Observe the following figures carefully and find the missing number in figure…

Concept

In this figure series, the three branches of each Y-shape are related by one fixed rule: the bottom number equals the square root of the difference between the top-left number and the top-right number (top-left minus top-right).

Application

Apply the rule to figure (iii), where the top-left value is 100 and the top-right value is 19:

1. Subtract the top-right value from the top-left value: 100 - 19 = 81.

2. Take the square root of that difference: √81 = 9.

3. So the missing number at the bottom of figure (iii) is 9.

Cross-check

Confirm the same rule against the two given figures before trusting it:

• Figure (i): 64 - 28 = 36, and √36 = 6, which matches the bottom value shown (6).

• Figure (ii): 36 - 11 = 25, and √25 = 5, which matches the bottom value shown (5).

Since the rule reproduces the given bottom values in both figures (i) and (ii), the same rule applied to figure (iii) reliably gives 9.