Difficulty: Medium
Correct Answer: 0.18
Explanation:
Introduction / Context:
This question explores the concept of the greatest common divisor (GCD) for decimal numbers. Although GCD is usually taught with integers, decimal values can be handled by scaling them up to integers, performing the GCD calculation, and then scaling the result back down to a decimal. This technique is very useful in quantitative aptitude and data interpretation problems.
Given Data / Assumptions:
Concept / Approach:
To find the GCD of decimal numbers, we eliminate the decimals by multiplying each number by a suitable power of 10 so that all become integers. We then compute the GCD of the integers using standard methods. Finally, we divide the result by the same power of 10 to obtain the GCD in decimal form.
Step-by-Step Solution:
Multiply each number by 100 to remove decimal places:
1.08 * 100 = 108
0.36 * 100 = 36
0.90 * 100 = 90
Now find GCD of 108, 36, and 90.
GCD(108, 36) = 36.
GCD(36, 90) = 18.
So GCD of 108, 36, and 90 is 18.
Scale back by dividing by 100: 18 / 100 = 0.18.
Verification / Alternative check:
Check divisibility of the original decimals by 0.18:
1.08 / 0.18 = 6
0.36 / 0.18 = 2
0.90 / 0.18 = 5
All quotients are integers, showing that 0.18 divides all the numbers exactly and is a common divisor. Since it comes from the integer GCD, it is the greatest common divisor in decimal form.
Why Other Options Are Wrong:
0.90, 0.36, and 1.08 are larger than 0.18 and do not divide all three values exactly.
0.06 divides all three numbers but is not the greatest such divisor, because 0.18 is a larger common divisor.
Common Pitfalls:
Students sometimes try to work directly with decimals without scaling, which can be confusing. Another mistake is not using the same power of 10 for all numbers or forgetting to scale back at the end. Always convert decimals to integers in a consistent way, find the GCD, and then convert back to decimals for the final answer.
Final Answer:
0.18
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