Question

Marc frames two puzzles, A and B, on a green board as shown below. Both puzzles follow a logical pattern.
Follow the pattern, and find the sum of the missing values a, b, c, and d.

• A. 22
• B. 42
• C. 40
• D. 32

Answer 1

The correct option is B 42

$PuzzleA:$



Row-wise:
Row 1: 5 + 9 = 14
Row 2: 6 + 7 = 13

Column-wise:
Column 1: 5 + 7 =12
Column 2: 9 + 6 = 15

$Diagonal:$
9 + 7 = 16


$PuzzleB:$
Following the same pattern as puzzle A, we get:


Row-wise:
⇒ Row 1: 3 + 8 = 11
⇒ Row 2: a + b = 13

Column-wise:
⇒ Column 1: 3 + a =12
a = 12 – 3
Thus, a = 9

⇒ Column 2: 8 + b = d

Since a + b = 13 and a = 9, we get:
b = 13 – 9 = 4
Thus, b = 4

As 8 + b = d and b = 4, we get:
d = 8 + 4 = 12
Thus, d = 12

$Diagonal:$
8 + a = c
8 + 9 = 17
Thus, c = 17

a = 9, b = 4, c = 17, d = 12

Sum of a, b, c, and d = 9 + 4 + 17 + 12
= 42

Thus, the sum of a, b, c, and d is 42.