Number 6
Number Theory
Level
3
A number leaves a remainder of 5 when it is divided by a certain divisor. And the same number leaves a remainder of 45 when it is divided by twice the value of the same divisor. Find the value of this divisor.
The answer is 40.
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1 solution
Let's assume that the number is N. Then we can write :
N= d×a+5
N= 2d×b+45
where a & b are the quotient and d is the divisor.
Now equating both you get -
d×a + 5 = 2d×b + 45 or,
d×a - 2d×b = 45–5 or,
(a-2b)×d = 40 or,
(a-2b) = 40÷d
Now minimum value of d for you get the difference as an integral value (a&b can't be non-integral here) is 40. So now solving it we get :
(a-2b) = 1 or,
a = 2b + 1
Set of values corresponding to (a,b) are (3,1) ,(5,2) , (7,3) and so on..
The divisor is 40 and the number could be 125 and you will get another number by putting those set of values.