The sum of three consecutive negative even integers is -102. What is the absolute value of… — Armed Services Vocational Aptitude Battery (ASVAB)

The sum of three consecutive negative even integers is $-102$ . What is the absolute value of the smallest of these integers?

Answer: 36

By defining the consecutive even integers algebraically, the smallest integer is correctly identified as

-36

. Taking the absolute value of

-36

yields

36

Define variables for the three consecutive even integers.

Let the smallest integer be

x

. The next consecutive even integers are

x + 2

and

x + 4

Consecutive even integers are always 2 units apart.

Set up the equation.

x + (x + 2) + (x + 4) = -102

The sum of the three integers is given as

-102

Solve for

x

3x + 6 = -102

leads to

3x = -108

, yielding

x = -36

Isolating

x

provides the value of the smallest integer.

Calculate the absolute value.

|-36| = 36

The question specifically asks for the absolute value of the smallest integer.

Consecutive integers and absolute value properties

Question