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can anyone solve the puzzle below:

There are some books on the table. If you group them by 3, you get some number of full groups and 2 books remain; if you group them by 4, you get some number of full groups and 3 books remain; if you group them by 5, you get some number of full groups and 4 books remain. What is the number of books on the table, if it is less than 100?
in Mathematical Logic by (17 points) | 52 views

1 Answer

+1 vote
Best answer
ans will be 59.
Explaination -

Let the total number of books is B,
then from 1st statement (If you group them by 3, you get some number of full groups and 2 books remain) , it implies B = 3X + 2
from 2nd stmt similarly B = 4Y + 3
and from 3rd stmt similarly B = 5Z = 4

so the problem is reduced to find a number such that when divided by 3, 4 and 5 gives remainder 2, 3, 4 respectively.

Now how to find such number---
1st observation numbers which divided by 5 and leaves remainder 4 are like 9,14,19,24, ....... that is one'sdigit is either 4 or 9
and as mentioned in question that number is less than 100, it means it is either 1digit number or two digit numbers.

case 1 ( when unit digit is 9) - now we have to guess ten's digit that is number in the form   _9 , so the possibilities are 0,1,2,..9

now among these we can remove digits 0, 3, 6, and 9 because such digits in tens place will make number divisible by 3 for ex- 09, 39, 69, 99 (how i guess these number- simple from primarly class math login - any number is divisible by 3 if sum of digits in number is divisible by 3)

from remaining try one by one-
19 - not possible bcz when divied by 3 leaves 1 remiander
29 - not possible bcz when divided by 4 leaves 1 remainder
49 - not possible bcz when divided by 4 leaves 1 raminder
59 - correct ans bcz when divided by 3 leaves 2 remainder, when divided by 4 leaves 3 remainder, and divided by 5 leaves 4 remainder
by Junior (917 points)
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