A divisor of y

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ivancj: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Mar 25, 2009 3:06 am; Location: Madrid

A divisor of y

by ivancj » Fri Apr 03, 2009 9:04 am

Hi mates!

I've found the following problem, which I don't know how to solve:

[i]If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?[/i]
A) 4
B) 5
C) 6
D) 7
E) 8

Any ideas?

Many thanks in advance!!

Ivan

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Source: Beat The GMAT — Problem Solving | Fri Apr 03, 2009 9:04 am

Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 am; Thanked: 32 times; Followed by:1 members

Re: A divisor of y

by Vemuri » Fri Apr 03, 2009 9:49 am

Answer should be C. Among the answer choices only 6 cannot be a divisor.

Lets substitute some values for x & see what numbers appear:
x=1 ==> 3*1+2=5 (divisible by 5)
x=2 ==> 3*2+2=8 (divisible by 4 & 8)
x=3 ==> 3*3+2=11
x=4 ==> 3*4+2=14 (divisible by 7)

The only number that is not a divisor is 6. Hope this explanation helps.

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

Re: A divisor of y

by dtweah » Sun Apr 05, 2009 4:54 pm

ivancj wrote:Hi mates!

I've found the following problem, which I don't know how to solve:

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

Any ideas?

Many thanks in advance!!

Ivan

Rearrange the equation.

y/3=x+2/3.

This is now in the familiar form of quotient + remainder/divisor. (5/3=1+2/3). From this we know y is not divisible by 3. Now if 3 cannot divide y, 6 will not since 6=3 x2. A simple way to show this is to see if

(3x+2)/6 is an integer. If an integer results, then the above expression is divisible by 6.
(3x +2)/6= x/2 +1/3. For no value of x this is an integer.
Caveat: This is not the same thing as saying any number divisible by 3 is also divisible by 6: 9/3 =3. But 6 cannot go into 9. We are only allowed to say that if 3 cannot make it, 6 cannot as well.