Analyze Number Pair Logic to Find the Outlier

The question requires identifying the number pair that does not follow the specific logic applied to the other three pairs. Let's analyze the relationship between the numbers in each pair.

Examining the Number Pairs

• Pair 1: 1331 - 144
  • The cube root of 1331 is 11 (since $11^3 = 1331$).
  • The square root of 144 is 12 (since $12^2 = 144$).
  • Here, $\sqrt[3]{1331} = 11$ and $\sqrt{144} = 12$. The values are not equal ($11 \neq 12$).
• Pair 2: 216 - 36
  • The cube root of 216 is 6 (since $6^3 = 216$).
  • The square root of 36 is 6 (since $6^2 = 36$).
  • Here, $\sqrt[3]{216} = 6$ and $\sqrt{36} = 6$. The values are equal.
• Pair 3: 729 - 81
  • The cube root of 729 is 9 (since $9^3 = 729$).
  • The square root of 81 is 9 (since $9^2 = 81$).
  • Here, $\sqrt[3]{729} = 9$ and $\sqrt{81} = 9$. The values are equal.
• Pair 4: 2197 - 169
  • The cube root of 2197 is 13 (since $13^3 = 2197$).
  • The square root of 169 is 13 (since $13^2 = 169$).
  • Here, $\sqrt[3]{2197} = 13$ and $\sqrt{169} = 13$. The values are equal.

Identifying the Logic Mismatch

The consistent logic observed in pairs 2, 3, and 4 is that the cube root of the first number equals the square root of the second number. Mathematically, for a pair $(N_1, N_2)$, the logic is $\sqrt[3]{N_1} = \sqrt{N_2}$.

Pair 1 (1331 - 144) is the only pair where this specific relationship does not hold true, as $\sqrt[3]{1331} = 11$ and $\sqrt{144} = 12$, which are unequal.

Therefore, the number pair 1331 - 144 does not follow the same logic as the others.