Problem Solving

BTGmoderatorDC 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

OA C

Source: Veritas Prep

Say the four accounts are A, B, C and D.

We know that the percentage values of investments are positive integers. Say the largest percentage values of the investments is for D; thus, with A, B and C being the minimum and distinct, A = 1%, B = 2% and C = 3%; thus D = 100 - 1 - 2 - 3 = 94%.

However, 94% is an incorrect answer. The question asks the minimum percent of the money that could be in the account with the largest balance.

To get the minimum percent, let's assume that A = B = C = D = 25% each; however, this is not possible since the values of A, B, C and D are not distinct. Say A < B < C < D; we have to get the minimum possible value of D. Median of A, B, C and D is 25%, which is the average of B and C. Thus, B = 24%, A = 23%, C = 26% and D = 27% (minimum possible value).

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC 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

OA C

Source: Veritas Prep

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 z
In order to MINIMIZE the value of the z, we must MAXIMIZE the values of w, x, and y.

Now let's test the answer choices

A. 25
In other words, z = 25
So, 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 = 26
So, 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 = 27
So, 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

BTGmoderatorDC 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

OA C

Source: Veritas Prep

Since we want to minimize the percent of Katrina's money in the account with the largest balance, we need to maximize the percents of the 3 accounts with the smallest balances. If we let one of these 3 accounts have 100/4 = 25 percent of her money, then the 3 accounts with the smallest balances could be 23, 24 and 25 percent. Combined, they make up

23 + 24 + 25 = 72 percent of the total balance.

So, the fourth account would have 28 percent of her money.

The accounts would have these percentages: 23, 24, 25, and 28.

However, we notice that 28 is not the smallest possible percent value, since we can decrease 28 by 1 and increase 25 by 1 to obtain 23, 24, 26 and 27 percent. Now, 27 is the minimum percentage for the largest account, since further decreasing 27 would result in multiple accounts with the same percent figure.

Answer: C