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# If a, b and c are even integers, which of the following coul

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Intern
Joined: 16 Jan 2011
Posts: 5
If a, b and c are even integers, which of the following coul [#permalink]

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08 Mar 2011, 12:03
4
8
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:23) correct 38% (02:01) wrong based on 195 sessions

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If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2,

a) 140
b) 246
c) 638
d) 862
e) 118
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Joined: 02 Sep 2009
Posts: 47015
Re: Sum of Square of Even intergers [#permalink]

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08 Mar 2011, 12:20
6
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rk21857 wrote:
If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2,

a) 140
b) 246
c) 638
d) 862
e) 118

As a, b and c are even integers then a^2+b^2+c^2=(2x)^2+(2y)^2+(2z)^2=4(x^2+y^2+z^2), so the sum must be a multiple of 4 (note that a number is divisible by 4 if the last two digits form a number divisible by 4), the only choice which is a multiple of 4 is A: 140=10^2+6^2+2^2.

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Intern
Joined: 04 Oct 2010
Posts: 8
Re: Sum of Square of Even intergers [#permalink]

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08 Mar 2011, 13:48
Can you explain the part where you take the 4 out of the equation in layman's terms. please
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Joined: 02 Sep 2009
Posts: 47015
Re: Sum of Square of Even intergers [#permalink]

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08 Mar 2011, 13:53
geisends wrote:
Can you explain the part where you take the 4 out of the equation in layman's terms. please

Just factor out 4 out of $$4x^2+4y^2+4z^2$$: $$(2x)^2+(2y)^2+(2z)^2=4x^2+4y^2+4z^2=4*(x^2+y^2+z^2)$$.
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Re: Sum of Square of Even intergers [#permalink]

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08 Mar 2011, 14:19
4x^2+4y^2+4z^2 : How do you know which number to manipulate it to. How do you know not to put a 6 or 8 as the coefficient instead of 4, or whether to leave it as 2 or change it to something else.
Math Expert
Joined: 02 Sep 2009
Posts: 47015
Re: Sum of Square of Even intergers [#permalink]

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08 Mar 2011, 14:25
2
1
geisends wrote:
4x^2+4y^2+4z^2 : How do you know which number to manipulate it to. How do you know not to put a 6 or 8 as the coefficient instead of 4, or whether to leave it as 2 or change it to something else.

Please read the stem: "If a, b and c are even integers..." So a, b and c can be expressed as a=2x, b=2y, and c=2z for some integers x, y, and z --> a^2+b^2+c^2=(2x)^2+(2y)^2+(2z)^2=4(x^2+y^2+z^2).
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Re: Sum of Square of Even intergers [#permalink]

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08 Mar 2011, 14:29
why does 2x)^2+(2y)^2+(2z)^2=4(x^2+y^2+z^2)? If you multiply 4 by each variable wouldnt that make 4x^2+4y^2+4z^2. I read the question stem Im just not getting it....
Math Expert
Joined: 02 Sep 2009
Posts: 47015
Re: Sum of Square of Even intergers [#permalink]

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08 Mar 2011, 14:48
geisends wrote:
why does 2x)^2+(2y)^2+(2z)^2=4(x^2+y^2+z^2)? If you multiply 4 by each variable wouldnt that make 4x^2+4y^2+4z^2. I read the question stem Im just not getting it....

I don't quite understand your question but anyway, step by step:

$$a^2+b^2+c^2=(2x)^2+(2y)^2+(2z)^2=4x^2+4y^2+4z^2=4*(x^2+y^2+z^2)$$.
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Posts: 684
Re: Sum of Square of Even intergers [#permalink]

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08 Mar 2011, 17:47

there is atleast one two in every even integer,in other words even integer can be expressed as 2 times something

and squares will have atleast one 4 in them.

so answer should be a multiple of 4 , out of the given answers only A is multiple of 4.
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Re: If a, b and c are even integers, which of the following coul [#permalink]

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05 Oct 2017, 11:24
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Re: If a, b and c are even integers, which of the following coul   [#permalink] 05 Oct 2017, 11:24
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