looking for a faster way

n reams = $ 6
1 ream = $ 6 / n

if price is increased by $ 0.25 / ream, the new price per ream =

6/n + 0.25

now, for n-4 reams, the price = $ 6

hence price per ream = 6 / (n-4)

6 / (n-4) = 6/n + 0.25

Solve the above equation and find the value of (n-4). That would be the answer.[/quote][/spoiler]

Thanks, I like your set up, but to solve that equation still seems to take a long time, this is how i went about it.

6/(n-4) = 6/n + 0.25
6/(n-4) - 6/n = 0.25
(6n-6n+24)/(n^2-4n) = 0.25 (adding the 1st half fractions together)
24 = (n^2-4n)x0.25
24/0.25=n^2-4n
n^2-4n-96=0
(n+8)(n-12)
n=-8, n=12 (disregard n=-8 because its not logical for this problem)
n-4 = 8
The answer is A

Does anyone have a faster way?

I got the following 2 equations:

x - cost per ream

nx=6
(x+1/4)(n-4)=6

solving for x:

(x+1/4)(6/x-4)=6
6-4x+3/2x-1=6
10x-8x^2+6x=12x multiply everything by 2x
0=8x^2-4x
0=2x^2-x
x=0 or x=1/2

x=1/2 and n = 12

the answer is n-4=12-4=8


The problem is simple but the calculation can be tricky. I guess you can try plugging in the answers once you have the equations setup. Since in this problem the correct answer is A, you would save a lot of time.

tony777 wrote:I thought this question was a simple one but I spent a ridiculous amount of time working through to an answer.

Any tips out there on how to approach it.

An agent was billed a total of $6.00 for n reams of paper. As a result of a price increase of $0.25 per ream, the agents next bill of $6.00 was for 4 fewer reams of paper. The second bill was for how many reams of paper?

(A) 8
(B) 12
(C) 24
(D) 25
(E) 48

Backsolving time!

When we have a complicated word problem and answers that are actual numbers (as opposed to, e.g., variables), working backward from the answers can be a great way to attack the question (and avoid the algebra).

Using the Kaplan method for backsolving, we start by quickly scanning the choices to see if any just don't make sense. In this particular case, we can actually eliminate 4 of the 5 choices!

We know that the answer is 4 reams fewer than the original number. If we jot down the original numbers beside the answers, we get:

(A) 8 12
(B) 12 16
(C) 24 28
(D) 25 29
(E) 48 52

Since the amount spent is $6.00, we know that both the original number and the new number MUST go into $6.00. Of all the choices, only (A) has two numbers that BOTH go into $6.00 - therefore, (A) must be the right answer.

* * *

Let's say, for the sake of the exercise, that we weren't able to use our advanced Kap-fu and figure out that only (A) makes sense. In that case, we'd actually go through the backsolving process, starting with either (B) or (D). Since (B) is a simpler number, let's begin there.

First, we assume that (B) is the right answer.

So, if the new # of reams is 12, then new price/ream is 6.00/12 = 50 cents.

Further, if the new # of reams is 12, then the original number is 16. Therefore, the original price/ream is 6.00/16 = .. umm.. doesn't work, but to estimate: 37ish cents.

Now, let's look at the difference: 50 cents - 37 cents = 13 cents. Does that match the story? NO - we wanted a difference of 25 cents: eliminate (B).

Next, figure out if we need a bigger or smaller number. Since we want the extra 4 reams to have a bigger impact (so we get a bigger difference), we need to REDUCE the number of reams: eliminate all the answers bigger than 12, i.e. (C), (D) and (E).

Only (A) remains - done!!

tony777 wrote:I thought this question was a simple one but I spent a ridiculous amount of time working through to an answer.

Any tips out there on how to approach it.

An agent was billed a total of $6.00 for n reams of paper. As a result of a price increase of $0.25 per ream, the agents next bill of $6.00 was for 4 fewer reams of paper. The second bill was for how many reams of paper?

(A) 8
(B) 12
(C) 24
(D) 25
(E) 48

before n = 6, now

1.25n-4 = 6,
1.25 = 10
n=8

HarvardDreamin,
n was not 6 before, n reams cost 6$.

This solution does not make sense. The fact that you also got 8 is a coincidence.

xilef wrote:HarvardDreamin,
n was not 6 before, n reams cost 6$.

This solution does not make sense. The fact that you also got 8 is a coincidence.

Before, the no of reams * price of reams = N

Hence using mathematical logic + info provided, it leads to the second equation:

"1.25n-4 = 6"

which when solved gives the right answer. I understand that this solution relies on my intuition and logic but I find it hard to understand how it could be a coincidence given the most important equation above is correct.

1.25n-4 = 6

You are multiplying the number of reams by 1.25, the price per ream was increased by 25 cents not 25% and then you are subtracting 4 reams from that and you get the total price for all reams. Can you explain your logic, because to me it seems to be off?