SOLUTION: I multiplied one whole number by 18. I multiplied a second whole number by 21. I then added the two products . Of the following , which could have been the resulting sum ? .Thanks

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Question 1168722: I multiplied one whole number by 18. I multiplied a second whole number by 21. I then added the two products . Of the following , which could have been the resulting sum ? .Thanks for any help
Options are —-
A. 1996
B 1997
C 1998
D. 1999
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
x and y are the numbers
18x+21y is their sum
55*18+48*21=990+1008=1998
54*18+49*21=2001
56*18+47*21=1008+987=1995
57*18+46*21y=1992
The difference in combinations is 3.
1998 is the only even dividend in the group. When one is increased, the other decreased, there is a change of 3.
27*18+72*21=1998, so there are other combinations, but the change in difference is always 3, and 1998 is always a sum. So are 1995 and 2001, but they aren't choices.
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.

We start with numbers  x  and  y.

The resulting number is   18x + 21y = 3*(6x+7y).

The resulting number is a multiple of  3.

Of the four given optional numbers, only  1998  is a multiple of  3.

Other three optional numbers are not multiples of  3.

So,  the only answer is option  (C)  with the number of  1998. 

    The rule of divisibility by 3 is THIS:


        +------------------------------------------------+
        |    a number is divisible by 3 if and only if   |
        |    the sum of its digits is divisible by 3.    |
        +------------------------------------------------+



    For the number 1998 the sum of its digits is  1+9+9+8 = 27.

    This sum is divisible by 3 - - - so the number 1998 is divisible by 3,

         while the other three numbers ARE NOT divisible by 3.

-----------

I answered your question in full,  giving a full explanation.


On the divisibility rules,  see the lessons
    - Divisibility by 2 rule
    - Divisibility by 3 rule
    - Divisibility by 4 rule
    - Divisibility by 5 rule
    - Divisibility by 6 rule
    - Divisibility by 9 rule
    - Divisibility by 10 rule
    - Divisibility by 11 rule
    - Restore the omitted digit in a number in a way that the number is divisible by 9
    - Restore the omitted digit in a number in a way that the number is divisible by 11
in this site.



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