JEE Advanced Maths: Number System / Comparing Fractions questions with solutions

Q1. Compare the fractions in each pair and identify which is larger: (a) 13/17 or 17/21 (b) 31/35 or 37/41

1. (a) 17/21 is larger; (b) 37/41 is larger
2. (a) 13/17 is larger; (b) 31/35 is larger
3. (a) 17/21 is larger; (b) 31/35 is larger
4. (a) 13/17 is larger; (b) 37/41 is larger

Answer: (a) 17/21 is larger; (b) 37/41 is larger

Use cross-multiplication, or note that each pair has fractions of the form n/(n+4), which strictly increase toward 1 as n grows, so the fraction with the larger numerator is larger.