Log In
0 votes
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 94 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

selected by

Related questions

1 vote
1 answer
how many way we can select 4 candies from 6 different groups?
asked Mar 16, 2017 in Set Theory & Algebra Shreya Roy 709 views
11 votes
3 answers
An anthropologist is visiting the island of knights and knaves one after the other.. This particular island is a very peculiar place, for it has only two kinds of inhabitants, namely, knights and knaves! Now, knights always tell the truth and knaves always lie! There are cluster of island on ... Maya. B: A is a knave, and this is the island of Maya. Is this the island of Maya? What are A and B ?
asked Apr 20, 2016 in Verbal Ability pC 885 views
6 votes
3 answers
A bad king has a cellar of 1000 bottles of delightful and very expensive wine. A neighboring queen plots to kill the bad king and sends a servant to poison the wine. Fortunately (or say unfortunately) the bad king's guards catch the servant after he has only poisoned one bottle. ... is in mind of the king, how will he be able to do so ? (of course he has less then 1000 prisoners in his prisons)
asked Apr 9, 2016 in Puzzles pC 758 views