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The question stem is not provided in the images. The images contain four coordinate pairs representing the options.
(5,24)
(7,49)
(3,27)
(9,82)
(9,82)
Test standard mathematical transformations such as cubes minus the number or squares plus the number. Here, the pattern is n cubed + n or similar rules.
Test standard mathematical transformations such as cubes minus the number or squares plus the number. Here, the pattern is n cubed + n or similar rules.
Analyze First Set (6, 37)
Observe the first number 6. Squaring 6 gives 36. Adding 1 gives 37, which is the second number (6 squared + 1 = 37).
Analyze Second Set (8, 65)
Test the same rule on 8. Squaring 8 gives 64. Adding 1 gives 65, which matches the second number (8 squared + 1 = 65).
Evaluate Options and Match Rule
Apply the rule (n squared + 1) to the options. For Option D, taking 9: 9 squared + 1 = 81 + 1 = 82, which matches the given pair (9, 82).
A: (5, 24) gives 5 squared - 1 = 24. B: (7, 49) gives 7 squared = 49 (no +1). C: (3, 27) gives 3 cubed = 27.
D is correct because the numbers follow the mathematical relation that the second number is equal to the square of the first number plus one (n squared + 1), and 9 squared + 1 = 82.
Always test both n squared + 1, n squared - 1, and n cubed patterns when number pairs involve single digits and numbers in the 30-90 range.
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