A number when divided successively by 4 and 5 leaves reminders 1 and 4 respectively. When it is successively
divided by 5 and 4, then the respective remainders will be:
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let me give you a technique:
write the numbers as follows:
divisors: 4 5
reminders: 1 4
leave the right-most top number 5
multiply 4 and 4, then add 1 which is down below the divisor 4; you get 17
add this 17 to the product of 4, 5, (divisors) and k a constant
20k+17 (this is the number we want)
when k=1, the number is 37
when 37 is divided by 5, remainder is 2.
when 7 is divided by 4, remainder is 3.
Example
divisors: 4 5 6
remainders: 1 2 3
step 1: 3x5+2 = 17
step 2: 17x4+1 = 69
step 3: 4x5x6 = 120
the number is 120k+69
when k= 1, the first number is 189
Got it!
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