It is currently 16 Jan 2018, 23:32

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# At the end of each year, the value of a certain antique

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 17 Aug 2005
Posts: 387

Kudos [?]: 154 [3], given: 0

Location: Boston, MA
At the end of each year, the value of a certain antique [#permalink]

### Show Tags

12 Mar 2006, 09:14
3
KUDOS
28
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

72% (02:39) correct 28% (02:17) wrong based on 659 sessions

### HideShow timer Statistics

At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?

A. m+1/2(m-k)
B. m+1/2((m-k)/k)m
C. (m*sqrt(m))/sqrt(k)
D. m^2/2k;
E. km^2
[Reveal] Spoiler: OA

Kudos [?]: 154 [3], given: 0

Manager
Joined: 20 Mar 2005
Posts: 201

Kudos [?]: 16 [2], given: 0

Location: Colombia, South America

### Show Tags

12 Mar 2006, 12:03
2
KUDOS
1
This post was
BOOKMARKED
buckkitty wrote:
At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?

A) m+1/2(m-k)
B) m+1/2((m-k)/k)m
C) (m*sqrt(m))/sqrt(k)
D)m^2/2k;
E) km^2

m = k*(1+c)^2
m/k = (1+c)^2
(m/k)^(1/2) = 1+c
c= (m/k)^(1/2) - 1

the value of the watch in jan 1 1995 is:

m(1+c)
so m(1+(m/k)^(1/2) - 1)
= m(m/k)^(1/2))

that is C

Kudos [?]: 16 [2], given: 0

Intern
Joined: 02 Apr 2012
Posts: 2

Kudos [?]: 2 [0], given: 0

Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

11 May 2012, 20:28

m = k*(1+c/100)^2 ? Since it says in the question, 'c percent more'..

Kudos [?]: 2 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 43304

Kudos [?]: 139237 [12], given: 12781

Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

12 May 2012, 01:25
12
KUDOS
Expert's post
12
This post was
BOOKMARKED
Thiagaraj wrote:

m = k*(1+c/100)^2 ? Since it says in the question, 'c percent more'..

Yes, it should.

At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?
A. m+1/2(m-k)
B. m+1/2((m-k)/k)m
C. (m*sqrt(m))/sqrt(k)
D. m^2/2k;
E. km^2

Price in 1992 - $$k$$;
Price in 1993 - $$k*(1+\frac{c}{100})$$;
Price in 1994 - $$k*(1+\frac{c}{100})^2=m$$ --> $$(1+\frac{c}{100})=\sqrt{\frac{m}{k}}$$;
Price in 1995 - $$m*(1+\frac{c}{100})=m*\sqrt{\frac{m}{k}$$.

_________________

Kudos [?]: 139237 [12], given: 12781

Director
Joined: 29 Nov 2012
Posts: 861

Kudos [?]: 1535 [0], given: 543

Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

08 Jan 2013, 05:07
Bunuel wrote:
Thiagaraj wrote:

m = k*(1+c/100)^2 ? Since it says in the question, 'c percent more'..

Yes, it should.

At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?
A. m+1/2(m-k)
B. m+1/2((m-k)/k)m
C. (m*sqrt(m))/sqrt(k)
D. m^2/2k;
E. km^2

Price in 1992 - $$k$$;
Price in 1993 - $$k*(1+\frac{c}{100})$$;
Price in 1994 - $$k*(1+\frac{c}{100})^2=m$$ --> $$(1+\frac{c}{100})=\sqrt{\frac{m}{k}}$$;
Price in 1995 - $$m*(1+\frac{c}{100})=m*\sqrt{\frac{m}{k}$$.

Shouldn't this year be raised by the third power? since its the third year.
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Kudos [?]: 1535 [0], given: 543

Math Expert
Joined: 02 Sep 2009
Posts: 43304

Kudos [?]: 139237 [3], given: 12781

Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

08 Jan 2013, 09:59
3
KUDOS
Expert's post
fozzzy wrote:
Bunuel wrote:
Thiagaraj wrote:

m = k*(1+c/100)^2 ? Since it says in the question, 'c percent more'..

