If the price of a gallon of milk and a loaf of bread both increased by 10% from 1987 to 1990...

[BTGmoderatorLU]

Source: Manhattan Prep

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.

The OA is E

[Jay@ManhattanReview]

Source: Manhattan Prep

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.

The OA is E

Say in 1987, the price a gallon of milk was $x and that of a loaf of bread was $y.

Thus, in 1990, the price a gallon of milk was $1.1x and that of a loaf of bread was $1.1y.

We have to get the value of y.

Let's take each statement one by one.

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

x + y = 3.60. Can't get the value of y. Insufficient.

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

1.1x + 1.1y = 3.96

=> x + y = 3.60. It's the same equation, we got in Statment 1. Insuffcient.

Even both statements combined can't help. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

Source: Manhattan Prep

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.

The OA is E

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