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When x and y are integers, is x an even number?

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When x and y are integers, is x an even number? [#permalink]

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When x and y are integers, is x an even number?

1) 2x+y is an odd number.
2) 5x+3y is an odd number.


* A solution will be posted in two days.
[Reveal] Spoiler: OA

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Re: When x and y are integers, is x an even number? [#permalink]

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New post 17 Mar 2016, 21:51
St1: 2x + y = odd
even + y = odd
y = odd - even = odd
y is odd, but x can be even or odd. Not sufficient

St2: 5x + 3y = odd
even + odd = odd or
odd + even = odd
Again x can be even or odd. Not sufficient

Combining St1 and St2, we have,
y = odd
5x + 3y = odd
5x + odd = odd
5x = even
So x has to be even. Sufficient.

Answer: C

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Re: When x and y are integers, is x an even number? [#permalink]

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New post 21 Mar 2016, 04:23
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

When x and y are integers, is x an even number?

1) 2x+y is an odd number.
2) 5x+3y is an odd number.


In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), 2x becomes even and y=odd. If y=odd, 5x+3y=odd -> x=even, which is yes and sufficient.
Therefore, the answer is C.
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Re: When x and y are integers, is x an even number? [#permalink]

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New post 22 Aug 2016, 03:27
Using the statement 1=> y is odd
using the statement 2 => x can be even and odd
combining them => since y is odd => 5x=even => x must be even
Smash that C
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Re: When x and y are integers, is x an even number? [#permalink]

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New post 20 Sep 2016, 06:46
MathRevolution wrote:
When x and y are integers, is x an even number?

1) 2x+y is an odd number.
2) 5x+3y is an odd number.


* A solution will be posted in two days.


1. x odd y odd - we get an odd number. x even y odd - we get again odd. Not sufficient.
2. x even y odd - we get an odd number. x odd, y even - we get again odd number. Not sufficient.

1+2. add these two equations.
7x+4y = even
4y is even for sure
that only means that 7x is even, meaning that X is even. sufficient.

C

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Re: When x and y are integers, is x an even number? [#permalink]

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New post 21 Sep 2017, 07:17
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Re: When x and y are integers, is x an even number?   [#permalink] 21 Sep 2017, 07:17
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