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Difficulty: HardAnalogy and Classification

Match each number pair analogy in List-I with its corresponding underlying mathematical rule in List-II.

  • 8:4488 : 448x:x3−x2x : x^3 - x^2
  • 7:3367 : 336x:x3−xx : x^3 - x
  • 6:2226 : 222x:x3+xx : x^3 + x
  • 5:1505 : 150x:x3+x2x : x^3 + x^2

Answer

The pair 8:4488 : 448 matches x:x3−x2x : x^3 - x^2; 7:3367 : 336 matches x:x3−xx : x^3 - x; 6:2226 : 222 matches x:x3+xx : x^3 + x; and 5:1505 : 150 matches x:x3+x2x : x^3 + x^2.
Each pair in List-I represents a cubic transformation of the first number. Evaluating 83−82=4488^3 - 8^2 = 448, 73−7=3367^3 - 7 = 336, 63+6=2226^3 + 6 = 222, and 53+52=1505^3 + 5^2 = 150 confirms the one-to-one mapping with the respective rules in List-II.

Step-by-Step Solution

1
Analyze the relationship for the first pair 8:4488 : 448
Calculate 83=5128^3 = 512. Subtracting 82=648^2 = 64 gives 512−64=448512 - 64 = 448, establishing the rule x:x3−x2x : x^3 - x^2.
Identify the operation involving cubes and squares of the base number 88.
2
Analyze the relationship for the second pair 7:3367 : 336
Calculate 73=3437^3 = 343. Subtracting 77 gives 343−7=336343 - 7 = 336, establishing the rule x:x3−xx : x^3 - x.
Identify the operation involving subtracting the base number from its cube.
3
Analyze the relationship for the third pair 6:2226 : 222
Calculate 63=2166^3 = 216. Adding 66 gives 216+6=222216 + 6 = 222, establishing the rule x:x3+xx : x^3 + x.
Identify the operation involving adding the base number to its cube.
4
Analyze the relationship for the fourth pair 5:1505 : 150
Calculate 53=1255^3 = 125. Adding 52=255^2 = 25 gives 125+25=150125 + 25 = 150, establishing the rule x:x3+x2x : x^3 + x^2.
Identify the operation involving adding the square of the base number to its cube.

Key Concept

Polynomial operations on base numbers in numerical analogies
Estimated Time:2m 0s
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Topics

Analogy and Classification

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