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

 It is currently 13 Dec 2019, 17:29

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

M08-01

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59721

Show Tags

16 Sep 2014, 00:36
1
16
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:39) correct 33% (02:22) wrong based on 103 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. $$NM^{\frac{3}{2}}$$

_________________
Intern
Joined: 13 Jun 2014
Posts: 27
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q48 V33

Show Tags

04 Nov 2014, 13:27
16
5
Hi, Bunuel,
The official solution seems to be lengthy

Here is an Easy Way to solve the Problem......

Consider M as the price in 2001.

Then, M(1+x/100) will be the price in 2002 ----> We are asked to find this value

And, M(1+x/100)^2 will be the price in 2003, and this price is given as N

So,
M(1+x/100)^2 = N
(1+x/100) ^2 = N/M
(1+x/100) = sqrt. (N/M)
M(1+x/100) = sqrt. (N/M) x M
M(1+x/100) = sqrt. (NM) <------> This is the Answer... Thats it

PLease give kudos if you like the solution
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 59721

Show Tags

16 Sep 2014, 00:36
2
1
Official Solution:

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

Use plug-in method 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.

_________________
Manager
Joined: 02 Nov 2014
Posts: 181
GMAT Date: 08-04-2015

Show Tags

08 Nov 2015, 21:37
1
Let 2002 = P.
So, M(1+X/100) = P = N/(1+X/100)
or, MN = P^2
or, P = sqrt(MN) -----> A.
Senior Manager
Joined: 23 Sep 2015
Posts: 369
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

Show Tags

01 Dec 2015, 06:29
2
1
We have:
$$2002= M(1+x)$$
$$2003= M(1+x)^2 = N$$

Convert $$(1+x)^2$$ into M and N
$$(1+x)^2 = \frac{N}{M}$$

$$(1+x) = \sqrt{\frac{N}{M}}$$

So 2002 becomes:
$$2002= M*\sqrt{\frac{N}{M}}$$ which equals $$\sqrt{MN}$$
_________________
Current Student
Status: Remember to Always Think Twice
Joined: 04 Nov 2014
Posts: 54
Location: India
GMAT 1: 740 Q49 V40
GPA: 3.51

Show Tags

03 Dec 2015, 18:06
1
Can be solved using simpler Geometric progression logic.
In 2000 : a
In 2001 : ax
In 2002 : ax^2
In 2003 : ax^3
In 2004 : ax^4

Then we can verify with the answer choices and find out that only (A) suffices.
_________________
breathe in.. and breathe out!
Manager
Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 73

Show Tags

05 Jan 2016, 09:16
1
You could also do dimensionality check
consider dimensionality of N or M as 1

A. $$\sqrt{MN}$$ >> 1
B. N*$$\sqrt{NM}$$ >> 2
C. N*$$\sqrt{M}$$>>1.5
D. N*M/$$\sqrt{N}$$ >> 1.5
E. NM^ $$3/2$$>>1.5

Manager
Joined: 05 Jul 2015
Posts: 93
GMAT 1: 600 Q33 V40
GPA: 3.3

Show Tags

19 Feb 2016, 11:54
I thought that this was more of an understanding the question and staying organized type of problem.

2000 = P
2001 = M = Px
2002 = PxM
2003 = N = P(M^2)

So the question stem asks for 2002 (x*M) in terms of M and N

The square root of N = M The squareroot of M = X

Intern
Joined: 20 Aug 2014
Posts: 7
Location: United States
GMAT 1: 690 Q49 V34
GPA: 3.27

Show Tags

16 Jul 2016, 08:50
Since we know that the 2001 value time the constant rate should equal the 2003 value divided by the constant rate, we set the equation and solve for X
M*(X) = N / X

X^2 = N/M

X= sqrt(N/M)

Next we multiply the rate by the 2001 value to get the 2002 value, and rearrange to get it in terms similar to the answer choices

M* sqrt(N/M) = sqrt(NM^2/M) = sqrt(NM)
Manager
Joined: 30 Apr 2016
Posts: 71
Location: India
GMAT 1: 720 Q50 V38
GPA: 4

Show Tags

05 Dec 2016, 11:06
1
since the resulting sequence will be a Geometric progression so the middle value will be the geometric mean of the prices of 2001 and 2003
Intern
Joined: 29 Sep 2016
Posts: 16
Location: United States
Concentration: Finance, Economics
GPA: 3.01

