Section – III

49. There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and last three is 12673. Find the first number.

A. 19

B. 17

C. 13

D. None of the above

Solution:

Let the four numbers be a, b, c and d, where

a < b < c < d.

abc = 7429 and bcd = 12673

7429 = 7600 – 171 = 19(400) – 19(9) = 19 (391) = (19) (20² – 3²)

= (19) (20 + 3) (20 – 3) = (19) (23) (17)

\ a = 17, b = 19 and c = 23.

\ First number = 17.

Note:- The product of last three numbers 12673 is redundant data. Choice (B)