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Senior Manager  Joined: 17 Aug 2005
Posts: 279
Location: Boston, MA
At the end of each year, the value of a certain antique  [#permalink]

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40 00:00

Difficulty:   55% (hard)

Question Stats: 73% (02:52) correct 27% (03:03) wrong based on 569 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 61549
Re: At the end of each year, the value of a certain antique  [#permalink]

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14
21
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 - $$m*(1+\frac{c}{100})=m*\sqrt{\frac{m}{k}$$.

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

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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
##### General Discussion
Manager  Joined: 20 Mar 2005
Posts: 165
Location: Colombia, South America

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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
Intern  Joined: 02 Apr 2012
Posts: 2
Re: At the end of each year, the value of a certain antique  [#permalink]

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m = k*(1+c/100)^2 ? Since it says in the question, 'c percent more'..
Director  Joined: 29 Nov 2012
Posts: 677
Re: At the end of each year, the value of a certain antique  [#permalink]

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 61549
Re: At the end of each year, the value of a certain antique  [#permalink]

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3
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.
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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. Veritas Prep GMAT Instructor V Joined: 16 Oct 2010 Posts: 10130 Location: Pune, India Re: Arithematic [#permalink] ### Show Tags 1 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 Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Senior Manager  Status: Gonna rock this time!!! Joined: 22 Jul 2012 Posts: 416 Location: India GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29 WE: Information Technology (Computer Software) Re: Arithematic [#permalink] ### Show Tags 1 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 Intern  Joined: 11 Sep 2013 Posts: 3 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 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.. Manager  Joined: 26 Sep 2013 Posts: 182 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 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 Manager  B Joined: 10 Mar 2013 Posts: 166 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 GPA: 3 Re: At the end of each year, the value of a certain antique [#permalink] ### Show Tags 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. Manager  Joined: 24 Nov 2013 Posts: 55 Re: At the end of each year, the value of a certain antique [#permalink] ### Show Tags 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 Manager  Joined: 28 Dec 2013 Posts: 65 Re: At the end of each year, the value of a certain antique [#permalink] ### Show Tags Bunuel wrote: Thiagaraj wrote: conocieur: Shouldn't the equation read 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 - $$m*(1+\frac{c}{100})=m*\sqrt{\frac{m}{k}$$. Answer: C. 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 ? Retired Moderator Joined: 29 Oct 2013 Posts: 248 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 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. _________________ Please contact me for super inexpensive quality private tutoring My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876 Senior Manager  S Joined: 08 Dec 2015 Posts: 282 GMAT 1: 600 Q44 V27 At the end of each year, the value of a certain antique [#permalink] ### Show Tags excuse me, c=100% K=10$, m=40$so 92-> 10$
93-> 20$94-> 40$ (m)
95->80$so m^2/2k -> 40^2/2*10 or 1600/20=80 Answer D What is wrong here? Manager  G Joined: 02 Jun 2015 Posts: 169 Location: Ghana Re: At the end of each year, the value of a certain antique [#permalink] ### Show Tags iliavko wrote: excuse me, c=100% K=10$, 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

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

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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

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