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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

I am not sure about the answer, I just picked 246.

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.

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.

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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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....

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:

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

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05 Oct 2017, 10:24

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