An agent was billed a total of $6.00 for n reams of paper. As a result

price per ream ; 6/n
and with price increase of .25 $ ;
6/n+.25 = 6/(n-4)
or say
n-4 * ( 6/n+1/4)=6
solve for n
we get
n^2-4n-96 = 0
(n-12)*(n+8) =0
n=12 ,-8
n has to be +ve so 12
so second bill has 12-4 ; 8
OPTION A

Alternative method:

Let's say that
n = quantity of reams of papers
p = price per each ream

FORMULA 1: P(N) = $6

As a result of a price increase of $0.25 per ream, the agent's next bill of $6.00 was for 4 fewer reams of paper.
If P is increased by 0.25 cents, n decrease by 4, but still equals to 6. When we translate that into math.

FORMULA 2: (P + 0.25)(N - 4) = $6

We can use the answer choices to help us solve this problem
Let's choose choice B, or 12.

The second bill is N - 4, which equals 12. So N =16
Plug N=16 to the first formula
P(16) = 6

P = \(\frac{6}{16}\)

P = \(\frac{3}{8}\)

Plug in \(\frac{3}{8}\) into the second formula

(3/8 + 1/4)(12) = $6
Divide 12 on each side and add the fractions together

Does \(\frac{5}{8}\) = \(\frac{1}{2}\)? Clearly NO, so B is incorrect. But it tells us that we need to increase the right hand [\(\frac{1}{2}\)] side. The only way to do to so is to reduce (N - 4), so the answer has to be A!

______________

If you didn't realize that, you can test answer choice D to determine that pattern
P(n) = 6
(P + 0.25)(N - 4) = $6

N - 4 = 25, so N = 29
P(29) = 6
P = \(\frac{6}{29}\)
Plug P into the 2nd formula

(6/29 + 1/4)(25) = $6
Divide 25 by each side and add the fractions together

\(\frac{53}{116}\) = \(\frac{24}{100}\)

Clearly they're not equal, but the difference between \(\frac{53}{116}\) and \(\frac{24}{100}\) is much larger than \(\frac{5}{8}\) and \(\frac{1}{2}\) from Answer Choice B

Plugged In Numbers and sure enough the 1st one worked perfectly...... around 1 minute.

$6 = $c * n

$6 = $(c + 1/4) * (n - 4)

Q: the 2nd bill was for how may reams of paper?

Q: (n - 4) = Answer Choice ?


-A- 8


n - 4 = 8
n = 12

Plugging 12 into the 1st Bill: $c = 6/12

Plugging 12 into the 2nd Bill:

6 = (c + 1/4) (n - 4)
6 = (c + 1/4) (12 - 4)

6 = 8c + 2

4 = 8c

$c = 4/8 = 6/12

Since the $c Variable matches across the 2 bills, Answer Choice -A- is Correct


Edit: Realize that I was extremely lucky that the 1st A.C worked perfectly. Otherwise, it would have taken longer.

\(np = 6\)

\((n-4)(p+0.25) = 6\)

\(np + 0.25n - 4p - 1 = 6\)

\(0.25n - 4p - 1 = 0\)

\(n - 16p - 4 = 0\)

\(n - 16(\frac{6}{n}) - 4 = 0\)

\(n - \frac{96}{n} - 4 = 0\)

\(n^2 - 4n - 96\)

\((n-12)(n+8)\)

\(n = 12\)

Since the second bill was for 4 fewer reams, \(n - 4 = 8\).

Answer is A.

p: price per ream

6 = n * p = (n - 4) * (p + 0.25)

6 = 8 * 0.75
   = 12 * 0.5
   = 24 * 0.25
   = 25 * 0.24

n = 12; p = 0.5
n - 4 = 8; p + 0.25 = 0.75

==> 8 reams of paper for 2nd bill

­Classic two equation setup:




Similiar problems:
https://gmatclub.com/forum/at-his-regul ... l#p2619153
https://gmatclub.com/forum/d01-183487.html­

The quickest way is to plug in the values in the difference, since the price per ream rose by 0.25 we can say that

(6/n-4) - (6/n) = 1/4 (or 0.25)

Solving for n is a longer process.

Plug in the choices one by one

A) 8. 6/4 - 6/8 = 3/4 NO

B) 12. 6/8 - 6/12 = 1/4 YES

Note that this is the value of n. Since n = 12, the number of reams for new order = n-4 = 12-4 = 8.