Question 89

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 greatest number is:

(A) 14
(B) 15
(C) 12
(D) 17
✓ Correct Answer: Option A 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.
  • Integers in ascending order: A, E, B, C, D.
  • Difference between adjacent integers is 8.
  • 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 D = A + 32 = -18 + 32 = 14

Thus, the greatest number is 14.

Answer: (A) 14

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