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What is the sum of positive integers x and y ? (1) 3x + y =

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What is the sum of positive integers x and y ? (1) 3x + y = [#permalink] New post 17 Jun 2007, 00:01
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What is the sum of positive integers x and y ?

(1) 3x + y = 6
(2) 4x + y = 7
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 [#permalink] New post 17 Jun 2007, 00:42
D.

Since x and y are +ve integers, the given statements are SUFF by themselves.
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 [#permalink] New post 17 Jun 2007, 01:40
One more D

Only one option per stmnt since they are both +ive integers
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 [#permalink] New post 17 Jun 2007, 01:42
(D) for me too :)

x+y = ?

From 1
3x + y = 6 : is the equation of a line. So, there are an infinite way to combine x & y.... But what if x & y must be positive integers? Well, it seems the same but we should check it.

As y = 6 - 3*x and y > 0, we have:
y > 0
<=> 6 - 3*x > 0
<=> 3*x < 6
<=> x < 2

As x > 0 and an integer, it gives us only x = 1.

SUFF.

From 2
4x + y = 7
<=> y = 7 - 4*x

Again, as y > 0, we have:
y > 0
<=> 7 - 4*x > 0
<=> x < 7/4

Here also, x > 0 and an integer, so we arrive to x = 1.

SUFF.
  [#permalink] 17 Jun 2007, 01:42
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