The product of two positive consecutive even integers is 168. Find the integers. ( Hint: Let x= the smaller even integer and x+2= the larger even integer.)
A) $14,16$
B) $16,18$
C) $12,14$
D) $10,12$
E) $8,10$

Question

Quizplus · Accepted Answer

Let x be the smaller even integer, then the larger even integer is x + 2. Their product is (x)(x + 2) = x^2 + 2x. Since the two integers are consecutive even integers, x must be an even integer. Let's list the first few even integers: 2, 4, 6, 8, 10, 12, 14, ... We can see that 12 is the largest even integer that is less than the square root of 168, so we can try x = 12. Then the larger even integer is x + 2 = 14, and their product is (12)(14) = 168. Therefore, the two consecutive even integers are 12 and 14, and the answer is C.

The Product of Two Positive Consecutive Even Integers Is 168 14,1614,1614,16

The Product of Two Positive Consecutive Even Integers Is 168 $14,16$