Explanation:We are to find the missing number in the pattern:
[\text{First pair: } 9, 49 \Rightarrow 21] [\text{Second pair: } 9, 81 \Rightarrow 27] [\text{Third pair: } 9, 36 \Rightarrow ?] Pattern check:
[\text{Formula: } \frac{(\text{first number} + \text{second number})}{\text{some rule}}] Let’s see if we can find a simpler relationship.
Check ratios:
For first: ( 9 + 49 = 58 ), but 21 not related directly.
Try another pattern:
[\sqrt{9} = 3, \sqrt{49} = 7, 3 \times 7 = 21] Works perfectly.
Now, ( \sqrt{9} = 3, \sqrt{81} = 9, 3 \times 9 = 27 ) — also correct.
For the third:

Answer: (2) 18

Explanation:Numbers given:
[16, 24, 28 \Rightarrow 4] [12, 24, 30 \Rightarrow 6] [24, 40, 48 \Rightarrow ?] Pattern:
doesn’t fit.
Let’s test another relation:
Notice differences:
(24 – 16 = 8)
(28 – 24 = 4)
Average of differences (= (8+4)/3 \approx 4)? Not quite.
Let’s check ratio pattern:
, inconsistent.
Try the relationship similar to previous:
(\sqrt{16} + \sqrt{24} + \sqrt{28})? no integer pattern.
We check the example pattern consistency with previous Q61:
Maybe ( \sqrt{first} + \sqrt{second} + \sqrt{third} = \text{some rule}).
Testing gives decimals, not integers.
Let’s test multiplication/division pattern:
( 16 : 4 = 4, 24 : 4 = 6, 28 : 4 = 7) not consistent.
Instead check relation: middle number is roughly geometric mean of the outer two:
[\sqrt{16 \times 28} = \sqrt{448} \approx 21.1; \frac{24}{4} = 6] Hmm — check pattern 2:
[\text{Middle number} / \text{Result} = 24/4 = 6] [24/6 = 4, 24/7 = 3.43; \text{maybe consistent?}] Try next: ( \text{difference between second and first} = 8, \text{difference between third and second} = 4, \text{sum of digits of first}? 1+6=7 ) hmm.
Check example pattern across rows:
(16, 24, 28 → 4), (12, 24, 30 → 6)
Notice the middle number divided by result =
(24/4 = 6), (24/6 = 4).
So, pattern:
middle number / result = first number’s square root.
√16 = 4 → works for 4.
√12 ≈ 3.46 → not 4, close pattern not exact.
Try another reasoning: differences between outer two divided by 2?
Let’s see:
(28 – 16)/3 = 12/3 = 4
(30 – 12)/3 = 18/3 = 6
(48 – 24)/3 = 24/3 = 8
Matches pattern: result = (difference between outer numbers)/3.
Answer = 8.
Answer: (1) 8

Explanation:We have triangles:
[10, 15 \text{ (top sides)}; \text{center } 5; \text{bottom } 20] [12, 18; \text{center } 6; \text{bottom } 24] [16, 24; \text{center } ?; \text{bottom } 32] Pattern:

Check:
20/4 = 5 (Correct)
24/4 = 6 (Correct)
32/4 = 8 (Correct)