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 Your Progress

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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

From the total amount available, a man keeps 25,000$ for [#permalink]

Show Tags

16 Sep 2012, 02:54

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

78% (03:01) correct
22% (02:52) wrong based on 202 sessions

HideShow timer Statistics

From the total amount available, a man keeps 25,000$ for himself and then distributes the remaining between two of his sons in the ratio of 3:2 (3 parts for the elder and 2 parts for the younger son). Later, he decides to give the dollar 25,000 (which he had initially kept for himself) to his younger son. This makes the ratio of amount with elder son to ratio of amount with younger son 2:3. Find the amount received by the elder brother.

Re: From the total amount available, a man keeps 25,000$ for [#permalink]

Show Tags

16 Sep 2012, 03:08

2

This post received KUDOS

Expert's post

Pansi wrote:

From the total amount available, a man keeps 25,000$ for himself and then distributes the remaining between two of his sons in the ratio of 3:2 (3 parts for the elder and 2 parts for the younger son). Later, he decides to give the dollar 25,000 (which he had initially kept for himself) to his younger son. This makes the ratio of amount with elder son to ratio of amount with younger son 2:3. Find the amount received by the elder brother. A. 30,000 B. 100,000 C. 25,000 D. 40,000 E. 500

There are two conventional algebraic ways to solve these types of problems. In the first, we just introduce an unknown for the amounts each brother received. We then use the fact that a ratio is just a fraction in order to translate each statement in the question into algebra:

If the elder brother initially got $e, and the younger brother initially got $y, then from the ratio given, we know that e/y = 3/2, or 2e = 3y. Further, if the younger brother is given $25,000, he will then have y + 25000 dollars. We know the ratio of e to y+25000 is 2 to 3, so e/(y + 25000) = 2/3, or 3e = 2y + 50000. We now have two equations in two unknowns:

3e = 2y + 50,000 2e = 3y

If we multiply the first equation by 3 and the second equation by 2, we can then subtract the second from the first:

9e = 6y + 150,000 4e = 6y 5e = 150,000

So e = 30,000.

It's faster to still to use a multiplier. If the ratio of the amounts given to the elder and younger brothers is 3 to 2, then for some number x, the elder brother got $3x and the younger brother got $2x. We want to find $3x. Since the ratio of 3x to 2x+25,000 is 2 to 3, we have

And since we wanted to find 3x, the answer is 30,000.

Finally, you can solve this in a kind of conceptual way. If we rewrite each ratio so that the elder brother's amount is the same in each we have:

* before any money is transferred, ratio of elder's $ to younger's $: 6 to 4 * after the money is transferred, ratio of elder's $ to younger's $: 6 to 9

So the $25,000 transfer is equivalent to 5 parts in the ratio (the difference between 9 and 4). Since the amount the elder brother has is equivalent to 6 parts, his amount is $30,000.

And I suppose you could also backsolve the question fairly easily, though if the numbers were different, that could be a very bad approach. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: From the total amount available, a man keeps 25,000$ for [#permalink]

Show Tags

16 Sep 2012, 03:10

1

This post was BOOKMARKED

Pansi wrote:

From the total amount available, a man keeps 25,000$ for himself and then distributes the remaining between two of his sons in the ratio of 3:2 (3 parts for the elder and 2 parts for the younger son). Later, he decides to give the dollar 25,000 (which he had initially kept for himself) to his younger son. This makes the ratio of amount with elder son to ratio of amount with younger son 2:3. Find the amount received by the elder brother.

A. 30,000 B. 100,000 C. 25,000 D. 40,000 E. 500

Let us say Elder got 3x and younger 2x. So after addition of 25,000 the ratio changes to 2:3. we can write that as follows:

Re: From the total amount available, a man keeps 25,000$ for [#permalink]

Show Tags

16 Sep 2012, 08:09

2

This post received KUDOS

IanStewart wrote:

Pansi wrote:

From the total amount available, a man keeps 25,000$ for himself and then distributes the remaining between two of his sons in the ratio of 3:2 (3 parts for the elder and 2 parts for the younger son). Later, he decides to give the dollar 25,000 (which he had initially kept for himself) to his younger son. This makes the ratio of amount with elder son to ratio of amount with younger son 2:3. Find the amount received by the elder brother. A. 30,000 B. 100,000 C. 25,000 D. 40,000 E. 500

There are two conventional algebraic ways to solve these types of problems. In the first, we just introduce an unknown for the amounts each brother received. We then use the fact that a ratio is just a fraction in order to translate each statement in the question into algebra:

If the elder brother initially got $e, and the younger brother initially got $y, then from the ratio given, we know that e/y = 3/2, or 2e = 3y. Further, if the younger brother is given $25,000, he will then have y + 25000 dollars. We know the ratio of e to y+25000 is 2 to 3, so e/(y + 25000) = 2/3, or 3e = 2y + 50000. We now have two equations in two unknowns:

3e = 2y + 50,000 2e = 3y

If we multiply the first equation by 3 and the second equation by 2, we can then subtract the second from the first:

9e = 6y + 150,000 4e = 6y 5e = 150,000

So e = 30,000.

It's faster to still to use a multiplier. If the ratio of the amounts given to the elder and younger brothers is 3 to 2, then for some number x, the elder brother got $3x and the younger brother got $2x. We want to find $3x. Since the ratio of 3x to 2x+25,000 is 2 to 3, we have

And since we wanted to find 3x, the answer is 30,000.

Finally, you can solve this in a kind of conceptual way. If we rewrite each ratio so that the elder brother's amount is the same in each we have:

* before any money is transferred, ratio of elder's $ to younger's $: 6 to 4 * after the money is transferred, ratio of elder's $ to younger's $: 6 to 9

So the $25,000 transfer is equivalent to 5 parts in the ratio (the difference between 9 and 4). Since the amount the elder brother has is equivalent to 6 parts, his amount is $30,000.

And I suppose you could also backsolve the question fairly easily, though if the numbers were different, that could be a very bad approach.

For the conceptual solution, the attached drawing can be helpful. Initially, elder son gets 6 parts and younger son gets 4 parts. Then, the $25,000 received by the younger son is represented by the 5 short line segments. One segment represents 25,000/5 = 5,000. So, elder son gets 6*5,000 = 30,000.

Attachments

Ratios-Concept(IanStewart).jpg [ 13.84 KiB | Viewed 2425 times ]

_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: From the total amount available, a man keeps 25,000$ for [#permalink]

Show Tags

26 Feb 2013, 21:07

I spend around 20 mins trying to solve the problem and the answer is 20,000 then I realized that I was solving for the youngest son. LOL I Keep doing these careless mistakes

Re: From the total amount available, a man keeps 25,000$ for [#permalink]

Show Tags

24 May 2013, 19:30

EvaJager wrote:

For the conceptual solution, the attached drawing can be helpful. Initially, elder son gets 6 parts and younger son gets 4 parts. Then, the $25,000 received by the younger son is represented by the 5 short line segments. One segment represents 25,000/5 = 5,000. So, elder son gets 6*5,000 = 30,000.

Re: From the total amount available, a man keeps 25,000$ for [#permalink]

Show Tags

22 Jun 2014, 23:46

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: From the total amount available, a man keeps 25,000$ for [#permalink]

Show Tags

25 Oct 2015, 05:39

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Last year when I attended a session of Chicago’s Booth Live , I felt pretty out of place. I was surrounded by professionals from all over the world from major...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...