Question

A lady is carrying a basket of eggs. a truck races past her. scared by the noise, she drops the basket and all the eggs broke. when asked how many eggs were there in the basket, the lady replies by saying that she is poor in arithmetic but she remembers that when she grouped the eggs in twos, threes, fours, and fives,she had remainders of 1,2,3, and 4 eggs respectively. how many eggs were there in her basket before she dropped it?

a.59 b)39 c)49 d)69 e)79

Answer 1

ans is 59............

Answer 2

Number of eggs in the basket was 59.

When divided by 2,3,4,5 the resulting remainders are 1,2,3,4

Hence we can infer that number is odd

Also, number has a unit place of 4 or 9

but since it is odd, the last digit is always 9

The number leaves a remainder of 3 when divided by 4 i.e. number is a part of set : { 19,39,59,79,99......}

Subtracting 2 from all these numbers and then testing for divisibility by 3

{ 17,37,57,77,97.......}

Numbers divisible by 3 are: 57 , 117, 177......

hence, the number of eggs was 57 +2 = 59 or 117 +2 = 119 and so on.