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

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by imane81 » Mon Feb 15, 2010 2:44 pm
Please advise on this one.. thank you

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)/k)m
C. (m sqrt(m))/ sqrt (k)
D. m^2/2k
E. km^2
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by komal » Mon Feb 15, 2010 6:54 pm
imane81 wrote:Please advise on this one.. thank you

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)/k)m
C. (m sqrt(m))/ sqrt (k)
D. m^2/2k
E. km^2
This question has already been discussed here :

https://www.beatthegmat.com/value-of-ant ... qrt(m/k)
Last edited by komal on Tue Feb 16, 2010 8:38 am, edited 1 time in total.
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by djkvakin » Mon Feb 15, 2010 6:55 pm
for this one you can use a 100 as the price in 92. in 93 the price would be 120, in 94 the price is 144, and in 95 it's 172.8.
now try backsolving. C is your choice.
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by sars72 » Mon Feb 15, 2010 8:14 pm
i tried to arrive at the answer algebraically, but got lost down the line... pls help!

since the answer is in terms of m and k, you have to substitute the value of c and bring it outta the equation

--> (k+ck/100)(1+c/100) = m
--> k+ck/100 + ck/100 + (kc^2 )/10000 = m
--> (c/100)(k+k+ck/100) = m-k
--> (c/100)(2k+ck/100) = m-k
--> (c/100)k(2+c/100) = m-k

value in jan 1995 = m + mc/100

:( pls help
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by shashank.ism » Mon Feb 15, 2010 9:20 pm
imane81 wrote:Please advise on this one.. thank you

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)/k)m
C. (m sqrt(m))/ sqrt (k)
D. m^2/2k
E. km^2

1992 ---> k
1993 --> k(1+0.01c)
1194 --> m= k(1+0.01c)(1+0.01c) =k(1+0.01c)^2 ---------(i)
(1+0.01c) = sqrt.(m/k) -------------------------------------------(ii)

1994 --> k(1+0.01c)^3 = k(1+0.01)^2 x (1+0.01)
putting values of k(1+0.01c)^2 and (1+0.01c) from 1st and 2nd, we get
[spoiler]sqrt(m/k) x m Ans C[/spoiler]
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by shashank.ism » Mon Feb 15, 2010 9:21 pm
djkvakin wrote:for this one you can use a 100 as the price in 92. in 93 the price would be 120, in 94 the price is 144, and in 95 it's 172.8.
now try backsolving. C is your choice.
your approach is also very good. By using 100 as the price and back solving..It would really save time....
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by komal » Tue Feb 16, 2010 8:39 am
m = k(1+c/100)^2
=> (1+c/100) = sqrt (m/k)

value of the watch on January 1, 1995 = m(1+c/100)
m * sqrt(m/k)
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by alanforde800Maximus » Mon May 07, 2018 4:12 pm
Can any expert help with this question?
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by GMATGuruNY » Mon May 07, 2018 5:01 pm
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 1st, 1995?

m + (1/2)(m-k)

m + (1/2)((m-k)/k)m

(m√m)/√k

m²/2k

km²
Let k=1 and c=200%, implying that the value of the $1 watch increases by 200% each year.
Value in 1993 = 1 + (200/100)(1) = 3.
m = value in 1994 = 3 + (200/100)(3) = 9.
Value in 1995 = 9 + (200/100)(9) = 27. This is our target.

Now plug k=1 and m=9 into the answers to see which yields our target of 27.

Only answer choice C works:
(m√m)/√k = (9√9)/√1 = 27.

The correct answer is C.
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by Scott@TargetTestPrep » Wed May 09, 2018 3:59 pm
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 1st, 1995?

m + (1/2)(m-k)

m + (1/2)((m-k)/k)m

(m√m)/√k

m²/2k

km²
We can create 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

Answer: C

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by Brent@GMATPrepNow » Tue Nov 05, 2019 6:18 am
imane81 wrote:Please advise on this one.. thank you

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)/k)m
C. (m sqrt(m))/ sqrt (k)
D. m^2/2k
E. km^2
For an algebraic approach, we need to recognize that the value of the watch increases by the same factor each year. So, for the ease of calculations, let's say that the value increases by a factor of F.

Aside: Notice that the answer choices do not include the variable c. This tells me that I don't need to keep that variable in my solution.

In 1992, the watch is valued at k dollars.
In 1993, the watch is valued at kF dollars (applying our constant increase of F)
In 1994, the watch is valued at kF^2 dollars
In 1995, the watch is valued at kF^3 dollars
GREAT, we now know the value in 1995. However, when we check the answer choices, none match the expression kF^3. So, we have some more work to do.

The question tells us that, in 1994, the watch is valued at m dollars.
So, we now know that kF^2 = m.
Let's solve this equation for F (you'll see why in a moment)
We get: F^2 = m/k
F = √(m/k)
We can rewrite this as: F = (√m)/(√k)

We know that the 1995 value = kF^3 dollars.
Rewrite, to get the 1995 value = (kF^2)(F)
If we replace kF^2 with m and replace F with (√m)/(√k), we get:
1995 value = (m)((√m)/(√k))
= (m√m)/(√k)
= C

Cheers,
Brent
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