Question

A small number of cards has been lost from a complete pack. If I deal among four people, three cards remain. If I deal among three people, two remain and if I deal among five people, two cards remain. How many cards are there?
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Answer 1

Answer:

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Answer 2

Answer:

Let the number of cards be n .

Note that

$n < 52$

Now

$n = 4a + 3 = 3b + 2 = 5c + 2 \\ \\ n = 3b + 2 = 5c + 2 \\ \\ n - 2 = 3b = 5c$

Where n , a , b and c are natural numbers .

Notice that n - 2 is multiple of both 5 and 3 so

$n - 2 = 15k \\ n = 15k + 2$

Now such numbers are 17 , 32 and 47 .

Which gives remainder 3 divided by 4 is only 47

So 5 card were lost .

There is no proper method to solve these question when remainder is different ,hit and trial is easiest . although by using right approach u can reduce criteria of your search .