eliminate B
if x = 2, y = 8, eliminate A, E,
if x = 4, y = 14, eliminate D

Logical reasoning:
If y is divisible by 6, then y is divisible by 3
If y is divisible by 3, then y - 2 cannot be divided by 3
Since y - 2 CAN be divided by 3, y is NOT divisible by 6

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: OG # Properties Question

by Ian Stewart » Mon Jul 14, 2008 4:30 pm

Canman 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

Even though this seems to be a simple problem, I'm a little hung up on the logic. I feel there may be a bigger, more important number properties lesson burried in here that is just on the verge of coming together for me, so I can let this problem go! Thanks for your help.

Yes, you're certainly right- there is a deeper number properties lesson here. If y = 3x + 2, the key fact here is that y can't be divisible by 3. y is two larger than a multiple of 3, which means that if you divide y by 3, the remainder will be 2. So y is not divisible by 3, and thus y certainly is not divisible by 6.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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