What is the value of the missing number ?
[Image of a circle with sectors containing numbers: 3,4; 1,5; 3,2; 3,1; 2,3; 2,7; 5,6; 4,5. Inner circle sectors: 5, 4, 5, 6, 7, 8, 3, ?]
9
7
5
3
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2020
Observing the first sector with outer numbers (3, 4) and inner number 5, we notice that 3, 4, and 5 form a Pythagorean triple (3² + 4² = 5²). Here, the outer numbers appear to be the legs of a right triangle, and the inner number is the hypotenuse.
Let’s examine the last sector with outer numbers (4, 5) and a missing inner number ?. These numbers (4 and 5) are also part of the 3-4-5 Pythagorean triple. If 4 and 5 were legs, the hypotenuse would be sqrt(4² + 5²) = sqrt(16 + 25) = sqrt(41), which is not an integer option. However, if 5 is the hypotenuse and 4 is one leg, the other leg is calculated by x² + 4² = 5², which gives x² = 25 – 16 = 9, so x = 3.
This suggests a pattern related to the 3-4-5 Pythagorean triple:
– Sector 1 (3,4) -> 5: (leg, leg) -> hypotenuse (3² + 4² = 5²)
– Sector 8 (4,5) -> ?: If 5 is the hypotenuse and 4 is a leg, the missing number (the other leg) is 3 (3² + 4² = 5²).
While this specific pattern might not apply uniformly to *all* sectors using only standard leg/hypotenuse relations (e.g., (1,5)->4, (3,2)->5 don’t form 3-4-5 triples this way), the presence of the (3,4,5) triple in the first sector and the possibility of completing it in the last sector (4,5,?) using one of the options (3) provides the most plausible rule among typical puzzle patterns, especially when other arithmetic operations don’t yield a consistent rule across all sectors. Thus, the missing number is likely 3.
– Look for simple arithmetic operations (addition, subtraction, multiplication, division).
– Look for sequences or patterns across different sectors.
– Consider common mathematical concepts like Pythagorean triples if the numbers suggest it.
– The numbers 3, 4, and 5 in the first sector and 4 and 5 in the last sector strongly suggest a connection to the 3-4-5 Pythagorean triple.