Question

ab is a two digit number. When ab is divided by 7 the remainder is 3. Find the sum of all positive values of ab.

Answer 1

Merhaba bir dakika yardım edeceğim

Answer 2

ingilizce mi soyleyim türkçe mi

Answer 3

Doesnt matter, so to start with
find all the numbers that are multiples of 7 and two digits:
(14,21,28,35,42,49,56,63,70,77,84,91,98)

Answer 4

Now you have to find a pattern which you can use:
So start with 14,
when you divide it by 7 you get no remainder
when you divide 13 by 7 you get 6 remainder
when you divide 12 by 7 you get 5 remainder
when you divide 11 by 7 you get 4 remainder
And finally when you divide 10 by 7 you get 3 as remainder
This means that the values you are looking for are x-4 ( where x are two digit multiples of 7)

Answer 5

So your new list of two digits with 3 remainder when divided by 7 will be
in a manner such as 14-4 , 21-4, 28-4 and so on till you get to 98-4
Tell me if you understand

Answer 6

I understand till now @denonakavro

Answer 7

Ok, so lets continue
The value we are looking for is the sum of our new list
So let me do the list for you
(10,17,24,31,38,45,52,59,66,73,80,87,94)
Now just add all these up and tell me what you get ?

Answer 8

I get 676 in total

Answer 9

Yes thats what I got too :) and should be the answer
Btw, are you from Turkey ?

Answer 10

Thank you for your really clear answer that was very helpful. Yes, I am from Turkey. How about you?

Answer 11

Ilk başta yazdım ama görmemişsin ben de türküm

Answer 12

Türk olduğunu elbette anladım ama Türkiye'de mi yaşıyorsun demek istedim.

Answer 13

Yaşıyordum diyelim, bir süredir yurt dışında yaşıyorum ve eğitim görüyorum. Herhangi bir matematik konusunda veya başka konularda yardım gerekirse soyleyebilirsin

Answer 14

Eğer olursa söylerim, tekrardan çok teşekkürler.

Answer 15

Rather than totalling them all using a calculator you should treat it as an arithmetic series with common difference = 7

Answer 16

I found the general term as Un=7n+3 and did the equations by that @MrNood