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9x + 10y = 180, x and y are natural numbers, then what can

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amansingla4
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9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   27 May 2006, 02:11
9x + 10y = 180, x and y are natural numbers, then what can be said about x?
1] x is always odd 2] x is always even 3] x is odd if y is even 4] None of these



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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   27 May 2006, 02:42
Since 10y and 180 are both even, 9x should also be even. So x is always even.
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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   27 May 2006, 11:22
amansingla4 wrote:
9x + 10y = 180, x and y are natural numbers, then what can be said about x?
1] x is always odd 2] x is always even 3] x is odd if y is even 4] None of these


x=(180-10y)/9 = 20 - 10y/9.
For x to be a natural number,
1. y <= 18
2. y is a multiple of 9.

For all possible values of y (0, 9, 18), x is (20, 10, 0) even.
Hence 2.
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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   30 May 2006, 14:00
X = even

odd * x + even = even
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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   30 May 2006, 23:53
X is always even.

Given 9x+10y = 180
Now 10y will always have 0 as the unit digit and 180 has 0 in the unit place hence x can never be odd.
Also 10y is always even....... and E + E = E
Therefore 9x = even and odd * even = even hence x is always even
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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   31 May 2006, 09:49
amansingla4 wrote:
9x + 10y = 180, x and y are natural numbers, then what can be said about x?
1] x is always odd 2] x is always even 3] x is odd if y is even 4] None of these


Ans - 2. X is always even

It doesn't matter what y is since 10y is always even. Since 9x MUST be even as well (in order to add up to 180), x is always even.
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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   Updated on: 31 May 2006, 11:22
9x + 10y = 180

For result to be 180 (an even number) both numbers (9x and 10y) must be either even or both odd. 10y can not be odd in any case. So 9x must be even. For 9x to be even x must be even.

Originally posted by ps_dahiya on 31 May 2006, 10:45.
Last edited by ps_dahiya on 31 May 2006, 11:22, edited 1 time in total.
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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   31 May 2006, 10:50
ps_dahiya wrote:
9x + 10y = 180

For result to be 180 (an even number) both numbers (9x and 10y) must be either even or both odd. 10y can not be odd in any case. So 9x must be even. For 9x to be even x must be odd.



If 9x is even, then x must be even:

9(2) = 18
9(3) = 27
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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink] New post   31 May 2006, 11:21
tl372 wrote:
ps_dahiya wrote:
9x + 10y = 180

For result to be 180 (an even number) both numbers (9x and 10y) must be either even or both odd. 10y can not be odd in any case. So 9x must be even. For 9x to be even x must be odd.



If 9x is even, then x must be even:

9(2) = 18
9(3) = 27


I am sorry that was a typo. I edited that.



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Re: 9x + 10y = 180, x and y are natural numbers, then what can [#permalink]
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