If the sum of three consecutive even integers is 42, what is the smallest of these integer… — GMAT

If the sum of three consecutive even integers is $42$ , what is the smallest of these integers?

12

The arithmetic mean (average) of three consecutive even integers is equal to the middle integer. Dividing the total sum

42

3

yields

14

, which is the middle integer. Subtracting

2

gives the smallest integer,

12

Define the three consecutive even integers algebraically

Let the three consecutive even integers be

n

n + 2

, and

n + 4

, where

n

represents the smallest integer.

Consecutive even integers differ by

2

Set up the equation for their sum

n + (n + 2) + (n + 4) = 42 \implies 3n + 6 = 42

The problem states that the sum of the three integers equals

42

Solve for

n

3n = 36 \implies n = 12

Subtract

6

from both sides and divide by

3

to find the smallest integer.

Properties and Sums of Consecutive Even Integers

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