Question

A, B, C and D are four consecutive odd numbers and their average is 42. What is the product of B and D?

• A. 1845
• B. 1848
• C. 1645
• D. 1658

Hint:

Identify the sequence and use the average to find the specific numbers.

Answer 1

The Correct Option is A

To find the product of B and D: 1. Let the four consecutive odd numbers be $A, B, C, D$. 2. Given their average is 42: _[ _frac{A + B + C + D}{4} = 42 _implies A + B + C + D = 168 _] 3. Since they are consecutive odd numbers, let $A = x$, $B = x+2$, $C = x+4$, $D = x+6$. 4. Substitute into the sum equation: _[ x + (x+2) + (x+4) + (x+6) = 168 _implies 4x + 12 = 168 _implies 4x = 156 _implies x = 39 _] 5. Therefore, $B = 39 + 2 = 41$ and $D = 39 + 6 = 45$. 6. The product of B and D is: _[ B _times D = 41 _times 45 = 1845 _] Therefore, the correct answer is (1) 1845.