The first and the third digit of a five digit number d6d41 are the same. If the number is divisible by 9, the sum of its digit is
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Answer:
physics is a branch of science
Answer:
In the 5-digit number a6a41 each of the a's represent the same number. If the number is divisible by 9, what is the digit represented by a?
I first approached this by saying
2a+11
since it's divisible by 9. I got stuck because I didn't know what to equate it to. So I randomly said 2a+11=27 and then I got a=8 and indeed the number was divisble by 9
Step-by-step explanation:
There is nothing overtly in here about equality, although there is an explanation with a type of equality I'll discuss in a second.
Bottom line is, no matter what digit you pick a to be, as long as 2a+11 is divisible by 9, that a will work.
If you are learning modular arithmetic, then you really can find an equality. A number n satisfies n≡0(mod9) iff 9 divides n.
So the rule you mentioned above can be rephrased as
A number is equal to 0 mod 9 iff the sum of its digits is equal to 0 mod 9.
Solving 2a+11≡0(mod9) for a is not really much different than solving 2a+11=0. You can say that 2a≡−11(mod9), and then you need to find an inverse for 2 (that us, a number to multiply it with that turns it into a 1. Module 9, it's easy to discover that 5 does the trick. So, a≡5⋅2a≡5(−11)≡−55(mod9). To get a to be a digit, we need to shift it by multiples of 9. As you can see, −55≡−55+63≡8(mod9).