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

 It is currently 14 Oct 2019, 07:05 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.  The price of a certain commodity increased at a rate of

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

Hide Tags

Manager  Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 158
Location: Kuwait
Schools: Columbia university
The price of a certain commodity increased at a rate of  [#permalink]

Show Tags

1
10 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:30) correct 33% (03:01) wrong based on 123 sessions

HideShow timer Statistics

The price of a certain commodity increased at a rate of $$X$$ % per year between 2000 and 2004. If the price was $$M$$ dollars in 2001 and $$N$$ dollars in 2003, what was the price in 2002 in terms of $$M$$ and $$N$$ ?

A. $$\sqrt{MN}$$

B. $$N\sqrt{\frac{N}{M}}$$

C. $$N\sqrt{M}$$

D. $$N\frac{M}{\sqrt{N}}$$

E. $$NM^{\frac{3}{2}}$$

_________________
Sky is the limit

Originally posted by manalq8 on 23 Jan 2012, 14:25.
Last edited by Bunuel on 05 Apr 2019, 06:19, edited 4 times in total.
Edited the answer choices
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4473
Re: The price of a certain commodity increased at a rate of  [#permalink]

Show Tags

6
1
Hi there! I'm happy to help with this! Let's say, the price in 2000 is A. That the original amount. Each year it increases X%. To represent a percent increase (a) write the percent as a fraction/decimal, here X/100; (b) add one ---> 1 + X/100; (c) that's the multiplier -- multiplying a number by that multiplier results in a X% increase.

price in 2000 = A
price in 2001 = A*(1 + X/100)
price in 2002 = A*(1 + X/100)^2
price in 2003 = A*(1 + X/100)^3
price in 2004 = A*(1 + X/100)^4

For simplicity, I am going to define r = (1 + X/100). Then these equations become:

price in 2000 = A
price in 2001 = A*r
price in 2002 = A*r^2
price in 2003 = A*r^3
price in 2004 = A*r^4

Now, suppose we have M = 2001 price = A*r and N = 2003 price = A*r^3. How do we represent the 2002 prince (A*r^2) in terms of M and N?

There are two methods.

Method One: express r in terms of M and N

This is more a crank-it-out algebraic solution approach. We notice that N/M = (A*r^3)/(A*r) = r^2, so r = sqrt(N/M). Well,

2002 price = (2001 price)*(r) = M * sqrt(N/M) = [sqrt(M)*sqrt(M)]*[sqrt(N)/sqrt(M)] = sqrt(M)*sqrt(N) = sqrt(NM).

Through some fast-and-loose manipulation of the laws of squareroots, we arrive at answer .

Method Two: a more elegant solution for a more civilized age . . .

When you have an arithmetic sequence --- that is, adding the same number to get new terms (e.g. 8, 11, 14, 17, 20, 23, . . . ), when you take any three numbers in a row, the middle number is the mean, the arithmetic average, of the outer two. For example ---11, 14, 17 --- (11 + 17)/2 = 14. The arithmetic average is the ordinary average --- add the two numbers, and divide by two.

When you have a geometric sequence -- that is, multiplying the same ratio to get new terms (e.g. 2, 6, 18, 54, 162, . . . ), when you take any three numbers in a row, the middle number is the geometric mean of the outer two. The geometric mean of two numbers means multiply the two numbers and take the squareroot. For example --- 6, 18, 54 --- 6*54 = 324, and sqrt(324) = 18.

When you apply a fixed percentage increase from one term to the next, as we have in this problem, that's a geometric sequence. Thus, to find the 2002 price, all you have to do is take the geometric mean of the 2001 price and the 2003 price. 2002 price = sqrt(MN). Bam. Done. Again, answer = .

The ideas about arithmetic & geometric sequences, and the associated means, are good tricks to have up your sleeve for the more challenging GMAT math problems.

Does all this make sense? Please let me know if you have any questions.

