SOLUTION: consider the following statements: A number a1a2a3a4a7 is divisible by 9 if 1.a1+a2+a3+a4+a7 is divisible by9. 2.a1-a2+a3-a4+a7 is divisible by 9. which of the above statements

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: consider the following statements: A number a1a2a3a4a7 is divisible by 9 if 1.a1+a2+a3+a4+a7 is divisible by9. 2.a1-a2+a3-a4+a7 is divisible by 9. which of the above statements      Log On


   

Question 887110: consider the following statements:
A number a1a2a3a4a7 is divisible by 9 if
1.a1+a2+a3+a4+a7 is divisible by9.
2.a1-a2+a3-a4+a7 is divisible by 9.
which of the above statements is correct?
a.1 only.
b.2 only.
c. both 1 and 2.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let's find a random 5 digit numbers that is
divisible by 9 and see which one or both are true.

Take an arpitrary 5 digit number, say 79269
Divide it by 9
Get 8807.6666666
So if we take 8807x9 we get a five-digit number 79263, 
which is divisible by 9.

Then a1=7, a2=9, a3=2, a4=6, a7=3  [Why the 7 subscript instead of 5???]

a1+a2+a3+a4+a7 = 7+9+2+6+3 = 27, which is divisible by 3, so 1 is true

a1-a2+a3-a4+a7 = 7-9+2-6+3 = -3 not divisible by 9.  So 2 is not true.

Answer: Only the first one is true.

Edwin