Question

Three consecutive integers have a sum of \(-84\). Compare:
Quantity A: The least of the three integers
Quantity B: \(-28\)

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.
• E.

Hint:

When dealing with consecutive integers, always use algebraic representation \( x, x+1, x+2 \). Their sum simplifies easily.

Answer 1

The Correct Option is B

Step 1: Represent the integers.
Let the three consecutive integers be \( x, x+1, x+2 \). Their sum is given as: \[ x + (x+1) + (x+2) = -84. \] Step 2: Simplify.
\[ 3x + 3 = -84 \quad \Rightarrow \quad 3x = -87 \quad \Rightarrow \quad x = -29. \] Step 3: Compare with \(-28\).
The least of the integers is \(-29\). Clearly, \[ -29<-28. \] Step 4: Conclusion.
Hence, Quantity B (\(-28\)) is greater. \[ \boxed{\text{(B) Quantity B is greater.}} \]