If the price of a gallon of milk and a loaf of bread both increased by

Question

If the price of a gallon of milk and a loaf of bread both increased by 10% from 1987 to 1990, what was the price of a loaf of bread in 1987?

(1) Together, a loaf of bread and a gallon of milk cost $3.60 in 1987.
(2) Together, a loaf of bread and a gallon of milk cost $3.96 in 1990.

Kudos for a correct  solution .

Patronus · Answer

Price of Gallon of milk in 1987 =  M , Price of Loaf of Bread in 1987 =  B 
Price of Gallon of milk in 1990 =  1.1*M , Price of Loaf of Bread in 1990 =  1.1*B 
Question is to find value of  B ?

Statement (1): B + M = $3.60 
Possible solutions:
 B = $1.00, M = $2.60 
 B = $2.60, M = $1.00 
NOT Sufficient

Statement (2):  1.1*B + 1.1*M = $3.96 
 B + M = $3.6 
Equation same as found in Statement (1)
Hence, NOT Sufficient

Statement (1) & Statement (2) together, both provide no information on the split of B & M, hence still NOT sufficient.

Answer (E)

ENGRTOMBA2018 · Answer

Let L1 be the price of loaf in 1987 and M1 be the price of milk in 1987.

Thus the same prices in 1990 will become 1.1*L1 and 1.1*M1

The question asks: L1=?

1. Per statement 1, L1+M1=3.6

2 variables but only 1 equation. Not sufficient to solve.

2. Per statement 2, 1.1*L1+1.1*M1 = 3.96

L1+M1 = 3.6

2 variables but only 1 equation. Not sufficient to solve.

Combining, as both the statements provide the same linear equation in 2 variables, we still can not solve for M1 or L1. Thus E is the correct answer.

reto · Answer

Statement 1:
Price of the basket is $3.60. All you can do from here is calculate the price for the year 1990 for the TOTAL BASKET. 1.1*3.6 = 3.96. The statement does not give you any information about the single components. Insufficient.

Statement 2:
All you can do with this is calculate backwards 3.96/1.1 = 3.60 for the Total Basket. Insufficient.

Since Statement 2 does not add new information to Statement 1, Answer E.

vishwaprakash · Answer

Statement 1 : M + B = 3.60 Two unknown one equation hence Not sufficient to find B Statement 2 : 1.1 M + 1.1B = 3.96 M + B = 3.60 Two unknown one equation hence Not sufficient to find B Combining statement 1 and 2 we get only one equation , hence Not sufficient -- Option E This is very typical Gmat Type DS, where combining statements present 2 equation to solve two unknown . However in reality it is just one equation and 2 unknown. GHOST EQUATION -

reto · Answer

You mean answer choice E not option A right?

GMATinsight · Answer

Let, Price of Milk in 1987 = M
and Price of Bread in 1987 = B

i.e. Price of Milk in 1990 = 1.1M
and Price of Bread in 1990 = 1.1B

Questions : M = ?

Statement 1 : Together, a loaf of bread and a gallon of milk cost $3.60 in 1987. 
M+B = $3.6
One Equation and Two variables will give Infinite many solutions for M and B so
 NOT SUFFICIENT

Statement 2 : Together, a loaf of bread and a gallon of milk cost $3.96 in 1990. 
1.1M+1.1B = $3.96
i.e. M+B = $3.6
One Equation and Two variables will give Infinite many solutions for M and B so
 NOT SUFFICIENT

Combining the Two statements  
Since both statements are leading to the same equation so combining them doesn't solve the purpose either. Hence,
 NOT SUFFICIENT

Answer: Option E

vishwaprakash · Answer

reto  .. thanks for correcting. Yes it is Option E

ScottTargetTestPrep · Answer

Solution:

We can let the price of a gallon of milk and a loaf of bread in 1987 be m and b, respectively. Thus their prices were 1.1m and 1.1b in 1990, respectively. We are looking for the value of b.

Statement One Only:

Together, a loaf of bread and a gallon of milk cost $3.60 in 1987.

This means b + m = 3.60. Since we have one equation with two unknowns. Statement one alone is not sufficient.

Statement Two Only:

Together, a loaf of bread and a gallon of milk cost $3.96 in 1990.

This means 1.1b + 1.1m = 3.96. Since we have one equation with two unknowns. Statement two alone is not sufficient.

Statements One and Two Together:

Using the two statements, we have two equations:

b + m = 3.60 and 1.1b + 1.1m = 3.96

It seems we have enough information to solve for b. However, upon a closer look, if we divide 1.1b + 1.1m = 3.96 by 1.1, we have b + m = 3.60, which is exactly the same as the first equation. That is, the second equation doesn’t give us any more information than the first. Therefore, we still can’t determine the value of b.

Answer: E

bumpbot · Answer

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