Question

A, B, C, D, and E are five different integers. When written in 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 greatest number has the value:

• A. 14
• B. 15
• C. 12
• D. 17

Hint:

Always assign variables to ordered numbers with given gaps, and use inequalities to fix positions.

Answer 1

The Correct Option is D

Step 1: Let the five integers in ascending order be:
Let them be \( x, x+8, x+16, x+24, x+32 \) These differ by 8 and are in order. So: \[ A = x, \quad B = ?, \quad C = ?, \quad D = x + 32, \quad E = ? \] Step 2: Use the condition "B is greater than E but less than C"
So their positions must be:
A = x
E = x + 8
B = x + 16
C = x + 24
D = x + 32
Step 3: Use the condition: "Sum of the integers is equal to E"
Sum of all 5 terms: \[ x + (x+8) + (x+16) + (x+24) + (x+32) = 5x + 80 \] Set this equal to \( E = x + 8 \): \[ 5x + 80 = x + 8 \Rightarrow 4x = -72 \Rightarrow x = -18 \] Step 4: Calculate all values \[ A = -18, \quad E = -10, \quad B = -2, \quad C = 6, \quad D = 14 \] So the greatest number \( D = 14 \)