CAT 2008 had a question lifted from ‘Puzzles to Puzzle you’ by Shakuntala Devi.
A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x.
1) 2 ≤ x ≤ 6
2) 5 ≤ x ≤ 8
3) 9 ≤ x ≤ 12
4) 11 ≤ x ≤ 14
5) 13 ≤ x ≤ 18
Here is the solution:
If we go in the reverse sequence,
Left: 0, gave: 0.5 + 0.5 = 1
1 + 0.5 = 1.5 * 2 = 3
3 + 0.5 = 3.5 * 2 = 7
Hence x = 7
This question was similar to puzzle no. 12 from Shakuntala Devi’s book ‘Puzzles to Puzzle you’ Have a look.
Something for the Marmalade
A little girl I know sells oranges from door to door. One day while on her rounds she sold 1/2 an orange more than half her oranges to the first customer. To the second customer she sold 1/2 an orange more than half of the reminder and to the third and the last customer she sold 1/2 an orange more than half she now had, leaving her none. Can you tell the number of oranges she originally had? Oh, by the way, she never had to cut an orange.
Surprisingly, I found a similar question in a Mensa Puzzle book by Dr. Abbie F. Salny
You’ve bought your weekly egg supply at the local farm store. The first morning you have company for breakfast and use half the eggs plus one-half an egg. The next morning you use one-half of what’s left plus one-half an egg. The third morning you use one-half of what’s left plus one-half an egg, and on the fourth morning, you’re down to one solitary egg, so you make a French toast. In all this cooking, you’ve never had one-half an egg to carry over to the next day. How many eggs did you buy originally?
Answer: 15 (Slight variation from Shakuntala Devi’s question but the method of solving remains the same)
Hence, we recommend solving not only questions from CAT specific books, but also solving a lot of puzzles. They develop your logical skills, and tolerance level. And who knows, your exam might have a question lifted from one such book!