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antique watch is c percent

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by Needgmat » Tue Sep 20, 2016 9:12 am
At the end of each year, the value of 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 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 f watch, in dollars, on January 1, 1995?

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

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

C) m under root m/under root k

D) m^2/2k

E) km^2

OAC

Please explain.

Many thanks in advance.

Kavin
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by [email protected] » Tue Sep 20, 2016 9:19 am
Hi Kavin,

This question can be solved by TESTing VALUES. I'm going to help start you off, then you should try to finish the question on your own...

To start, let's TEST these VALUES:

K = 100
C = 10

So the starting price of the watch is $100 and the percent increase in value each year is 10%. What would that make the value of M and what would the value of the watch be on January 1, 1995? Once you have those values, you can plug K and M into the answer choices and find the correct answer.

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by Brent@GMATPrepNow » Tue Sep 20, 2016 10:11 am
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√m)/(√k)
D) (m^2)/(2k)
E) k(m^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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by GMATGuruNY » Tue Sep 20, 2016 10:59 am
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
To make the math easier:
Let k=1, so that the original value is $1.
Let c=200, so that the value increases by 200% -- in other words, so that the value TRIPLES -- every year.

Value in 1993 = 3*1 = 3.
m = value in 1994 = 3*3 = 9.
Value in 1995 = 3*9 = 27.

Since the question stem asks for the value in 1995, our target is 27.
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 » Tue Jan 09, 2018 9:45 am
Needgmat wrote:At the end of each year, the value of 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 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 f watch, in dollars, on January 1, 1995?

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

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

C) m under root m/under root k

D) m^2/2k

E) km^2b
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

Answer: C

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