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

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BTGmoderatorLU: Moderator; Posts: 2589; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

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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Source: Beat The GMAT — Problem Solving | Sun Feb 18, 2024 7:56 am

mapadvantageprep: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Tue Feb 13, 2024 8:47 am

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.

The correct answer is A

Bernard Baah
MS '05, Stanford
GMAT and GRE Instructor
MapAdvantage Prep

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