GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 02:10 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  All assets in Karina's investment portfolio are divided between an IRA

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58297
All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

1
7 00:00

Difficulty:   75% (hard)

Question Stats: 52% (02:12) correct 48% (02:22) wrong based on 149 sessions

HideShow timer Statistics

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

_________________
examPAL Representative P
Joined: 07 Dec 2017
Posts: 1140
Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

2
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.
_________________
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3337
Location: India
GPA: 3.12
All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

2
1
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.
_________________
You've got what it takes, but it will take everything you've got
CEO  V
Joined: 12 Sep 2015
Posts: 3990
Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

Top Contributor
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

Cheers,
Brent
_________________
Intern  B
Joined: 19 Aug 2016
Posts: 2
Location: United States
GMAT 1: 670 Q28 V56 GPA: 3.5
Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

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?
Intern  B
Joined: 15 Jul 2016
Posts: 34
Location: India
Concentration: Operations, Marketing
GMAT 1: 560 Q46 V21 GMAT 2: 620 Q48 V26 GPA: 4
WE: Operations (Manufacturing)
Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

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.

regards
examPAL Representative P
Joined: 07 Dec 2017
Posts: 1140
Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

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!
_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

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 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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: All assets in Karina's investment portfolio are divided between an IRA  [#permalink]

Show Tags

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

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

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.

GMAT assassins aren't born, they're made,
Rich
_________________ Re: All assets in Karina's investment portfolio are divided between an IRA   [#permalink] 28 Feb 2019, 20:27
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  