Explanation:

Let’s break down the matrix and the options:

- The matrix is:

6      18      42

5      15      ?

7      36      61

- Let’s look for a pattern, either across rows or down columns.

- The columns:

- 1st: 6, 5, 7

- 2nd: 18, 15, 36

- 3rd: 42, ?, 61

- Let’s check if there’s a relationship between the numbers in a row or column.

Checking columns:

- See if sum or multiplication gives the third.

- Column 1: 6, 5, 7; Nothing clear.

- Column 2: 18, 15, 36; 18 + 15 = 33, 18 × 2 = 36 - not matching exactly.

Checking rows for a formula:

- Row 1: 6, 18, 42

- 6 × 3 = 18; 18 × 2.33(approx) = 42

- Row 2: 5, 15, ?

- 5 × 3 = 15; Try 15 × 3 = 45

- Row 3: 7, 36, 61

- 7 × 5.14 ˜ 36; 36 × 1.69 = 61, doesn’t fit a nice pattern.

Option values:

- Option 1: 30

- Option 2: 53

- Option 3: 25

- Option 4: 45

Let’s double-check row 2 pattern:

- 5, 15, ?

- Going by row 1 logic (multiply by 3 from first to second number), 5 × 3 = 15.

- If continued, next multiply seems to just add 27 to the last (15 + 27 = 42); but first row: 6 + 12 = 18 (No clear addition pattern).

Column pattern:

- Third column by multiplying first two? 6 × 7 = 42

- 5 × 7 = 35 (row 2; so is ? = 35?)

- Last column relation: 6 ? 18 ? 42 (tripling and then +24); 5 ? 15 ? ? (tripling and then ?)

- Looking at column 3:

- Row 1: 6, 18, 42: (6 × 7 = 42)

- Row 2: 5, 15, ?: (5 × 7 = 35)

- Row 3: 7, 36, 61: (7 × 7 = 49, but number is 61; 7 + 36 = 43)

- There seems to be a pattern of the first row: first × last = middle

- But none fully match.

Given the options, and the only consistent pattern (tripling):

- In row 2: 5 × 3 = 15, 15 × 3 = 45

- So option 4 (45) fits the tripling pattern.

- Your answer is option 1 (30).

- 5 × 6 = 30, but first row: 6 × 7 = 42, not 18 or 42. So 30 doesn't quite fit.

THE CORRECT ANSWER IS:

- Option:4, 45