If the cost of House L increased by 20% over the same time that the

Question

If the cost of House L increased by 20% over the same time that the cost of House M decreased by 20%, then the ratio of the new price of House M to the new price of House L is what percent of the original cost of House M ?

(1) If House L had increased by 30%, then the increased price of House L would have been equal to the original price of House M.

(2) The price of House L is $300,000.

Ritwick91 · Accepted Answer

The only explanation that I can come up with this:

Question: Ratio/Original Price * 100 %
Lets consider 
L(O)=Original price of house L
L(N)=New price of house L
M(O)=Original price of house M
M(N)=New price of house M

Given in the Q-stem, 
 L(N)=1.2*L(O)  
 M(N) = 0.8* M(O)

Now we have to find,   ((\frac{M(N)}{L(N)})/M(O))*100  .......................(i)

Now let's consider the given statements,

St.1 : If House L had increased by 30%, then the increased price of House L would have been equal to the original price of House M. 
=>  1.3* L(O) = M(O) 
=>  L(O)= \frac{M(O)}{1.3} .............(ii)

Now from the Q-stem, 
 L(N)=1.2*L(O) 
=>  L(N)= 1.2 * \frac{M(O)}{1.3}  .............from (ii)

Also from the Q-stem, we have  M(N) = 0.8* M(O)

So putting these values in (i),
 \frac{(0.8* M(O))}{(1.2 *M(O)/1.3)}/M(O))*100 
=>  (\frac{0.8*1.3}{1.2}/M(O))*100

Now as M(O) is unknown to us, this statement is insufficient.

St.2: The price of House L is $300,000 
=>  L(O)=$300,000

From Q-stem, we have 
 L(N)=1.2*L(O)  
=> L(N)=360,000

and
 M(N) = 0.8* M(O)

So putting these values in (i),
 ((\frac{M(N)}{L(N)})/M(O))*100 
=>  (\frac{(0.8*M(O)}{360,000})/M(O))*100 
=>  \frac{(0.8*100)}{360,000}

Hence we do have a value for the required question and thus statement 2 is sufficient.

HarryStamper · Answer

original cost of 'house M' is M; original cost of 'house L' is L

Converting the prompt into an equation=0.8M/1.2L

this is equal to 2M/3L (the ratio of new price of M to the new price of L)

next step: this ratio is  %

this equation is simplified in to (2/3L)%...you only need L to solve the question and that is statement 2. Answer is B

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