When 52416 is divided by 312, the quotient is 168. Using this information, what will be the quotient when 52.416 is divided by 0.0168?

Introduction / Context:
This question tests your understanding of how scaling both the dividend and divisor by powers of 10 affects the quotient. It shows how known division facts can be used to quickly evaluate related divisions with decimal numbers, a common trick in aptitude tests to save time.

Given Data / Assumptions:

• We know that 52416 ÷ 312 = 168.
• We must find the value of 52.416 ÷ 0.0168.
• Both division problems involve the same digits but with different decimal placements.
• We assume all computations are exact, with no rounding.

Concept / Approach:
The key idea is that multiplying or dividing both the numerator and denominator of a fraction by the same nonzero number does not change its value. We represent 52.416 ÷ 0.0168 as a fraction and then scale numerator and denominator by a power of 10 so that we can relate it back to 52416 ÷ 312. By counting decimal places, we can see how to transform one expression into the other.

Step-by-Step Solution:
Write the required quotient as a fraction: 52.416 ÷ 0.0168 = 52.416 / 0.0168.Count decimal places: 52.416 has three decimal places, 0.0168 has four.Multiply numerator and denominator by 10,000 to clear decimals: (52.416 × 10,000) / (0.0168 × 10,000).Compute: 52.416 × 10,000 = 524,160 and 0.0168 × 10,000 = 168.So 52.416 / 0.0168 = 524,160 / 168.Notice that 524,160 / 168 = (52416 × 10) / 168.We know 52416 ÷ 312 = 168, which implies 52416 = 168 × 312.Now, 524,160 / 168 = (168 × 312 × 10) / 168 = 312 × 10 = 3120.Thus, 52.416 ÷ 0.0168 = 3120.

Verification / Alternative check:
You can also verify on a calculator or by simplified division. Since 0.0168 is very small, dividing 52.416 by it should give a large number. Direct computation produces 3120, confirming our result. The relationship with 52416 ÷ 312 helps to see the connection of digits and provides a quick mental confirmation of the magnitude of the answer.

Why Other Options Are Wrong:
Option 3.12 or 31.2 are far too small; dividing by a small number like 0.0168 should increase the value substantially. Option 312 is closer in scale but still smaller by a factor of 10 than the correct answer. Option 168 is simply the known quotient from a different division problem and does not correspond to the new combination of decimal shifts. Only 3120 is consistent with both the scaling logic and the known division fact.

Common Pitfalls:
A common error is to move the decimal in the numerator and denominator by different numbers of places, which changes the value of the fraction. Another mistake is to assume that the new quotient must be the same as the old one because the digits look similar. Properly tracking the total shifts in place value and maintaining equal scaling for numerator and denominator prevents these errors.

Final Answer:
The quotient when 52.416 is divided by 0.0168 is 3120.