A bookstore that sells used books sells each of its paperbac

Option E.
From S1:Let price per paperback=x &
price per hardcover=y
2x+3y=12.50.Not suff since two variables,one equation can't be solved.

From S2:4x+6y=25
Nothing but 2(2x+3y)=25
OR repetition of eqn from S1.Not suff.

Combining we can't sove since both are basically the same equations.

Let the price of paperbacks be 'x'
the price of hard cover book be 'y'

From Statement 1:- Joe bought 2 paperback books and 3 hardcover books for $12.50.
Thus 2x+3y = 12.50
This is one equation with 2 unknowns hence it cannot be solved. So statement 1 alone is insufficient

From Statement 2:- Paul bought 4 paperback books and 6 hardcover books for $25.00
Thus 4x+6y = 25
Again it is one equation with 2 unknowns. So statement 2 alone is insufficient.

Combining both the statements we get 2 equations:-
1. 2x+3y = 12.5
2. 4x+6y = 25

Now linear equations with 2 unknowns can only be solved it both the equations are different i.e not the same or multiplies of each other.
Here equation 2 is a multiple of equation 1. Equation 2 = (Equation 1)x2

Thus this pair of equations cannot be solved. and hence even after combining both the equations the solution is not possible.

Hence Option (E) is the answer

Hi Bunuel ,

Can't we get Answer as' D' by using trial and error method.

2 PB + 3 HC = 12.50$
The equation satisfies for PB =4 AND HC = 1.5 ;This is the only pair that satisifies the above equation ;
Therefore, can't we say that for one PB +one HC = 2+ 1.5 = 3.5 $

Please explain whether my approach is correct (or ) wrong.

Help is appreciated.

How did you get that p=4 and h=1.5 is the only solution of 2p + 3h = 12.5 ? What about p=4.75 and h=1, p=3.25 and h=2, ... ?

Here is a visual that should help.

Observations:

1) Since the cost of all the goods is the same for everyone, it is irrelevant who bought what, so don't bother complicating the question by including this information.

2) Usually, when we have two equations with two variables, this is sufficient...unless the 2nd equation happens to be the same as the first, which is what happened here.

What i have noticed in such question types is that, we dont have any relationship between these 3 people, if we had some relationship, we could have actually commented on the cost of 1 paperback book and 1 hardcover book for Maria, Since nothing is there and both the statements give the same relationship

answer is E

from 1) 2 x + 3 y = 12.50
from 2) 2x + 3y = 12.50

Check out this video explanation:­

https://www.youtube.com/watch?v=3bCo0kkKtP4­