Yes, it should.

At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?
A. m+1/2(m-k)
B. m+1/2((m-k)/k)m
C. (m*sqrt(m))/sqrt(k)
D. m^2/2k;
E. km^2

Price in 1992 - $$k$$;
Price in 1993 - $$k*(1+\frac{c}{100})$$;
Price in 1994 - $$k*(1+\frac{c}{100})^2=m$$ --> $$(1+\frac{c}{100})=\sqrt{\frac{m}{k}}$$;
Price in 1995 - $$m*(1+\frac{c}{100})=m*\sqrt{\frac{m}{k}$$.

Shouldn't this year be raised by the third power? since its the third year.

It is actually.

Price in 1994 is $$k*(1+\frac{c}{100})^2$$ which is $$m$$, so the price in 1995 is $$k*(1+\frac{c}{100})^2*(1+\frac{c}{100})$$ or $$m*(1+\frac{c}{100})$$.

Hope it's clear.
_________________

Kudos [?]: 139237 [3], given: 12781

Manager
Joined: 04 Oct 2011
Posts: 212

Kudos [?]: 65 [5], given: 44

Location: India
GMAT 1: 440 Q33 V13
GPA: 3
Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

09 Jan 2013, 23:55
5
KUDOS
3
This post was
BOOKMARKED
buckkitty wrote:
At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?

A. m+1/2(m-k)
B. m+1/2((m-k)/k)m
C. (m*sqrt(m))/sqrt(k)
D. m^2/2k;
E. km^2

I went with smart numbers.

c= 10 %
1992 => k = 100
1994 => m = 121
obviously,
1995 => 133.1

Only choice c gives desired result.

$$(m*sqrt(m))/sqrt(k)$$ = $$121 \sqrt{121} / \sqrt{100}$$ = 133.1
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like

Kudos [?]: 65 [5], given: 44

Manager
Joined: 18 Oct 2011
Posts: 88

Kudos [?]: 99 [0], given: 0

Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3

### Show Tags

11 Feb 2013, 18:40
I find using real numbers helps the most with these types of q's. Let's say the value in 1992 is $100 (this would be k). Let's use a 10% growth rate for c. This means the value in '93 is$110, and '94 is $121 (this would be m). In 1995 the value of the antique would be 133.1 based on the 10% growth rate. So we have k=100, m=121. By substituting m and k into the answer choices we must arrive at 133.1. By estimating it a little you can start eliminating answer choices fairly quickly. Only answer choice C gives you the desired result. Kudos [?]: 99 [0], given: 0 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7862 Kudos [?]: 18454 [1], given: 237 Location: Pune, India Re: Arithematic [#permalink] ### Show Tags 11 Feb 2013, 20:45 1 This post received KUDOS Expert's post 4112019 wrote: At the end of each year, the value of a certain antique watch is c percent more than its value one year earlier, where c has the same value each year. If the value of the watch was k dollars on January1, 1992, and m dollars on January 1, 1994, then in terms of m and k, what was the value of the watch, in dollars, on January 1, 1995 ? A. m +1/2(m–k) B. m +1/2(m - k)m Cm square root m /square root k D.$$m^2$$/2k E. k$$m2$$ Value on Jan 1, 1992 = k Value on Jan 1, 1993 = k(1+c/100) Value on Jan 1, 1994 = $$k(1 + c/100)^2 = m$$ So, $$(1 + c/100) = \sqrt{\frac{m}{k}}$$ Value on Jan 1 1995 = $$k(1+c/100)^3 = k(1 + c/100)^2 * (1 + c/100)$$ = $$m*\sqrt{\frac{m}{k}}$$ Yes, I generally prefer plugging in numbers but the calculations here are a little painful (with squares and roots) so using algebra is not a bad idea. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 18454 [1], given: 237

Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 504

Kudos [?]: 73 [1], given: 562

Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

### Show Tags

06 Mar 2013, 05:41
1
KUDOS
VeritasPrepKarishma wrote:
4112019 wrote:
At the end of each year, the value of a certain antique watch is c percent more than its
value one year earlier, where c has the same value each year. If the value of the watch
was k dollars on January1, 1992, and m dollars on January 1, 1994, then in terms of m
and k, what was the value of the watch, in dollars, on January 1, 1995 ?

A. m +1/2(m–k)
B. m +1/2(m - k)m
Cm square root m /square root k
D.$$m^2$$/2k
E. k$$m2$$

Value on Jan 1, 1992 = k
Value on Jan 1, 1993 = k(1+c/100)
Value on Jan 1, 1994 = $$k(1 + c/100)^2 = m$$
So, $$(1 + c/100) = \sqrt{\frac{m}{k}}$$
Value on Jan 1 1995 = $$k(1+c/100)^3 = k(1 + c/100)^2 * (1 + c/100)$$
= $$m*\sqrt{\frac{m}{k}}$$

Yes, I generally prefer plugging in numbers but the calculations here are a little painful (with squares and roots) so using algebra is not a bad idea.

frankly , it would take more than 10 mins if we plug in the numbers. GMAT Writers know tat folks would use pluggin in and hence they create crazy algebra.

Aside, this question appeared in question pack1 and this thread was created in 2006.. I wonder how this question had leaked back then.
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Kudos [?]: 73 [1], given: 562

Intern
Joined: 11 Sep 2013
Posts: 3

Kudos [?]: 6 [0], given: 4

Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 670 Q47 V35
GPA: 3.65
WE: Editorial and Writing (Journalism and Publishing)
Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

13 Sep 2013, 03:46
Assume values, that is the fastest way to do this..

ex:

Value in 1992 - k - 100
percent increase - c - 10
=> Value in 1994 - m - 121

=> Answer should be 121 + 10% of 121 = 133.1

A quick check gives c as the only answer..

Kudos [?]: 6 [0], given: 4

Manager
Joined: 26 Sep 2013
Posts: 217

Kudos [?]: 190 [0], given: 40

Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

23 Nov 2013, 17:47
I solved without algebra, at least after the first step I noticed there would be a quadractic in there, and the only answer that had a sqrt in it was C

Kudos [?]: 190 [0], given: 40

Senior Manager
Joined: 10 Mar 2013
Posts: 263

Kudos [?]: 138 [0], given: 2405

GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

01 Jul 2015, 20:43
Sample numbers is a great strategy here. Looking at the answer choices, we should choose numbers that are perfect squares. In this way, we won't have to waste time solving for c, since we know that it is the same each year.
c=100
k=25
m = 25(2)^2=100
P_1995=200

Going through the answer choices, we see that only C produces 200.

Kudos [?]: 138 [0], given: 2405

Manager
Joined: 24 Nov 2013
Posts: 60

Kudos [?]: 21 [0], given: 115

Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

25 Aug 2015, 20:34
TooLong150 wrote:
Sample numbers is a great strategy here. Looking at the answer choices, we should choose numbers that are perfect squares. In this way, we won't have to waste time solving for c, since we know that it is the same each year.
c=100
k=25
m = 25(2)^2=100
P_1995=200

Going through the answer choices, we see that only C produces 200.

both c and d give 200 when we consider k=25 and m =100..isnt it?

option d
(m^2)/2k

(100^2)/(2*25) = 200

Kudos [?]: 21 [0], given: 115

Manager
Joined: 28 Dec 2013
Posts: 74

Kudos [?]: 5 [0], given: 3

Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

24 Dec 2015, 09:45
Bunuel wrote:
Thiagaraj wrote:

m = k*(1+c/100)^2 ? Since it says in the question, 'c percent more'..

Yes, it should.

At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?
A. m+1/2(m-k)
B. m+1/2((m-k)/k)m
C. (m*sqrt(m))/sqrt(k)
D. m^2/2k;
E. km^2

Price in 1992 - $$k$$;
Price in 1993 - $$k*(1+\frac{c}{100})$$;
Price in 1994 - $$k*(1+\frac{c}{100})^2=m$$ --> $$(1+\frac{c}{100})=\sqrt{\frac{m}{k}}$$;
Price in 1995 - $$m*(1+\frac{c}{100})=m*\sqrt{\frac{m}{k}$$.

Price in 1995 - $$m*(1+\frac{c}{100})=m*\sqrt{\frac{m}{k}$$.

How come in 1995 you don't do k * (1 + c/100) ^ 3 ?

Kudos [?]: 5 [0], given: 3

Retired Moderator
Joined: 29 Oct 2013
Posts: 284

Kudos [?]: 518 [0], given: 197

Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
At the end of each year, the value of a certain antique [#permalink]

### Show Tags

06 Feb 2016, 14:34
Almost no calculations approach:

choose smart numbers.

c= 200 %
1992 => k = 1
1993 => 3
1994 => m = 9
So,
1995 => 27

Only choice c gives the desired result.
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Kudos [?]: 518 [0], given: 197

Senior Manager
Joined: 08 Dec 2015
Posts: 315

Kudos [?]: 28 [0], given: 36

GMAT 1: 600 Q44 V27
At the end of each year, the value of a certain antique [#permalink]

### Show Tags

13 Apr 2016, 09:50
excuse me, c=100% K=10$, m=40$
so 92-> 10$93-> 20$
94-> 40$(m) 95->80$

so m^2/2k -> 40^2/2*10 or 1600/20=80

What is wrong here?

Kudos [?]: 28 [0], given: 36

Manager
Joined: 02 Jun 2015
Posts: 190

Kudos [?]: 324 [0], given: 407

Location: Ghana
Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

22 Aug 2016, 15:44
iliavko wrote:
excuse me, c=100% K=10$, m=40$
so 92-> 10$93-> 20$
94-> 40$(m) 95->80$

so m^2/2k -> 40^2/2*10 or 1600/20=80

What is wrong here?

Let's try a different number to test only options (C) & (D)

Say c = 10% and K = 100

1st Jan 1992 = k = 100 (starting number)

1st Jan 1993 = 1.1 * 100 = 110

1st Jan 1994 = m = 1.1% * 110 = 121

1st Jan 1995 = 1.1 * 121 = 133.1

Option (C) m * √((m/k)) must equal 133.1 ===> 121 * √((121/100)) = 121 * 11/10 = 133.1 Yes

Option (D) m^2/2k must equal 133.1 ===> 121^2/(2 * 100) = (121 *121)/ (2 * 100) =121 * 60.5/100 =73.205 No

_________________

Kindly press kudos if you find my post helpful

Kudos [?]: 324 [0], given: 407

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2014

Kudos [?]: 1081 [0], given: 4

Location: United States (CA)
Re: At the end of each year, the value of a certain antique [#permalink]

### Show Tags

05 Nov 2017, 07:30
buckkitty wrote:
At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?

A. m+1/2(m-k)
B. m+1/2((m-k)/k)m
C. (m*sqrt(m))/sqrt(k)
D. m^2/2k;
E. km^2

We can make the following expressions:

Value of the watch in 1992 = k

Value of the watch in 1993 = k*(1 + c/100)

Value of the watch in 1994 = k*(1 + c/100)^2 = m

Value of the watch in 1995 = k*(1 + c/100)^3 = m(1 + c/100)

Since k*(1 + c/100)^2 = m (the value of the value in 1994), we have:

(1 + c/100)^2 = m/k

1 + c/100 = √(m/k)

Thus, the value of the watch in 1995 is:

m(1 + c/100) = m*√(m/k) = m*√m/√k

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Kudos [?]: 1081 [0], given: 4

Re: At the end of each year, the value of a certain antique   [#permalink] 05 Nov 2017, 07:30
Display posts from previous: Sort by