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:

82% (01:21) correct 18% (01:20) wrong based on 1069 sessions

HideShow timer Statistics

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

03 Sep 2012, 05:07

1

This post received KUDOS

Value after 1 year: 10,000 * 1.1 = 11,000 Value after 2 years: 11,000 * 1.05 = 11,550 Value today: 11,550 * 0.9 = 10,395

Answer B is correct.

The first equation is easy. In the second, first calculate 10% (1,100) and divide that by 2 (550). Add that to 11,000. In the final equation, calculate 10% again (1,155) and subtract it from 11,550.

WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

03 Sep 2012, 05:51

2

This post received KUDOS

Bunuel wrote:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

This is a question of successive % change. This question ultimately reduces to a multiplication problem. Final value after successive % change on $10,000 = $10,000 X 1.1 X 1.05 X .9 1.1 X 1.05 X .9 = 1.0395 Answer is B)
_________________

Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

03 Sep 2012, 06:45

I also followed the same approach and got the answer as B. But I am wondering if there is any better method of calculating in any problem with successive year interest rates given.
_________________

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Answer: B.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

19 Oct 2012, 01:06

1

This post received KUDOS

Stupid lucy! If she sees that there is a crisis in the world and her accounts diminishes every year, why hasn't she redraw her money after the second year?!?... I multiplied the last year with 1.1 instead of 0.9 and i got the D answear... This is lucy's fault! :D

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

15 Dec 2012, 11:14

Bunuel wrote:

SOLUTION

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

The value of the account today would be \(10,000*1.1*1.05*0.9\). Now, the question is how to calculate this efficiently.

\(10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}\) --> 10,000 will cancel and we'll get: \(11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395\).

Answer: B.

Thank you for the answer Bunuel, but i was just wondering. When you chose the denominators for the different fractions, was your goal to get 10 000 in the denominator so we could cancel Lucy's initial investment? Smart move by the way

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

16 Dec 2012, 03:07

1

This post received KUDOS

Ans:: the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10395. So the answer is (B).
_________________

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

02 May 2013, 10:12

.10x10,000= $1,000 end of y1 = 11,000 .05x11,000= $550.00 end of y2 = 11,550 .10x11,550= 1,150 -1,155 (subtract y2 with the loss of y3) end of y3= 10,395

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

10 Sep 2014, 02:43

Bunuel wrote:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

16 Nov 2014, 07:51

1

This post received KUDOS

I cut corners this way: 10% of 10 000=1000 (move the dot one spot) next year you have 11 000 5% of 11 000= 550 (move the dot one spot 1100 = 10%, divide by two to get 5% 1100/2=550) So then you have 11 550, and subtract 10% from this --> 11 550 - 1155. Well it has to be less than 11 000 since more than 1000 is subtracted (eliminating D & E), and it has to end in 5 since you're subtracting a number ending in five (eliminating A & C) that leaves only B.

Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink]

Show Tags

19 Dec 2015, 08:19

year 1 Increases 10% 1000 Value became 11000 Year 2 increase 5% 550 value became 11550 Year 3 decrease 10% 1155 value became 11550-1155 = $10395.
_________________

Discipline does not mean control. Discipline means having the sense to do exactly what is needed.

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

To determine the value of the account today we want to set up an expression showing the various percent increases and decreases.

Remember we are multiplying each percent increase or decrease against the original value of $10,000.

Also, we must remember that a 10% increase is the same as multiplying by 1.1, a 5% increase is the same as multiplying by 1.05, and a 10% decrease is the same as multiplying by 0.9. That is:

10,000(1.1)(1.05)(0.9)

Because the multiplication may get a bit complicated in the equation above, we should convert each decimal to a fraction, allowing us to reduce before multiplying. Thus, we have:

10,000(11/10)(105/100)(9/10)

This is equivalent to: 10,000(11 x 105 x 9/10,000)

Thus we see the the two values of 10,000 cancel out, and we are left with:

11 x 105 x 9 = 99 x 105 = 10,395

Note: If you did not want to perform the multiplication of the final step, you could have used a combination of units digits and estimation to come to the correct answer. Keep in mind that the product of 99 and 105 will have a units digit of 5. That leaves us with only B ($10,395) and E ($12,705) as possible answer choices. Next, by rounding up 99 to 100 and multiplying 100 by 105 we get a product of 10,500. Because we rounded up and answer choice E is LARGER than 10,500, it’s not a possible answer choice. Thus, the correct answer is B, $10,395.
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

Many GMAT Quant questions require 3-5 'steps' to get to the solution, so you shouldn't try to do all of the steps at once. Thankfully, the steps tend to be pretty easy to do, so you shouldn't rush through any of them and you should be sure to write everything on your pad (so that you can physically see the work).

Here, we're starting with $10,000. In the first year, the value increased by 10%....

Let's deal with THAT step right now:

10% of $10,000 = $1,000 New Total = $10,000 + $1,000 = $11,000

...increased by 5% during the second year....

Now we have $11,000, so the numbers will be a little different:

10% of $11,000 = $1,100 5% of $11,000 = $550 New Total = $11,000 + $550 = $11,550

...DECREASED by 10% during the third year...

10% of $11,550 = $1,155 New Total = $11,550 - $1,155 = $10,395

There's actually a great shortcut in this last calculation. If you look at the 'units digits' of the two numbers, you can deduce that when you subtract one from the other, you end up with a number that ends in 5... Take a good look at the answer choices; how many are LESS than $11,550 AND end in a 5?