The price of a gallon of milk in 1990 was ten percent higher than it

Question

The price of a gallon of milk in 1990 was ten percent higher than it was in 1985, and the price of a pound of butter in 1990 was ten percent higher than it was in 1985. What was the price of a gallon of milk in 1990?

(1) The sum of the prices of a gallon of milk and a pound of butter in 1985 was $5.00.

(2) The sum of the prices of a gallon of milk and a pound of butter in 1990 was $5.50.

BrentGMATPrepNow · Answer

Given : The price of a gallon of milk in 1990 was ten percent higher than it was in 1985, and the price of a pound of butter in 1990 was ten percent higher than it was in 1985.  
Let M = the price of a gallon of milk in 1985
So, 1.1M = the price of a gallon of milk in 1990

Let B = the price of a pound of butter in 1985
So, 1.1B = the price of a pound of butter in 1990

Target question :    What is the value of 1.1M?

Statement 1 : The sum of the prices of a gallon of milk and a pound of butter in 1985 was $5.00.  
We can write:  M + B = 5 
There are many possible solutions to this equation. Here are two:
 Case a : M = 1 and B = 4. In this case, the answer to the target question is  1.1M = 1.1(1) = 1.1 
 Case b : M = 2 and B = 3. In this case, the answer to the target question is  1.1M = 1.1(2) = 2.2 
Since we can’t answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : The sum of the prices of a gallon of milk and a pound of butter in 1990 was $5.50 
We can write: 1.1M + 1.1B = 5.5
Divide both sides of the equation by 1.1 to get:  M + B = 5 
Aha! This is the same equation we got for statement 1. 
So, since we already determined that statement 1 is NOT SUFFICIENT, we can also conclude that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Since statements 1 and 2 both provide the same information, and since we already determined that both statements ALONE are insufficient, we can also be certain that the statements COMBINED are insufficient. 
If you're not convinced, here are two contradictory cases that satisfy BOTH statements: 
 Case a : M = 1 and B = 4. In this case, the answer to the target question is  1.1M = 1.1(1) = 1.1 
 Case b : M = 2 and B = 3. In this case, the answer to the target question is  1.1M = 1.1(2) = 2.2 
Since we can’t answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

aishu0091 · Answer

BrentGMATPrepNow , thank you for the brilliant explanation!

Just a quick query: I eliminated A,B,D based on loose intuition as there is insufficient info to tackle the statements alone and went to C directly. In C:

1985=> X+Y=5
1990=> 1.1X +1.1Y =5.5

Taking x= 5-y
1.1(5-Y) +1.1Y =5.5 
5.5-1.1Y+1.1Y =5.5 ---> Insufficient

Hence (E)

BrentGMATPrepNow · Answer

Your intuition is correct. 
Rather than try to solve the system X+Y=5 and 1.1X +1.1Y =5.5, we might just recognize that these are identical equations, since we can take 1.1X +1.1Y =5.5 and divide both sides of the equation by 1.1 to get X + Y = 5

Aside: There's a small error in your solution (highlighted above)

aishu0091 · Answer

BrentGMATPrepNow , thank you so much for the explanation!

The price of a gallon of milk in 1990 was ten percent higher than it

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