In this fraction comparison aptitude question, choose the fraction that is not equal to 4/11 from the given options.

Introduction / Context:
This question tests your understanding of equivalent fractions. You are asked to identify which of the given fractions is not equal to 4/11. Being able to recognize and simplify fractions quickly is a core skill in many entrance exams, bank tests and general aptitude assessments.

Given Data / Assumptions:

• Reference fraction: 4/11.
• Options: 32/88, 84/209, 64/176, 20/55.
• Exactly one option does not represent the same rational value as 4/11.
• We assume basic knowledge of simplifying fractions by dividing numerator and denominator by common factors.

Concept / Approach:
Two fractions are equivalent if they reduce to the same lowest terms when numerator and denominator are divided by their greatest common divisor. In this problem we can either simplify each option or rewrite 4/11 with different numerators and denominators by multiplying both parts by the same integer. If an option cannot be matched to 4/11 in this way, it is the odd one out.

Step-by-Step Solution:
Step 1: Check 32/88.Divide numerator and denominator of 32/88 by 8: 32 / 8 = 4 and 88 / 8 = 11, so 32/88 = 4/11.Step 2: Check 64/176.Divide numerator and denominator of 64/176 by 16: 64 / 16 = 4 and 176 / 16 = 11, so 64/176 = 4/11.Step 3: Check 20/55.Divide numerator and denominator of 20/55 by 5: 20 / 5 = 4 and 55 / 5 = 11, so 20/55 = 4/11.Step 4: Check 84/209.There is no integer k such that 4 * k = 84 and 11 * k = 209 at the same time. 84 / 4 = 21 but 11 * 21 = 231, not 209. Also, the fraction 84/209 does not simplify to 4/11 by any common factor.Step 5: Conclude that 84/209 is the only fraction not equal to 4/11.

Verification / Alternative check:
We can also compare approximate decimal values. 4/11 is about 0.3636. The equivalent fractions 32/88, 64/176 and 20/55 share this value because they reduce exactly to 4/11. Meanwhile, 84/209 is roughly 0.402, which is clearly larger than 0.36 and does not match the target fraction. This confirms that 84/209 is not equivalent to 4/11.

Why Other Options Are Wrong:
32/88: Reduces exactly to 4/11, so it is equal to the reference fraction.
64/176: Also simplifies to 4/11, so it represents the same rational number.
20/55: When reduced, becomes 4/11, and therefore is not the required odd fraction.

Common Pitfalls:
Some test takers try to compare fractions only through approximate decimals or visual estimation, which can be slow or inaccurate without a calculator. A more reliable method is to use factorization to reduce fractions to lowest terms. Another mistake is to forget that both numerator and denominator must be multiplied or divided by the same integer to preserve equivalence. Any change that does not treat numerator and denominator in the same way will change the value of the fraction.

Final Answer:
The fraction that is not equal to 4/11 is 84/209.