Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency

byRituparna Nath Content Writer at Study Abroad Exams

Question: Paint X costs $15 per gallon, and Paint Y costs $20 per gallon. If 10 gallons of Mixture M consists of r gallons of Paint X and s gallons of Paint Y, is the total cost of Paint X in Mixture M greater than the total cost of Paint Y in Mixture M?

(1) s gallons of Paint X costs more than r gallons of Paint Y.
(2) In Mixture M, the total cost of Paint X is more than 2/5 of the total cost of Paint Y.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

“Paint X costs $15 per gallon, and Paint Y costs $20 per gallon.” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

Paint X and Paint Y costs, as well as the variables r and s, which represent the number of gallons of each paint in 10 gallons of Mixture M. The question asks whether the total cost of Paint X in the mixture exceeds the total cost of Paint Y in the mixture.
Let us attempt to determine whether 15r > 20s below by evaluating both the statements
According to statement 1
s gallons of Paint X costs more than r gallons of Paint Y.
so,
15s > 20r
($\frac{3}{4}$)*15s > 20r * ($\frac{3}{4}$)
$\frac{45s}{4}$> 15r
15r < 11.25s
This equation is sufficient
According to statement 2
In Mixture M, the total cost of Paint X is more than 2/5 of the total cost of Paint Y.
So,
15r > ($\frac{2}{5}$)*(20s)
15r > 8s
This equation is insufficient
The answer is A , Statement 1 is sufficient and Statement 2 is insufficient

Correct Answer: A

Approach Solution 2:

Let us have another approach to find the solution,
Let us not use the variable s, and let us replace it with 10−r.
so
Is 15r > 20(10−r)?
Is 35r > 200 ?
Is r > $\frac{40}{7}$?
Lets evaluate both our statements-
Statement 1 says
15(10−r) > 20r
35r < 150
As said above, 35r cannot be greater than 200, this is sufficient
Lets see statement 2
The correct way to check is, if A > B,
but since we are only given A > $\frac{2}{5}B$, so this is insufficient.
The answer is A , Statement 1 is sufficient and Statement 2 is insufficient

Correct Answer: A

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