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Are both of the integers X and Y divisible by 3? (1) X+Y and

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Are both of the integers X and Y divisible by 3? (1) X+Y and [#permalink] New post 22 May 2004, 06:31
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Are both of the integers X and Y divisible by 3?

(1) X+Y and X-Y are divisible by 3
(2) X^2 and Y^2 are divisible by 9
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 [#permalink] New post 22 May 2004, 06:53
Can be solved by each individually so ....(d)

Please note that it is already given that X and Y are intergers. If it was not specifically given then (2) may not hold good.

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 [#permalink] New post 22 May 2004, 07:17
Can you explain (1) ? I am trying to solve the equation but I am not so sure it's the right method.

If x+y is divisible by 3 => x+y = 3n , when n = integer -(a)
If x-y is divisible by 3 => x-y = 3m, when m = integer -(b)

From (a) and (b) => x = 3(m+n)/2 and y = 3(n-m)/2
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 [#permalink] New post 22 May 2004, 07:26
becoolja wrote:
Can you explain (1) ? I am trying to solve the equation but I am not so sure it's the right method.

If x+y is divisible by 3 => x+y = 3n , when n = integer -(a)
If x-y is divisible by 3 => x-y = 3m, when m = integer -(b)

From (a) and (b) => x = 3(m+n)/2 and y = 3(n-m)/2


SORRYYYYYYYYYYYYYYYYYYY

was wrong above.

Cannot be solved by (1)

I hope it can be solved by (2) so (b)
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 [#permalink] New post 22 May 2004, 07:31
Maybe, we can wait other idea....Anyone please :-)
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Re: DS_10_15 [#permalink] New post 22 May 2004, 10:32
1. x+y = 0 (3) x-y = 0 (mod 3)
or x = y = 0 (3) sufficient

2. x^2 = 0 (9), x = 0 (3)
sufficient.

D it is.
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 [#permalink] New post 23 May 2004, 07:10
becoolja wrote:
Can you explain (1) ? I am trying to solve the equation but I am not so sure it's the right method.

If x+y is divisible by 3 => x+y = 3n , when n = integer -(a)
If x-y is divisible by 3 => x-y = 3m, when m = integer -(b)

From (a) and (b) => x = 3(m+n)/2 and y = 3(n-m)/2


Just extend your analysis further...

Since x and y are integers then (m+n)/2 and (m-n)/2 have to either integers
or k/3.
For no integers pairs (m,n) (m+n)/2 or (m-n)/2 yields k/3 Hence
(m+n)/2 and (m-n)/2 have to be integers. If they are integers then both x and y are divisible by 3
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 [#permalink] New post 23 May 2004, 18:24
Thanks for anandnk's explanation. :-)
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 [#permalink] New post 23 May 2004, 18:27
Anyway, if n=3 and m= 3, is your explanation still applicable? Quite headache :-(
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 [#permalink] New post 23 May 2004, 18:28
anandnk wrote:
becoolja wrote:
Can you explain (1) ? I am trying to solve the equation but I am not so sure it's the right method.

If x+y is divisible by 3 => x+y = 3n , when n = integer -(a)
If x-y is divisible by 3 => x-y = 3m, when m = integer -(b)

From (a) and (b) => x = 3(m+n)/2 and y = 3(n-m)/2


Just extend your analysis further...

Since x and y are integers then (m+n)/2 and (m-n)/2 have to either integers
or k/3.
For no integers pairs (m,n) (m+n)/2 or (m-n)/2 yields k/3 Hence
(m+n)/2 and (m-n)/2 have to be integers. If they are integers then both x and y are divisible by 3


Got a technical question here,
is 0 divisible by 3?
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 [#permalink] New post 23 May 2004, 22:47
Of course, yes.

0 = 3*0

or 0 is a multiple of any integer!
  [#permalink] 23 May 2004, 22:47
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