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At the end of each year, the value of a certain antique [#permalink]
 12 Mar 2006, 10:14
Question Stats:
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41% (02:14) wrong based on 4 sessions
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
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Re: PS-value of watch [#permalink]
12 Mar 2006, 13:03
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
please show any work and explanations please. OA to follow.
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
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Re: At the end of each year, the value of a certain antique [#permalink]
11 May 2012, 21:28
@Conocieur: Shouldn't the equation read
m = k*(1+c/100)^2 ? Since it says in the question, 'c percent more'..
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Re: At the end of each year, the value of a certain antique [#permalink]
12 May 2012, 02:25
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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.
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Re: At the end of each year, the value of a certain antique [#permalink]
08 Jan 2013, 06:07
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. Shouldn't this year be raised by the third power? since its the third year.
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Re: At the end of each year, the value of a certain antique [#permalink]
08 Jan 2013, 10:59
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fozzzy wrote: 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. 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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Re: At the end of each year, the value of a certain antique [#permalink]
10 Jan 2013, 00:55
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
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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 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. km2
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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.
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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. km2 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 = mSo, (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.
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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. km2 Merging similar topics. Please refer to the solutions above.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
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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. km2 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 = mSo, (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.
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