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

Question

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 agent's 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

PS20419

A. 8
B. 12
C. 24
D. 25
E. 48

PS20419

yashikaaggarwal · Answer

Let cost per real be x
The equation will be 
6/n=x ----(1)

When the cost per real increase by 0.25, 4 fewer reals were purchased.
Therefore, 6/n-4=x+0.25
6/(n-4)-0.25 = x ----(2)

Equating both.
6/n=6/(n-4)-0.25
6/n=6-0.25n+1/(n-4)
6n-24=6n-0.25n^2+n
0.25n^2-n-24=0
25n^2-100n-2400=0
N^2-4n-96=0
N^2-12n+8n-96
(N-12)(N+8)
N=12 & -8

Since real can't be negative
N=12
4 fewer reals were purchased second time.
So 12-4=8
Answer is A

Posted from my mobile device

Siak0730 · Answer

this is my first post, apology in advance for any typing mistakes.

"n" reams for 6$ ==> 1 ream = 6$/n

price per ream, or price of 1 ream increased by 0.25$= by(1/4)$
new price per ream or new price of 1 ream = (6$/n)+(1/4)$
per new price per ream, number of reams bought (n-4)
total price is again same 6$

equation from above==> (n-4)* =6
==> (n-4)* =6
multiplying both sides by 4n, we get
==> (n-4)*(24+n)= 6*4n
==> (n^2)-4n-96=0
==> (n^2)-12n+8n-96=0
==> (n-12)(n+8)=0
n=12, or n=-8
n cant be negative 
so n=12.

questions asked, numbers of reams in second billing= (n-4)= 12-4=8= option A

Archit3110 · Answer

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

Jsound996 · Answer

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

THE ANSWER IS A

Fdambro294 · Answer

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.

Basshead · Answer

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.

Gemmie · Answer

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

DanTheGMATMan · Answer

Classic two equation setup: https://www.youtube.com/watch?v=Ulzem72d4M8 Similiar problems: https://gmatclub.com/forum/at-his-regul ... l#p2619153 https://gmatclub.com/forum/d01-183487.html

sarthak1701 · Answer

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.

srosh2000 · Answer

Solved this under 2.5 mins without quadratic with product manipulation:

pq=6
(p+0.25)(q-4)=6

Test some options: 
I started with 12 and figured 1/2*12= 6
Then, 1/2+1/4 = 3/4
So, (3/4)*8= 6 
You will see here that difference between 1/2 and 3/4 is 1/4 (so the 0.25 increase in price) and 12-8= 4 (decrease in qty by 4) so it checks out.

We are asked q-4 which is 8 here so  ans (A)

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

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

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