Question Details

Find out the missing (?) number and letter.


Options

A

59 and K

B

61 and L

C

61 and K

D

59 and L

Show Answer

Correct Answer :

Option C

61 and K

Solution :

To find the missing number and letter, we can analyze the patterns of the numbers and letters separately across the four quadrants of the grid.

1. Finding the Missing Number:
Let us extract the numbers from the inner triangles of the quadrants and list them in ascending order:
5, 8, 13, 20, 31, 44, ?, 80

Let us look at the differences between consecutive numbers in this sequence:
8 - 5 = 3
13 - 8 = 5
20 - 13 = 7
31 - 20 = 11
44 - 31 = 13

The differences are the consecutive prime numbers: 3, 5, 7, 11, 13. Continuing this pattern, the next differences should be the next prime numbers, which are 17 and 19:
? - 44 = 17 ⇒ ? = 44 + 17 = 61
80 - 61 = 19 (which satisfies the sequence)

Thus, the missing number is 61.

2. Finding the Missing Letter:
Let us convert the letters in the outer triangles to their corresponding numerical positions in the alphabet (A = 1, B = 2, C = 3, etc.):
- Top-Left quadrant: A = 1, C = 3
- Top-Right quadrant: C = 3, F = 6
- Bottom-Right quadrant: E = 5, I = 9
- Bottom-Left quadrant: G = 7, ?

Now, let us find the difference between the alphabetical values of the two letters in each quadrant:
- Top-Left: C - A = 3 - 1 = 2
- Top-Right: F - C = 6 - 3 = 3
- Bottom-Right: I - E = 9 - 5 = 4
- Bottom-Left: ? - G = ? - 7 = 4

Following the pattern of differences (2, 3, 4, 4), the difference for the bottom-left quadrant is 4. Therefore, the numerical value of the missing letter is:
7 + 4 = 11

The 11th letter of the alphabet is K.

Therefore, the correct option is 61 and K.

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