If x and y are positive integers, which of the following : PS Archive
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# If x and y are positive integers, which of the following

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If x and y are positive integers, which of the following [#permalink]

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21 Apr 2008, 12:35
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If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x
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21 Apr 2008, 12:48
I guess B is the answer,considering if X and Y are equal
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21 Apr 2008, 15:46
say x=3 and y=2.
35*3=105 20*2=40
5(x-y) = 5(3-2) = 5
5 is greatest common divisor of 105 and 40. therefore, i don't think it's b.
i think it's c.
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21 Apr 2008, 19:18
JCLEONES wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

5,7,x1,x2,x3
2,2,5,y1,y2,y3

let x=1
and y=1
35 and 20
eliminate A

let x=4
and y=7
140
eliminate D and E

seongbae wrote:
say x=3 and y=2.
35*3=105 20*2=40
5(x-y) = 5(3-2) = 5
5 is greatest common divisor of 105 and 40. therefore, i don't think it's b.
i think it's c.

C
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21 Apr 2008, 20:06
Maple wrote:
JCLEONES wrote:

let x=4
and y=7
140
eliminate D and E

seongbae wrote:
say x=3 and y=2.
35*3=105 20*2=40
5(x-y) = 5(3-2) = 5
5 is greatest common divisor of 105 and 40. therefore, i don't think it's b.
i think it's c.

C

NICE
how did you pick x=4 and y=7

i mean on exam day i would have gone with B..just cause i dont think i could have easily figured out that 35*4 and 20*7 are going to be the same value..

i guess i would like to know how you thought about solving this problem..
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21 Apr 2008, 20:16
the hellish alt solution
JCLEONES wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

5,7,x1,x2,x3
2,2,5,y1,y2,y3

a. let x and y both = 1
5,7,(1)
2,2,5,(1)

b. ?

c.

let y=x1,x2,x3
7,[/b]5,x1,x2,x3[/b]
2,2,[/b]5,x1,x2,x3[/b]

I'm short two 2s in this case. I can only change one definition at a time so I'm stuck.

d.
let x be 2,2,y1,y2,y3
7,2,2,5,y1,y2,y3
2,2,5,y1,y2,y3

e.
let y be 7,x1,x2,x3
5,7,x1,x2,x3
2,2,5,7,x1,x2,x3
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21 Apr 2008, 20:21
JCLEONES wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

C

I picked C because if you divide 35x by 20x, you get 7/4, which is not possible. 35x must be divisible by its GCD.
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21 Apr 2008, 20:22
fresinha12 wrote:
NICE
how did you pick x=4 and y=7

i mean on exam day i would have gone with B..just cause i dont think i could have easily figured out that 35*4 and 20*7 are going to be the same value..

i guess i would like to know how you thought about solving this problem..

I know the following factors
2,2,5
5,7

the factors have to match to have the same value

2,2,5,7
2,2,5,7

2*2*5*7=140
Re: PS Number Properties   [#permalink] 21 Apr 2008, 20:22
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