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  Joined: 23 Jan 2012
Posts: 7
Location: India
Concentration: Strategy, Finance
GMAT 1: 620 Q51 V23 GPA: 3.29
WE: Engineering (Other)
Re: The price of a certain commodity increased at a rate of  [#permalink]

Show Tags

5
2
The price in 2001 is M
The price in 2002 is M(1+$$\frac{X}{100}$$) ----------------------(1)

The price in 2003 is M(1+$$\frac{X}{100}$$)(1+$$\frac{X}{100}$$) = N ---------(2)

Solving equation (2) we get
(1+$$\frac{X}{100}$$) = $$\sqrt{\frac{N}{M}}$$

Putting this value in equation (1) to get the desired answer
The price in 2002 is M$$\sqrt{\frac{N}{M}}$$ = $$\sqrt{MN}$$

Hence the option A
General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 58310
Re: The price of a certain commodity increased at a rate of  [#permalink]

Show Tags

1
1
manalq8 wrote:
The price of a certain commodity increased at a rate of $$X$$ % per year between 2000 and 2004. If the price was $$M$$ dollars in 2001 and $$N$$ dollars in 2003, what was the price in 2002 in terms of $$M$$ and $$N$$ ?

A. $$\sqrt{MN}$$

B. $$N\sqrt{\frac{N}{M}}$$

C. $$N\sqrt{M}$$

D. $$N\frac{M}{\sqrt{N}}$$

E. $$NM^{\frac{3}{2}}$$

I think that plug-in method is easiest for this problem.

Let the price in 2001 be 100 and the annual rate be 10%. Then:
2001 = 100 = M;
2002 = 110;
2003 = 121 = N;

Now, plug 100 and 121 in the answer choices to see which one gives 110:
A. $$\sqrt{MN}=\sqrt{100*121}=10*11=110$$, correct answer right away.

P.S. For plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.
_________________
Manager  Joined: 04 Oct 2013
Posts: 150
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: The price of a certain commodity increased at a rate of  [#permalink]

Show Tags

The price of a certain commodity increased at a rate of X % per year between 2000 and 2004. If the price was M dollars in 2001 and N dollars in 2003, what was the price in 2002 in terms of M and N ?

Given:
Price in 2001 : M
Price in 2003 : N
Rate per year: X %

Price in 2002 $$= M ( 1 + X/100)$$........................................(1)
And, Price in 2003: $$N = M( 1 + X/100)^2$$

Or, $$(1 + x/100) =\sqrt{(N/M)}$$........(2)

Substituting the value of (2) in (1) above,
Price in 2002 $$= M \sqrt{(N/M)} = \sqrt{MN}$$

Senior Manager  G
Joined: 03 Apr 2013
Posts: 264
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41 GPA: 3
Re: The price of a certain commodity increased at a rate of  [#permalink]

Show Tags

manalq8 wrote:
The price of a certain commodity increased at a rate of $$X$$ % per year between 2000 and 2004. If the price was $$M$$ dollars in 2001 and $$N$$ dollars in 2003, what was the price in 2002 in terms of $$M$$ and $$N$$ ?

A. $$\sqrt{MN}$$

B. $$N\sqrt{\frac{N}{M}}$$

C. $$N\sqrt{M}$$

D. $$N\frac{M}{\sqrt{N}}$$

E. $$NM^{\frac{3}{2}}$$

When no absolute values(or variables pertaining to them) are given, number plugging is the way to go..

Let the Value initially be = 1
and let X% = 100%(in other words..value doubles every year)

values are..
M = 2
N = 8

and we're looking for the value in 2002..which is equal to 4.

_________________
Spread some love..Like = +1 Kudos Intern  B
Joined: 31 Dec 2017
Posts: 4
Location: India
Concentration: Entrepreneurship, Technology
GPA: 3.05
Re: The price of a certain commodity increased at a rate of  [#permalink]

Show Tags

1
I think this is the easiest approach here:

2001 - M

2002 - ? (Let it be 'x')

2003 - N

Now according to ques, since the rate of increase is equal both year and the rates should be calculated on the previous year's price,

$$\frac{x-M}{M} * 100= \frac{N-x}{x}*100$$

$$x^2 - Mx = MN - Mx$$

$$x = \sqrt{MN}$$

Hope it helps
+1 Kudos would be nice Non-Human User Joined: 09 Sep 2013
Posts: 13117
Re: The price of a certain commodity increased at a rate of  [#permalink]

Show Tags

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: The price of a certain commodity increased at a rate of   [#permalink] 22 May 2019, 15:19
Display posts from previous: Sort by

The price of a certain commodity increased at a rate of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  