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All assets in Karina's investment portfolio are divided between an IRA

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All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

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New post 19 Jun 2018, 22:49
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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

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Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

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New post 19 Jun 2018, 23:13
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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


If we're not sure where to start, we'll look to the answers.
This is an Alternative approach.

Since we're looking for the minimum, we'll start with the smallest possible answer: 25.
If the minimum (in the largest account) was 25, then since none of the accounts have the same value, they must have less than 25 each. At most, they'll be 24, 23 and 22. But then their sum is 25 + 24 + 23 +22 which is less than 100. Impossible!
Similarly, if (B) were correct then the sum of the percentages would be at most 26 + 25 + 24 + 23 = 98 < 100. Also impossible.
(C) works out: 27 + 26 + 25 + 22 = 100 meaning that we can divide all the money between the 4 accounts.

(C) is our answer.
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All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

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New post 19 Jun 2018, 23:21
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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


Since there are 4 accounts in which all Karina' investments are divided &
we need a minimum percentage of the account with the largest balance,
the other 3 accounts must have the highest balance.

Let x be the minimum percentage of the account with the largest balance
\(x - 3 + x - 2 + x - 1 + x > 100\) -> \(4x - 6 > 100\) -> \(4x > 104\) -> \(x > 26\)

Therefore, Option C(27) is the minimum percent of Karina's money in the largest account.
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Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

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New post 07 Oct 2018, 07:52
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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 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
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Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

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New post 07 Oct 2018, 12:11
DavidTutorexamPAL wrote:
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


If we're not sure where to start, we'll look to the answers.
This is an Alternative approach.

Since we're looking for the minimum, we'll start with the smallest possible answer: 25.
If the minimum (in the largest account) was 25, then since none of the accounts have the same value, they must have less than 25 each. At most, they'll be 24, 23 and 22. But then their sum is 25 + 24 + 23 +22 which is less than 100. Impossible!
Similarly, if (B) were correct then the sum of the percentages would be at most 26 + 25 + 24 + 23 = 98 < 100. Also impossible.
(C) works out: 27 + 26 + 25 + 22 = 100 meaning that we can divide all the money between the 4 accounts.

(C) is our answer.


Why cannot the answer be (e) 29%? Couldn't you do 29, 25, 24, 22?
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Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

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New post 08 Oct 2018, 23:14
we can try like

25, 25, 25, 25 equal division
23, 24,26,27 min largest division.

adding and substracting 1 from the middle value.
adding and substracting 2 from extreme values.

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Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

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New post 08 Oct 2018, 23:25
Simmones wrote:
DavidTutorexamPAL wrote:
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


If we're not sure where to start, we'll look to the answers.
This is an Alternative approach.

Since we're looking for the minimum, we'll start with the smallest possible answer: 25.
If the minimum (in the largest account) was 25, then since none of the accounts have the same value, they must have less than 25 each. At most, they'll be 24, 23 and 22. But then their sum is 25 + 24 + 23 +22 which is less than 100. Impossible!
Similarly, if (B) were correct then the sum of the percentages would be at most 26 + 25 + 24 + 23 = 98 < 100. Also impossible.
(C) works out: 27 + 26 + 25 + 22 = 100 meaning that we can divide all the money between the 4 accounts.

(C) is our answer.


Why cannot the answer be (e) 29%? Couldn't you do 29, 25, 24, 22?


Hey Simmones
(E) can work, but we are asked what is the minimum amount - therefore, for (E) to be the answer, all the other answers (A)-(D) must not work. but since (C) does work, it is the answer, and (E) isn't.
Hope this helps!
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Re: All assets in Karina's investment portfolio are divided between an IRA &nbs [#permalink] 08 Oct 2018, 23:25
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