goodyear2013 wrote:
When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 8. If 1 < m < 200, what is the greatest possible value of m?
A. 47
B. 65
C. 103
D. 117
E. 164
I would probably go with Bunuel's solution, but here's another approach:
There's a nice rule that says
"If a number is divisible by 9, the sum of its digits will be divisible by 9" For example, we know that 551008 is divisible by 9, because the sum of its digits equals 18, and 18 is divisible by 9
We're told that when m is divided by 9, the remainder is 2.
So, my is TWO GREATER than some multiple of 9.
So, for a possible value of m to meet this condition, all we need to do is subtract 2 from that value and see if it is divisible by 9.
Let's check the answer choices:
A. 47 - 2 = 45 This is divisible by 9, so m MIGHT equal 47
B. 65 - 2 = 63 This is divisible by 9, so m MIGHT equal 65
C. 103 - 2 = 101 This is NOT divisible by 9, so ELIMINATE C
D. 117 - 2 = 115 This is NOT divisible by 9, so ELIMINATE D
E. 164 - 2 = 162 This is divisible by 9, so m MIGHT equal 164
Let's start with the largest answer choice (E) and see if it meets the second condition (When m is divided by 13, the remainder is 8.)
164 divided by 13 = 12 with remainder 8
DONE
Answer: E
Cheers,
Brent
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