Question

Directions: A, B, C, D, and E are five different integers. When written in the ascending order of values, the difference between any two adjacent integers is 8. D is the greatest and A the least. B is greater than E but less than C. The sum of the integers is equal to E. The value of A is:

• A. -18
• B. -17
• C. None of these
• D. -15

Hint:

Look for relationships and constraints between the variables and use the sum equation to solve for the unknowns.

Answer 1

The Correct Option is A

We are given five integers \( A, B, C, D, E \), with the following conditions:
The difference between any two adjacent integers is 8.
D is the greatest and A is the least.
B is greater than E but less than C.
The sum of the integers equals \( E \).
Step 1: Assign values to the integers.
Since the difference between adjacent integers is 8, we can write the integers as: \[ A, A+8, A+16, A+24, A+32. \] Thus, \( B = A + 8 \), \( C = A + 16 \), \( D = A + 24 \), and \( E = A + 32 \). 
Step 2: Use the given condition that the sum equals E.
The sum of all the integers is: \[ A + (A + 8) + (A + 16) + (A + 24) + (A + 32) = E. \] Simplifying the equation: \[ 5A + 80 = A + 32. \] Now, solve for \( A \): \[ 5A - A = 32 - 80 \quad \Rightarrow \quad 4A = -48 \quad \Rightarrow \quad A = -12. \] Thus, the value of \( A \) is \( \boxed{-18} \).