Problem Solving

Hi All,

We're told that all assets in Karina's investment portfolio are divided between an IRA, 401k, and two separate taxable accounts and that 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, we're asked for the MINIMUM percent of Karina's money that could be in the account with the LARGEST balance. This question can be solved in a number of different ways, including by TESTing THE ANSWERS.

While this prompt is wordy, it can be simplified to the following: since 100% of the money has to be spread across 4 accounts with DIFFERENT integer-percent totals, we need to find 4 DIFFERENT numbers that add up to 100. We're then asked to find the SMALLEST possible integer value for the LARGEST of the 4 numbers.

Let's TEST Answer A: 25
IF... largest = 25, then the next 3 could be as large as....24, 23 and 22
25+24+23+22 = 94
This is NOT large enough; the 4 numbers need to total 100. Eliminate Answer A

Answer B: 26
IF... largest = 26, then the next 3 could be as large as....25, 24 and 23
26+25+24+23 = 98
This is NOT large enough; the 4 numbers need to total 100. Eliminate Answer B

Answer C: 27
IF... largest = 27, then the next 3 could be as large as....26, 25 and 24
27+26+25+24 = 102
This is clearly too large, BUT we could reduce the smallest value....
The group could then be 27, 26, 25 and 22.... which would total 100.
Thus, the smallest possible value for the LARGEST percent is 27.

Final Answer: C

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

BTGmoderatorLU wrote:Source: Veritas Prep

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

The OA is C

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