Question:
Based on the relationship between each polygon and the number inside it, the value of 'X' is ______
Based on the relationship between each polygon and the number inside it, the value of 'X' is ______
Show Hint
Count the sides of each shape and compare with the number inside it.
Check if the number equals the factorial of the side count.
Check if the number equals the factorial of the side count.
Updated On: Aug 3, 2026
- 720
- 596
- 24
- 240
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The Correct Option is A
Solution and Explanation
Step 1: Understand the question:
We see four shapes, a triangle, a rectangle, a pentagon, and a hexagon, each with a number written inside.
We need to find a rule that connects the number of sides of each shape to the number inside it, then use that rule on the hexagon to find X.
Step 2: List the number of sides against each number:
The triangle has 3 sides and holds the number 6. The rectangle has 4 sides and holds the number 24. The pentagon has 5 sides and holds the number 120. The hexagon has 6 sides and holds the number X.
Step 3: Test the factorial pattern:
Factorial of 3 is \(3 \times 2 \times 1 = 6\), which matches the triangle's number. Factorial of 4 is \(4 \times 3 \times 2 \times 1 = 24\), which matches the rectangle's number. Factorial of 5 is \(5 \times 4 \times 3 \times 2 \times 1 = 120\), which matches the pentagon's number.
So the rule is that the number inside each shape equals the factorial of its number of sides.
Step 4: Apply the rule to the hexagon.
\[ X = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]
Step 5: Check option (A) 720.
This is exactly the value of 6 factorial found in Step 4, so this option is correct.
Step 6: Check option (B) 596.
596 does not equal 6 factorial and does not fit the pattern from the earlier three numbers, so this option is wrong.
Step 7: Check option (C) 24.
24 already belongs to the rectangle with 4 sides, so repeating it for the hexagon breaks the pattern and is wrong.
Step 8: Check option (D) 240.
240 is just double of 120, which looks tempting but does not match the factorial rule that fits all three known shapes, so this option is wrong.
Final Answer:
The hexagon holds the value of 6 factorial. \[ \boxed{X = 720} \]
We see four shapes, a triangle, a rectangle, a pentagon, and a hexagon, each with a number written inside.
We need to find a rule that connects the number of sides of each shape to the number inside it, then use that rule on the hexagon to find X.
Step 2: List the number of sides against each number:
The triangle has 3 sides and holds the number 6. The rectangle has 4 sides and holds the number 24. The pentagon has 5 sides and holds the number 120. The hexagon has 6 sides and holds the number X.
Step 3: Test the factorial pattern:
Factorial of 3 is \(3 \times 2 \times 1 = 6\), which matches the triangle's number. Factorial of 4 is \(4 \times 3 \times 2 \times 1 = 24\), which matches the rectangle's number. Factorial of 5 is \(5 \times 4 \times 3 \times 2 \times 1 = 120\), which matches the pentagon's number.
So the rule is that the number inside each shape equals the factorial of its number of sides.
Step 4: Apply the rule to the hexagon.
\[ X = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]
Step 5: Check option (A) 720.
This is exactly the value of 6 factorial found in Step 4, so this option is correct.
Step 6: Check option (B) 596.
596 does not equal 6 factorial and does not fit the pattern from the earlier three numbers, so this option is wrong.
Step 7: Check option (C) 24.
24 already belongs to the rectangle with 4 sides, so repeating it for the hexagon breaks the pattern and is wrong.
Step 8: Check option (D) 240.
240 is just double of 120, which looks tempting but does not match the factorial rule that fits all three known shapes, so this option is wrong.
Final Answer:
The hexagon holds the value of 6 factorial. \[ \boxed{X = 720} \]
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