K-numbers are positive integers with only 2's as their digits. For exa

Question

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

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

EMPOWERgmatRichC · Accepted Answer

Hi All,

This question has a great built-in Number Property 'shortcut' to it that will allow you to avoid almost all of the math involved.

We're asked to figure out how many K-numbers are needed to sum to 600. Since 600 ends in a 0, and K-numbers all end in 2s, there are only certain ways to get to a sum that ends in 0 (and they all fit a pattern).....there must be a MULTIPLE OF 5 K-numbers, since any multiple of 5 multiplied by any K-number will end in a 0.

There's only one answer that fits that pattern...

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

askhere · Answer

600 = 2*222 + (22*7) + 2
K weight of 600 = 2 +7+1 = 10

Answer  A

NavenRk · Answer

600 = 444 (222*2)
 154 ( 22*7 )
 2 (1)

Ans A) 10

tjerkrintjema · Answer

Should be answer A;

222+222+22+22+22+22+22+22+22+2 = 600
10 numbers of K so K Weight is 10.

Another quicker way how to solve it is;
600/222 = 2 R 156
156/22 = 7 R 2
2/2 = 1 R 0

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Since we are looking for the minimum number of K-numbers that sum to 600, a practical place to start is with the largest K-number less than 600, or 222. There are between 2 and 3 multiples of 222 in 600, so let's subtract out the two whole multiples! 
600 - 444 (= 2*222) = 156.

Now, the next largest K-number is 22. Again subtract as many whole multiples as possible: 
156 - 154 (= 7*22) = 2.

The next largest K-number is obviously 2:
2 - 2 ( =1*2) = 0.
 
Thus, 600 = 222(2) + 22(7) + 2(1), and the K-weight of 600 is 2 + 7 + 1 = 10.

The correct answer is A.

pacifist85 · Answer

So, I started it like this:

We have 600, so the greatest k-number can be 222.

600/222 = 2, and the remainder is 156. For now, 222*2
156/22 = 7, and the remainder is 2. Adding 22*7
2/2 = 0, so finally adding 2*1.

So, 7+2+1=10.  ANS A

noTh1ng · Answer

Is it possible to just look at how the K-weight of 60 is? Since 600 is a multiple I assumed that the pattern should be the same.

60 = 2*22 + 8*2 = k-weight of 10

Or is my idea wrong?

soumik0503 · Answer

Well.. Let's try with 100 and 10...
for 10 k weight is 5(5*2)...
for 100 it is 10( 22*4,6*2)...

Thanks & Regards.

Sent from my Redmi 3S using  GMAT Club Forum mobile app

Nunuboy1994 · Answer

We can easily attack this question by first finding and using the largest K values possible

222 + 222 = 444 - 2 k numbers

600- 444 = 156

22 x 7 = 154 - 7 k numbers

2- 1 k number

Thus

"A"

CAMANISHPARMAR · Answer

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

CAMANISHPARMAR · Answer

600 = 222(2) + 22(7) + 2(1), and the K-weight of 600 is 2 + 7 + 1 = 10.

Correct Answer is (A)

Bunuel · Answer

Merging topics. Please check the discussion above.

EgmatQuantExpert · Answer

Solution

Given:  
 • K-numbers are positive integers with only 2's as their digits.
 o 2, 22, and 222 are K-numbers. 
• K-weight of a number n is the minimum number of K-numbers that must be added together to equal n

To find:  
 • K-weight of 600

Approach and Working:

• K-weight of a number n is the minimum number of k-numbers that must be added to get n.
 o So, we should first try the form the n by adding the larger k-numbers that are less than n.
  Then only we should use the lower k-numbers.

K-weight of 600

• The k-number just less than 600 is 222.
 o Two times 222 is 444. 
  We can not use 3 times 222 as it is greater than 600.

• Next, we will use the k-umber less than 222 i.e. 22
 o Seven time 22 is 154. 
• 444 +154 = 598
 o Hence, we can write 600= 2 * 222 + 7*22 +2 
• Thus, k-weight of 600= 2 + 7 + 1

Hence, the correct answer is option A.
 
  Answer: A

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K-numbers are positive integers with only 2's as their digits. For exa

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