# Number Analogy Problem

$\frac{73}{67}: \frac{57}{55}::\frac{93}{87}:$ ?

Options are :

(1) $\frac{47}{67}$

(2) $\frac{53}{57}$

(3) $\frac{63}{61}$

(4) $\frac{73}{71}$

Source: NTSE 2016-17 Examination Bengaluru

• From NTSE Stage 1 examinations conducted at Bengaluru, India 2016-2017. I know the correct answer and can give it if required, but I don't know the reasoning behind it. – Prithvish Baidya Oct 26 '17 at 13:44
• OK, excellent. Could you please edit into the question the information about where it comes from? Sorry to be picky about this, but we try to be scrupulous about attribution here... – Gareth McCaughan Oct 26 '17 at 13:52
• (and Welcome to Puzzling!) – Sid Oct 26 '17 at 14:20
• Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) – Rubio Nov 8 '17 at 2:12

## 2 Answers

4)73/71

There is a pattern in the given fractions

73-67 is 6 and 93-87 is also 6. 73,67 are both prime and (57,55),(93,87) are composite. the next fraction should have both prime numbers with the difference between the numbers as 2 (57-55).

Going by the title of this puzzle and mathematically, answer could be

(4) 73/71

As,

All the given fractions are >1 and so the answer should be and fractions are made up entirely of prime numbers / composite numbers but not a mix. Hence option (4).