Use a known quotient to find a related one via scaling: Given 12276 ÷ 155 = 79.2, compute 122.76 ÷ 15.5 by relating both numerators and denominators to the known ratio.
Aptitude
Decimal Fraction
Difficulty: Easy
Choose an option
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A7.092
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B7.92
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C79.02
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D79.2
Answer
Correct Answer: 7.92
Explanation
Introduction / Context:When a quotient is already known, you can use proportional scaling to obtain another quotient rapidly. This avoids long division and leverages place-value reasoning with decimals—an essential skill in aptitude tests and quick calculations.
Given Data / Assumptions:
- Known: 12276 ÷ 155 = 79.2.
- Find: 122.76 ÷ 15.5.
Concept / Approach:Notice that 122.76 is 1/100 of 12276, and 15.5 is 1/10 of 155. Therefore, 122.76 ÷ 15.5 equals (12276/100) ÷ (155/10) = (12276 ÷ 155) × (10/100) = (12276 ÷ 155) × 0.1. This scaling logic preserves the ratio structure exactly.
Step-by-Step Solution:
Start with the known value: 12276 ÷ 155 = 79.2.Adjust numerator and denominator: 122.76 ÷ 15.5 = (12276/100) ÷ (155/10).Compute the scaling: = (12276 ÷ 155) × (10/100) = 79.2 × 0.1.Hence the result is 7.92.Verification / Alternative check:
Shift decimals equally: 122.76 ÷ 15.5 = 1227.6 ÷ 155 ≈ 7.92 (exact with given data).Why Other Options Are Wrong:
- 79.2 and 79.02: Fail to apply the 0.1 scaling factor correctly.
- 7.092: Incorrect adjustment of decimal places leads to an off-by-scale result.
Common Pitfalls:
- Mismatching the scaling of numerator and denominator.
- Dropping or adding extra zeros during decimal shifts.
Final Answer:
7.92