Question 88

Logical Reasoning Puzzles Easy

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 is the least. B is greater than E but less than C. The sum of the integers is equal to E
The sum of A and B is:

(A) -15
(B) -30
(C) -20
(D) None of these
✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Given five integers A, B, C, D, E with conditions:

  • A is the least, D is the greatest.
  • B is greater than E but less than C.
  • The integers in ascending order: A, E, B, C, D.
  • The difference between adjacent integers is 8.
  • The sum of all integers equals E.

Expressing in terms of A:

  • E = A + 8
  • B = E + 8 = A + 16
  • C = B + 8 = A + 24
  • D = C + 8 = A + 32

Sum condition: A + E + B + C + D = E

Substitute: A + (A+8) + (A+16) + (A+24) + (A+32) = A+8

Simplify: 5A + 80 = A + 8

4A = -72, so A = -18

Then B = A + 16 = -2

Sum A+B = -18 + (-2) = -20

Answer: (C) -20

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