Odd One Out — In the ordered pairs ( 2, 11 ), ( 3, 30 ), ( 7, 345 ), and ( 5, 128 ), identify the pair that does not satisfy the pattern y = x^3 + 3.
Verbal Reasoning
Classification
Difficulty: Medium
Choose an option
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A( 2, 11 )
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B( 3, 30 )
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C( 7, 345 )
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D( 5, 128 )
Answer
Correct Answer: ( 7, 345 )
Explanation
Introduction / Context:Recognizing a simple algebraic rule behind ordered pairs is a common pattern-recognition task. Three pairs follow one rule; one does not.
Given Data / Assumptions:
- Pairs: (2, 11), (3, 30), (7, 345), (5, 128).
- Candidate rule: y = x^3 + 3.
Concept / Approach:Compute x^3 + 3 for each x and compare with the given y.
Step-by-Step Solution:x = 2: 2^3 + 3 = 8 + 3 = 11, matches.x = 3: 3^3 + 3 = 27 + 3 = 30, matches.x = 5: 5^3 + 3 = 125 + 3 = 128, matches.x = 7: 7^3 + 3 = 343 + 3 = 346, which does not match 345.
Verification / Alternative check:Re-calc to avoid arithmetic slips; only the third pair misses by 1.
Why Other Options Are Wrong:
- ( 2, 11 ): satisfies y = x^3 + 3.
- ( 3, 30 ): satisfies y = x^3 + 3.
- ( 5, 128 ): satisfies y = x^3 + 3.
Common Pitfalls:Mistaking 7^3 as 342 or 344; 7^3 is 343 exactly.
Final Answer:( 7, 345 )