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# If a, b, c are three consecutive positive even integers, which of the

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Re: If a, b, c are three consecutive positive even integers, which of the [#permalink]
three consecutive numbers be x,x+2,x+4
sum ;3x+6 or say 3 * (x+2)
possible integer values would stand valid at I & III only
option D

Bunuel wrote:
If a, b, c are three consecutive positive even integers, which of the following must be an integer?

I. $$\frac{(a+b+c)}{2}$$
II. $$\frac{(a+b+c)}{4}$$
III. $$\frac{(a+b+c)}{6}$$

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
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If a, b, c are three consecutive positive even integers, which of the [#permalink]
Bunuel wrote:
If a, b, c are three consecutive positive even integers, which of the following must be an integer?

I. $$\frac{(a+b+c)}{2}$$
II. $$\frac{(a+b+c)}{4}$$
III. $$\frac{(a+b+c)}{6}$$

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III

Let the even positive integers be $$2n$$ , $$2n + 2$$ & $$2n + 4$$

I. $$\frac{(a+b+c)}{2} = \frac{2n + 2n +2 +2n +4}{2}= \frac{6n + 6}{2} = 3n +3$$
II. $$\frac{(a+b+c)}{4} = \frac{2n + 2n +2 +2n +4}{4}= \frac{6n + 6}{4}$$
III. $$\frac{(a+b+c)}{6} = \frac{2n + 2n +2 +2n +4}{6}= \frac{6n + 6}{6} = n+1$$

Hence, Answer must be I. & III, (D)
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Re: If a, b, c are three consecutive positive even integers, which of the [#permalink]
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Re: If a, b, c are three consecutive positive even integers, which of the [#permalink]
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