Choose the similar pair for the following: 9 : 1000 :: ______ : ______.
2019
Choose the similar pair for the following: 9 : 1000 :: ______ : ______.
- A.
5 : 125
- B.
6 : 49
- C.
8 : 64
- D.
2 : 27
Attempted by 17 students.
Show answer & explanation
Correct answer: D
Key idea: the relationship is number : (number + 1)^3.
Verify with the given pair:
For 9 : 1000, compute (9 + 1)^3 = 10^3 = 1000, so the pattern holds.
Check 5 : 125 — (5 + 1)^3 = 6^3 = 216, so 125 does not fit the pattern (125 = 5^3).
Check 6 : 49 — (6 + 1)^3 = 7^3 = 343, so 49 does not fit the pattern (49 = 7^2).
Check 8 : 64 — (8 + 1)^3 = 9^3 = 729, so 64 does not fit the pattern (64 = 8^2 or 4^3).
Check 2 : 27 — (2 + 1)^3 = 3^3 = 27, so this pair matches the pattern.
Conclusion: The similar pair is 2 : 27 because it follows the rule number : (number + 1)^3.