The sum of three consecutive even numbers is 36. What are the numbers?

10, 12, 14

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12, 14, 16

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5, 6, 7

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14, 15, 16

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Solution

The correct option is A 10, 12, 14
Let the smallest even number be ' $2 x$ '.
Because, the difference between any two consecutive even numbers is 2.
So, the other two numbers are $2 x + 2$ and $2 x + 4$ .
$2 x + (2 x + 2) + (2 x + 4) = 36 6 x + 6 = 36 6 x = 36 - 6 6 x = 30 x = \frac{30}{6} x = 5$

$2 x = 2 \times 5 = 10$
$2 x + 2 = 2 \times 5 + 2 = 12$
$2 x + 4 = 2 \times 5 + 4 = 14$
Thus, the three consecutive even numbers are 10, 12, 14.

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