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When [m]a, b[/m] and [m]c[/m] are consecutive positive even integers s

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Carcass
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When [m]a, b[/m] and [m]c[/m] are consecutive positive even integers s [#permalink] New post   07 Jul 2021, 08:31
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When \(a, b\) and \(c\) are consecutive positive even integers such that \(a>b>c\), which of the following must be an odd integer?

\(A. \frac{(a-c)}{2}\)
\(B. \frac{(c-a)}{2}\)
\(C. \frac{(a+c)}{2}\)
\(D. \frac{(a+c)}{4}\)
\(E. \frac{(a-c)}{4}\)
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E
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When [m]a, b[/m] and [m]c[/m] are consecutive positive even integers s [#permalink] New post   07 Jul 2021, 09:30
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\(a, b, c\) are consecutive even integers with \(c < b < a\)

Take \(a = 6, b = 4, c = 2\)

only \(\frac{a-c}{4}\) will be odd.

Answer E
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When [m]a, b[/m] and [m]c[/m] are consecutive positive even integers s [#permalink] New post   07 Jul 2021, 10:25
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Carcass wrote:
When \(a, b\) and \(c\) are consecutive positive even integers such that \(a>b>c\), which of the following must be an odd integer?

\(A. \frac{(a-c)}{2}\)
\(B. \frac{(c-a)}{2}\)
\(C. \frac{(a+c)}{2}\)
\(D. \frac{(a+c)}{4}\)
\(E. \frac{(a-c)}{4}\)


If a, b and c are consecutive EVEN integers, and a>b>c, then we we know that b is 2 greater than c, and a is 2 greater than b
So, we can write:
b = c + 2
a = c + 4

Now let's check the answer choices from E to A
-----ASIDE----------------
This is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.
------------------------------------------------

E) (a - c)/4 = [(c + 4 ) - (c)]/4
= 4/4
= 1 (ODD!)

Answer: E

Cheers,
Brent
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Re: When [m]a, b[/m] and [m]c[/m] are consecutive positive even integers s [#permalink] New post   23 Jul 2023, 15:11
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: When [m]a, b[/m] and [m]c[/m] are consecutive positive even integers s [#permalink]
23 Jul 2023, 15:11
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