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by rintoo22 » Wed May 01, 2013 12:34 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 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 ?

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by GMATGuruNY » Wed May 01, 2013 1:05 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 1, 1995?

A) m + 1/2(m-k)
B) m + 1/2((m-k)/k)) * m
C) (m√m)/√k
D) m²/2k;
E) km²
Let k=2.
Let c=200, implying that the value of the watch increases by 200% each year.
Thus:
Value in 1993 = 2 + (200/100)2 = 6.
Value in 1994 = 6 + (200/100)6 = 18. Thus, m=18.
Value in 1995 = 18 + (200/100)18 = 54.

The question stem asks for the value of the watch in 1995:
$54. This is our target.
Now we plug k=2 and m=18 into the answers to see which yields our target of 54.
Only C works:
(m√m)/√k = (18√18)/√2 = 18√9 = 18*3 = 54.

The correct answer is C.
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by Atekihcan » Wed May 01, 2013 11:50 pm
rintoo22 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 ?
If you go for plugging number way, you have to do a lot of calculations!
A less calculation intensive way to solve this problem is to simply go for the algebraic method.

Value of the watch in 1992 = k
Value of the watch in 1993 = k + c% of k = k(1 + c/100)
Value of the watch in 1994 = k(1 + c/100) + c% of k(1 + c/100) = k(1 + c/100)² = m ........ (1)
Value of the watch in 1995 = m + c% of m = m(1 + c/100) ........ (2)

From (1), (1 + c/100) = √(m/k)
So, value of the watch in 1995 = m(1 + c/100) = m*√(m/k) = m√m/√k
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by Brent@GMATPrepNow » Thu May 02, 2013 5:44 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
Brent Hanneson - Creator of GMATPrepNow.com
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