Section A – Quantitative Ability

17. A potter asked his two sons to sell some pots in the market. The amount received for each pot was same as the number of pots sold. The two brothers spent the entire amount on some packets of potato chips and one packet of banana chips. One brother had the packet of banana chips along with some packets of potato chips, while the other brother just had potato chips. Each packet of potato chips costs ` 10/- and the packet of banana chips costs less than ` 10/-. The packets of chips were divided between the two brothers so each brother received equal number of packets. How much money should one brother give to the other to make the division financially equitable?

A. 1

B. 2

C. 4

D. 5

E. 7

Explanation:

Each packet of potato chips costs `10 and the packet of banana chips costs `y (y < 10). Let the number of packets of potato chips be n.

\The total amount spent is 10n + y. This has to be a square. Also as there are n + 1 packets and the number of packets is even, n has to be odd. We can consider 10n + y = 16, or 36. As n > 1, (Qthe total number of packets n + 1 is greater than 2), 10n + y= 36, i.e. n = 3,

y = 6.

There are 3 + 1 or 4 packets. One brother got 2 packets of potato chips. The other got one packet of potato chips and one of banana chips. The values are `20 and `16 respectively.

\ The one who ‘got’ `20 should give `2 to the other, and both would ‘get’ `18. Choice (B)

Note: All the perfect squares with an odd digit in the tens place can have only 6 in the units place and such numbers are of the form

(10k ± 4)². In the exam scenario as there is no ‘Cannot be determined’ in the options, we can go ahead and solve with any perfect square ending with 6.