Question

If counted in pairs, one will remain;
If counted in threes, two will remain;
If counted in fours, three will remain;
If counted in fives, four will remain;
If counted in sixes, five will remain;
If counted in sevens, nothing will remain;
My basket cannot accomodate more than 150 eggs.
how many eggs were there?​

Answer 1

Let eggs=x

When divided by 2,3,4,5 and 6, the remainder is always one less than the divisor

Thus, x is one less than LCM(2,3,4,5,6) OR one less than a multiple of the same.

Thus, x is one less than LCM(2,3,4,5,6) OR one less than a multiple of the same.

LCM=60

now,

x= (60-1) OR (120-1) OR (180-1)

60-1= 59

NOT divisible by 7

120-1=119

Maybe x= 119

180-1= 179

Cannot be over 150.

We can safely conclude that x= 119

The trader was carrying 119 eggs

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