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.
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.
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