Viren sold his new novel in both paperback and e-book format

Question

Viren sold his new novel in both paperback and e-book formats. He received an average of $6.40 per copy sold, $2 more from each paperback copy than from each e-book copy. If 3/4 of the money he received from the sale of his novel came from e-book sales, how much did Viren receive from each e-book copy?

A. $5.40
B. $5.60
C. $5.75
D. $5.90
E. $6.00

A. $5.40
B. $5.60
C. $5.75
D. $5.90
E. $6.00

FerociousStorm · Answer

Let money earned from each ebook be x and from paperback be x+2. Also number of ebooks be a and paperback be b.

We know average earning from each book was $6.4 so from 100 books would be 640. 3 quarters were earned from ebooks and 1 quarter from paperback so total earnings from ebooks would be 640*3/4 = 480

Form the equation -->

x*a/(x+2)*b = 3/1

We x*a represents the 480 so put in the value.

480/(x+2)*b = 3/1 = 3

Transfer b and 3 to opposite sides

480/3(x+2) = b

b Must be an integer, putting in values from options only E satisfies the condition. So $6

sanjanaagrawal09 · Answer

Price 
 Qty (Rev/Price) 
 Revenue 
 
  Paperback 
 x+2 
 1/(x+2) 
 1 
 
  Ebook 
 x 
 3/x 
 3 
 
  Total

4

Let revenue = 4
hence revenue of ebook = 3/4 *(total revenue) = 3 and paperback = 4-3 = 1
let price of ebook =x
price of paperback = 2 more than ebook = x+2
calculate qty for both as revenue/price

average price = total revenue/total qty
6.4 = 4/  
Solving this we get x=-8/5 or x=6
x can't be negative here.
hence x=6.

kevincan · Answer

Total revenue 4x , e-book unit revenue p

4x/(3x/p + x/(p+2))= 6.4

4/(3/p + 1/(p+2))=6.4

40/64 = 3/p + 1/(p+2)

5/8 = (3p+6+p)/(p(p+2))

5p^2 + 10p = 32p + 48
5p^2 -22p - 48= 0
(5p .. )(5p .. )/5 = 0

Product -240
Sum -22
(5p - 30)(5p+8) = 0

P= 6 or p= -8/5 
Because P is positive , the correct answer is six

kevincan · Answer

How could we get this question right without solving a nasty second degree equation ?

diegoHdzZ · Answer

I used the teeter totter method

p + e = t
e = (3/4) t
Ratio of p / e = 1/3 -> We're going to look for this ratio

| -------6.4-------| 
e ------- ^ ------ p
x--------------- x+2
______
B) $5.60
Multiply 10 to make it easier
Distance from average
 8 12
|---------||--------|

| ------ 64 ------- | 
e------- ^---------p
56.....................76
(12)................. (8)

This gives us a ratio of
p/e = 8/12 = 2/3 ~ .66
Not the ratio that we're looking for
_____
D. $5.90

Distance from average 
 6 15
|---------||--------|
| ------ 64 --------| 
e -------^-------- p
59----------------79
(15).................(6)
This gives us a ratio of

p/e = 6/15 = 2/5 ~ .40

Not the ratio that we're looking for. However, since we're looking for .33 and the larger the price of e-books the closer we get to the ratio,  the answer must be E

aliassoluta · Answer

I did it like this, still nasty though, but I hate solving math equations especially in GMAT questions, took 2nd try to come to this convenient way:

at first I also mistook the question to be 3/4 OF THE VOLUME, so I do the "draw the line" trick, divided in 4 small gaps (for the ratio 3/4)
------|-|-|-|-|-----
first vertical line is ebook price, last one is paperback price, the gap from the first to last is 2$, 4 small gaps at 0.5$ each, 6.4 represents the second vertical line because ebook sold more so skewed toward it. I chose D but apparently it's wrong because I understood the question wrong.

piggybacking my method
if 3/4 ratio is copies -> have D -> but since it's not, it's money -> ebook must sell more -> 6.4 skews toward ebook more -> only choice left is E

Kinshook · Answer

Viren sold his new novel in both paperback and e-book formats. He received an average of $6.40 per copy sold, $2 more from each paperback copy than from each e-book copy.

If 3/4 of the money he received from the sale of his novel came from e-book sales, how much did Viren receive from each e-book copy?

Let the price of e-book be $x.
The price for paperback copy = $x + $2

Ratio of number of e-books : number of paperbacks = (x+2-6.4) : (6.4-x) = x - 4.4 : 6.4 - x

Revenue from e-books = 3*Revenue from paperbacks
x(x-4.4) = 3(x+2)(6.4-x)
x^2 - 4.4x = 3(4.4x + 12.8 - x^2) = 13.2x + 38.4 - 3x^2
4x^2 -17.6x - 38.4 = 0
x^2 - 4.4x - 9.6 = 0
x^2 - 6x + 1.6x - 9.6 =0
(x-6)(x+1.6) = 0

x = 6 since x = -1.6 is not feasible

IMO E

Viren sold his new novel in both paperback and e-book format

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

	Price	Qty (Rev/Price)	Revenue
Paperback	x+2	1/(x+2)	1
Ebook	x	3/x	3
Total			4

GMAT Problem Solving (PS) Questions

Viren sold his new novel in both paperback and e-book format

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards