Question

Find the odd term out: \[ \frac{41}{29},\ \frac{53}{43},\ \frac{67}{59},\ \frac{79}{73},\ \frac{89}{83},\ \frac{97}{91} \]

• A. \(\frac{97}{91}\)
• B. \(\frac{89}{83}\)
• C. \(\frac{67}{59}\)
• D. \(\frac{41}{29}\)

Hint:

When fractions appear in odd-one-out questions, examine numerator-denominator differences and also check whether the numbers are prime, composite, square numbers, etc.

Answer 1

The Correct Option is A

Concept: Observe the difference between numerator and denominator.

Step 1: Calculate the differences. \[ 41-29=12 \] \[ 53-43=10 \] \[ 67-59=8 \] \[ 79-73=6 \] \[ 89-83=6 \] \[ 97-91=6 \] The more important observation is that in all valid cases both numerator and denominator are prime numbers.

Step 2: Check primality. \[ 41,\ 29,\ 53,\ 43,\ 67,\ 59,\ 79,\ 73,\ 89,\ 83 \] are all prime. However, \[ 91=7\times13 \] which is not prime. Thus \[ \frac{97}{91} \] fails the prime-prime pattern.

Step 3: Conclusion. Hence the odd term is \[ \boxed{\frac{97}{91}}. \]