Difficulty: Easy
Correct Answer: 105/112
Explanation:
Introduction / Context:This question checks whether you can recognize a fraction that is not in simplest form. Simplifying fractions, or checking if they are reducible, is a frequent step in many aptitude calculations.
Given Data / Assumptions:
Concept / Approach:A fraction is in lowest terms if the greatest common divisor of numerator and denominator is 1. To test reducibility, we factor the numerator and denominator or at least check for obvious common factors such as 2, 3, 5, 7 and 11.
Step-by-Step Solution:
Step 1: Consider 79/26. The number 79 is a prime number and does not divide by 2 or 13, so 79 and 26 share no common factor other than 1. This fraction is irreducible.Step 2: Consider 105/112. Factor 105 as 3 * 5 * 7 and 112 as 16 * 7 = 2^4 * 7. Both numerator and denominator share a factor of 7.Step 3: Divide numerator and denominator of 105/112 by 7 to get 15/16. Thus 105/112 is reducible.Step 4: Consider 41/17. The number 41 is prime and not divisible by 17, so there is no common factor greater than 1.Step 5: Consider 91/15. The number 91 factors as 7 * 13 and 15 as 3 * 5, so there is no common factor greater than 1.Verification / Alternative check:If we compute the greatest common divisor of each pair, only gcd(105, 112) is greater than 1. This confirms that 105/112 is the only reducible fraction.
Why Other Options Are Wrong:79/26, 41/17 and 91/15 have numerators and denominators that are relatively prime. They are already in lowest terms and therefore are not reducible.
Common Pitfalls:Students often confuse reducibility with the size of the fraction or with whether it is proper or improper. A fraction can be large or improper and still be in simplest form. What matters is the common factors of numerator and denominator.
Final Answer:The only fraction that can be reduced further is 105/112.
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