# GMAT OFFICIAL GUIDE DS – Material A costs \$3 per kilogram, and Material B…

## Solution:

We are given that material A costs \$3 per kilogram and that material B costs \$5 per kilogram. We also know that 10 kilograms of material K consists of x kilograms of Material A and y kilograms of Material B. Thus, the cost equation of Material K is:

3x + 5y= Cost

The weight of material K is x + y. Since we know that the weight of material K is 10, we can say:

x + y = 10

We must determine whether x > y.

Statement One Alone:

y > 4

Knowing that y is greater than 4 does not provide enough information to determine whether x > y. For example, if y = 5, then x = 5 and x is not greater than y. However, if y = 4.5, then x = 5.5 and x is greater than y. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The cost of the 10 kilograms of Material K is less than \$40.

Using the information in statement two we can use the cost equation to create the following inequality.

3x + 5y< 40

We also have the weight equation x + y = 10. Isolating for x we have:

x = 10 – y

Using x = 10 – y, we can substitute 10 – y for x in the inequality 3x + 5y < 40.

3(10 – y) + 5y < 40

30 – 3y + 5y < 40

30 + 2y < 40

2y < 10

y < 5

Since x + y = 10, and y is less than 5, we see that x will always be greater than y. Statement two alone is sufficient to answer the question.