Show Tags

18 Dec 2016, 18:34
VinRag

Your method of solution has already been demonstrated by Bunuel on the similar question.
Current Student
Joined: 23 Nov 2016
Posts: 70
Location: United States (MN)
GMAT 1: 760 Q50 V42
GPA: 3.51

Show Tags

08 Mar 2017, 18:54
Let I = the initial amount and u=(1+x/100).

Value in 2000: I
Value in 2001: I*u=M
Value in 2002: I*u^2
Value in 2003: I*u^3=N
Value in 2004: I*u^4

Plug the above into the answer choices. A gives sqrt(M*N) = sqrt(I^2 * u^4 ) = Iu^2

A
Current Student
Joined: 05 Sep 2016
Posts: 10
Location: Argentina
GMAT 1: 650 Q43 V36
GPA: 3.4

Show Tags

25 May 2017, 08:40
vinraj wrote:
Hi, Bunuel,
The official solution seems to be lengthy

Here is an Easy Way to solve the Problem......

Consider M as the price in 2001.

Then, M(1+x/100) will be the price in 2002 ----> We are asked to find this value

And, M(1+x/100)^2 will be the price in 2003, and this price is given as N

So,
M(1+x/100)^2 = N
(1+x/100) ^2 = N/M
(1+x/100) = sqrt. (N/M)
M(1+x/100) = sqrt. (N/M) x M
M(1+x/100) = sqrt. (NM) <------> This is the Answer... Thats it

PLease give kudos if you like the solution

I´m a bit lost with roots properties, how sqrt. (N/M) x M = sqrt. (NM) ??
sorry for the basic question...
Manager
Status: Active
Affiliations: NA
Joined: 24 Oct 2012
Posts: 236
GMAT 1: 590 Q50 V21
GMAT 2: 600 Q48 V25
GMAT 3: 730 Q51 V37
GPA: 3.5

Show Tags

25 May 2017, 19:54
1
Hi,
Because M = sqrt M * sqrt M
Intern
Joined: 09 Sep 2015
Posts: 17

Show Tags

04 Jun 2018, 01:31
Shouldn't we also consider 2000 and 2004 also? How do we know from the question that we don't have to consider it?
Math Expert
Joined: 02 Sep 2009
Posts: 59721

Show Tags

04 Jun 2018, 06:32
Shouldn't we also consider 2000 and 2004 also? How do we know from the question that we don't have to consider it?

The question asks: 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? Why/how should we consider 2000 or 2004?
_________________
Intern
Joined: 07 Aug 2018
Posts: 2

Show Tags

07 Nov 2018, 09:47
M x X% = 2002 ---> 1
2002 x X% = N ---> 2

Now, we need 2002 in terms of X and M. So, eliminate the X%.

From equation 1,
X% = 2002/M

Substitute this into equation 2,
(2002^2)/M = N
2002^2= NM
2002 = sqrt(NM)

Posting my solution because for me I don't see how this question is difficult, or why Bunuel chose such a complicated method to solve. Cheers all.
Manager
Joined: 18 Jul 2018
Posts: 51
Location: United Arab Emirates

Show Tags

05 Apr 2019, 06:14
Bunuel wrote:
Official Solution:

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

Use plug-in method 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.

Hi Bunuel

Can you please post the algebraic solution as well?

How should i translate the rate of increase as ? (1+x/100) or simply x%??

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 59721

Show Tags

05 Apr 2019, 06:20
JIAA wrote:
Bunuel wrote:
Official Solution:

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

Use plug-in method 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.

Hi Bunuel

Can you please post the algebraic solution as well?

How should i translate the rate of increase as ? (1+x/100) or simply x%??

Thanks

You can find different solutions, including algebraic, here: https://gmatclub.com/forum/the-price-of ... 26464.html

Hope it helps.
_________________
Intern
Joined: 15 Nov 2018
Posts: 5
GMAT 1: 700 Q43 V42
GPA: 3.84

Show Tags

31 Oct 2019, 16:33
Somebody, please correct me if I'm wrong, but I believe there's an even quicker and dirtier way to solve this without doing any algebra. Every answer except A begins by multiplying N by some positive number. This will lead to a number larger than N. By simple logic and understanding the sequence, we can know that there is no way that the price in 2002 was MORE than the price in 2003, which all the answers have as N*pos numbers. The only answer that yields a chance of being more than M but less than N is A.
Re: M08-01   [#permalink] 31 Oct 2019, 16:33
Display posts from previous: Sort by

M08-01

Moderators: chetan2u, Bunuel