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# If x and y are positive integers, is x even?

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Math Expert
Joined: 02 Aug 2009
Posts: 5652
If x and y are positive integers, is x even? [#permalink]

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26 Feb 2017, 07:40
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If x and y are positive integers, is x even?
(1) x-3y=27
(2) x+2y=37

[Reveal] Spoiler: OA

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Joined: 21 Mar 2016
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Re: If x and y are positive integers, is x even? [#permalink]

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26 Feb 2017, 09:41
Statement 1 LEADS TO X being even
Intern
Joined: 20 May 2016
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Re: If x and y are positive integers, is x even? [#permalink]

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26 Feb 2017, 11:11
(1)NS:
x=27+3y, where our answer depends on the value of y, say y=1, to answer "yes"; y=2, leading to "no".
(2)S:
x=37-2y. we know y is more than one and less than nineteen by the condition of the question. Now, for any number of y in this range, the answer to the question is "no", so it is sufficient. Answer B.

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Intern
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Location: India
Concentration: General Management, General Management
Re: If x and y are positive integers, is x even? [#permalink]

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07 Mar 2017, 04:02
S1: x-3y=27

This means that x=27+3y. The value of x is dependent on y, ie. if y is odd then x is even and if y is even then x is odd.

eg. y=3 then x = 36
y=2 then x= 33

S2: x+2y=37

This means that x=37-2y. Please note that here 2y is even so no matter what the value of y. So this expression will always be odd. Hence the statement is sufficient.

Ans - B
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If x and y are positive integers, is x even? [#permalink]

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08 Mar 2017, 08:32
statement 1 = x-3y=27
i.e x= 27+3y
x can be even if y=odd and it can be odd when y= even so= not suff
statememt 2 = x+2y = 37
i.e x =37-2y (odd - odd = odd)= suff
ans b
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Re: If x and y are positive integers, is x even? [#permalink]

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10 Mar 2017, 09:28
chetan2u wrote:
If x and y are positive integers, is x even?
(1) x-3y=27
(2) x+2y=37

We are given that x and y are positive integers, and we need to determine whether x is even.

Statement One Alone:

x - 3y = 27

Simplifying statement one, we have:

x = 27 + 3y

x = 3(9 - y)

x/3 = 9 - y

We see that x must be divisible by 3; however, that is not enough information to determine whether x is even. For instance x could be 6, which is even, or x could be 9, which is not even. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x + 2y = 37

Simplifying statement two, we have:

x = 37 - 2y

Because 37 is odd and (2y) is even, we see that x = odd - even, which is always an odd number. Since we know that x is odd, statement two is sufficient to answer the question.

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Re: If x and y are positive integers, is x even?   [#permalink] 10 Mar 2017, 09:28
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