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When a, b and c are consecutive positive even integers such

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When a, b and c are consecutive positive even integers such

by Max@Math Revolution » Thu Jun 21, 2018 12:33 am

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[GMAT math practice question]

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. (a-c)/2
B. (c-a)/2
C. (a+c)/2
D. (a+c)/4
E. (a-c)/4
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by GMATGuruNY » Thu Jun 21, 2018 2:19 am
Max@Math Revolution wrote:[GMAT math practice question]

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. (a-c)/2
B. (c-a)/2
C. (a+c)/2
D. (a+c)/4
E. (a-c)/4
Test a=6, b=4 and c=2 in the five answer choices.
Eliminate any answer choice that does not yield an odd integer.

A: (a-c)/2 = (6-2)/2 = 2 --> Eliminate A.
B: (a-c)/2 = (2-6)/2 =- 2 --> Eliminate B.
C: (a+c)/2 = (6+2)/2 = 4 --> Eliminate C.
D: (a+c)/4 = (6+2)/4 = 2 --> Eliminate D.

The correct answer is E.
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by Brent@GMATPrepNow » Thu Jun 21, 2018 4:59 am
Max@Math Revolution wrote:[GMAT math practice question]

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. (a-c)/2
B. (c-a)/2
C. (a+c)/2
D. (a+c)/4
E. (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.
For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions
------------------------------------------------

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

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Jun 24, 2018 6:04 pm
=>

Write a = 2n + 2, b = 2n and c = 2n - 2. We check each of the alternatives.

A. ( a - c ) / 2 = ( 2n + 2 - ( 2n - 2 ) ) / 2 = 4 / 2 = 2.
B. ( c - a ) / 2 = ( 2n - 2 - ( 2n + 2 ) ) / 2 = -4 / 2 = -2.
C. ( a + c ) / 2 = ( 2n + 2 + 2n - 2 ) / 2 = 4n / 2 = 2n.
D. ( a + c ) / 4 = ( 2n + 2 + 2n - 2 ) / 4 = 4n / 4 = n.
E. ( a - c ) / 4 = ( 2n + 2 - ( 2n - 2 ) ) / 4 = 4 / 4 = 1

Only option E is guaranteed to be odd. Therefore, the answer is E.
Answer : E
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