Bunuel wrote:

All assets in Karina's investment portfolio are divided between an IRA, 401k, and two separate taxable accounts. No two accounts have the same amount of money and all four have at least some money in them. If each account has a whole-number percent of Karina's money, what is the minimum percent of Karina's money that could be in the account with the largest balance?

A. 25

B. 26

C. 27

D. 28

E. 29

Let's say Karina's entire portfolio is worth $100 altogether.

So, we want to divide this $100 into four integer amounts: w, x, y, z, where w < x < y <

z, and we want to minimize the value of

zIn order to MINIMIZE the value of the

z, we must MAXIMIZE the values of w, x, and y.

Now let's

test the answer choicesA. 25

In other words,

z = 25So, we have: w < x < y <

25 and all 4 values must add to 100

So, the greatest possible value of y is 24, the greatest possible value of x is 23, and the greatest possible value of w is 22

25 + 24 + 23 + 22 = 94.

No good. We want the 4 values to add to 100. ELIMINATE A

B. 26

In other words,

z = 26So, we have: w < x < y <

26 and all 4 values must add to 100

So, the greatest possible values of w, x and y are 23, 24, and 25 respectively.

26 + 25 + 24 + 23 = 98.

Unfortunately the 4 values do NOT add to 100, so we can ELIMINATE B

C. 27

In other words,

z = 27So, the greatest possible values of w, x and y are 24, 25, and 26 respectively.

27 + 26 + 25 + 24 = 102.

In this case the sum is greater than 100, but that's okay. We can just make one of the values smaller.

For example, the 4 values add to 100 when w, x, y and z equal 22, 25, 26, and

27 respectively

Answer: C

Cheers,

Brent

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