## $$K$$-numbers are positive integers with only $$2$$'s as their digits. For example, $$2, 22,$$ and $$222$$ are $$K$$

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### $$K$$-numbers are positive integers with only $$2$$'s as their digits. For example, $$2, 22,$$ and $$222$$ are $$K$$

by BTGmoderatorLU » Sun Feb 18, 2024 7:56 am

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$$K$$-numbers are positive integers with only $$2$$'s as their digits. For example, $$2, 22,$$ and $$222$$ are $$K$$-numbers. The $$K$$-weight of a number $$n$$ is the minimum number of $$K$$-numbers that must be added together to equal $$n.$$ For example, the $$K$$-weight of $$50$$ is $$5,$$ because $$50 = 22 + 22 + 2 + 2 + 2.$$ What is the K-weight of $$600?$$

A. $$10$$
B. $$11$$
C. $$12$$
D. $$13$$
E. $$14$$

The OA is A

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### Re: $$K$$-numbers are positive integers with only $$2$$'s as their digits. For example, $$2, 22,$$ and $$222$$ are $$K$$

by mapadvantageprep » Sun Feb 18, 2024 3:41 pm
To represent 600 as the sum of K-numbers, we need to find the minimum number of K-numbers that must be added together to equal 600.

The largest K-number less than or equal to 600 is 222. Therefore, we start by dividing 600 by 222:

600÷222=2 remainder 156

This tells us that we can represent 600 as 2 times 222 plus a remainder of 156.

Next, we check how many times we can represent the remainder of 156 using the next largest K-number, which is 22:

156÷22=7 remainder 2

This tells us that we can represent 156 as 7 times 22 plus a remainder of 2.

Finally, the remainder of 2 can be represented using the smallest K-number, which is 2 itself.

So, to represent 600 as the sum of K-numbers, we need:

2 times 222
7 times 22
1 time 2
Therefore, the K-weight of 600 is

2+7+1=10.