When a number is divisible by 42 and gives the remainder of 25 when divided by 14, what will be the remainder if the number is divisible by 14?
Let's first understand what it means for a number to be divisible by another number. A number is said to be divisible by another number if it can be divided exactly without leaving any remainder. For example, 6 is divisible by 3 because it can be divided exactly without leaving any remainder.
Now let's consider the given problem. We are given that a number is divisible by 42 and gives the remainder of 25 when divided by 14. This means that if we divide the number by 42, there will be no remainder. Also, if we divide the same number by 14, there will be a remainder of 25.
We can use this information to find the remainder when the same number is divided by 14 again. Since the number is divisible by 42, we can write it as:
N = 42k
where k is an integer. Now we know that if we divide N by 14, there will be a remainder of 25. We can write this as:
N = 14q + 25
where q is an integer. Substituting N = 42k in this equation, we get:
42k = 14q + 25
Simplifying this equation, we get:
q = (42k - 25)/14
We can see that q is an integer if and only if (42k - 25) is divisible by 14. Let's check this condition.
(42k - 25) mod 14 = (2 x (21k mod 7) -1) mod 14
Since k is an integer, (21k mod 7) can only take values from {0,1,2,3}. Therefore,
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