Plugging in Numbers Problem

Question

Hi this question is from the GMATPrep Question pack 1:

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

Correct answer is C.

However I'm running into the issue again that I am getting two answers when using a specific number set for "Picking Numbers"

I'm choosing c = 100%, k= $100, thus m = $400, and the price for 1995 will ultimately be $800.

However I'm getting C and D for the answer.

Math for C: 400*sqrt400/sqrt100 That equals 800 which is the right answer

Math for answer D: 400sqrd/2(100) That ALSO equals 800.

Can anyone explain this discrepancy?

theCodeToGMAT · Answer

in 1995 = k(1+c/100)(1+c/100)(1+c/100)
Since, m = k(1+c/100)(1+c/100)
in 1995 = m(1+c/100) -- (1)

Now,

m = k(1+c/100)(1+c/100)

(1+c/100)^2 = m/k
c/100 = sqrt(m/k) - 1
Putting in (1)

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

Answer [spoiler]{C}[/spoiler]

hungraa · Answer

theCodeToGMAT wrote:in 1995 = k(1+c/100)(1+c/100)(1+c/100)
Since, m = k(1+c/100)(1+c/100)
in 1995 = m(1+c/100) -- (1)

Now,

m = k(1+c/100)(1+c/100)

(1+c/100)^2 = m/k
c/100 = sqrt(m/k) - 1
Putting in (1)

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

Answer [spoiler]{C}[/spoiler]

Thanks Rahul, but do you think you can show me the method if you picked numbers? Specifically mine?

GMATGuruNY · Answer

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%.
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.

I'm choosing c = 100%, k= $100, thus m = $400, and the price for 1995 will ultimately be $800.

However I'm getting C and D for the answer.

Math for C: 400*sqrt400/sqrt100 That equals 800 which is the right answer

Math for answer D: 400sqrd/2(100) That ALSO equals 800.

Can anyone explain this discrepancy?

There is no discrepancy.
The general idea behind PLUGGING IN is to choose numbers, get a target, and see which answer choice yields the target.
Sometimes more than one answer choice will work.
For this reason, ALWAYS CHECK ALL 5 ANSWER CHOICES.
in your case, both C and D yield your target of 800.
If more than one answer choice works, DON'T JUST GUESS.
Instead, PLUG IN ONE MORE COMBINATION OF VALUES, get a NEW TARGET, and see which of the remaining answer choices works in BOTH CASES.

A word of advice: avoid plugging in the same value for different variables.
When you plugged in c=100 and k=100, you increased the likelihood that more than one answer choice would yield the target.

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Brent@GMATPrepNow · Answer

hungraa 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

Instead of plugging in numbers, we can 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

hungraa · Answer

Makes sense. Thanks all!

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