We are trying to figure out if 15r > 20s.

Statement 1)
15s > 20r
(3/4)*15s > 20r * (3/4)
45s/4 > 15r
15r < 11.25s
Sufficient

Statement 2)
15r > (2/5)(20s)
15r > 8s
Insufficient

IMO Ans is A

Note do not use the variable \(s\), we can replace it with \(10 - r\).

Is \(15r > 20(10 - r)\)?

Is \(35r > 200\) ?

Is \(r > \frac{40}{7}\) ?

Statement 1:

\(15(10 - r) > 20r\)

\(35r < 150\). Thus we know \(35r\) cannot be greater than 200, sufficient.

Statement 2:

Essentially we want to check if A > B, but we are only given \(A > \frac{2}{5}B\) so this would be insufficient.

Ans: A
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Offical solution
Analyze the question stem

This Yes/No question presents the costs of Paint X and Paint Y and the variables r and s, which represent the number of gallons of each of the paints in 10 gallons of Mixture M. The question asks whether the cost of all of Paint X in the mixture is greater than the cost of all of Paint Y in the mixture. Since you know the price of each paint, you can say that 15r + 20s equals the total cost of the 10 gallons of Mixture M. Thus, the question is really asking "is 15r > 20s ?" Simplifying this inequality further yields 15r/20>s or "Is 3/4r>s ?"

Evaluate the statements

Combining Statement (1) with the prices per gallon in the question stem yields 15s > 20r; dividing both sides by 5 yields 3s > 4r, which can be further simplified to s>4/3r. This can be rewritten as 4/3r<s. Since r is a positive number (you cannot have a negative number of gallons of paint), 3/4r<4/3r<s , and thus the answer to the question "Is 3/4r>s?" is no. This statement is sufficient. Eliminate (B), (C), and (E).

Statement (2) can be restated as 15r>2/5×20s, which simplifies to 15r > 8s or 15/8r>s. Since 15/8r is much larger than 3/4r, this statement does not establish whether 3/4r>s , so it's not sufficient. (A) is correct.

TAKEAWAY: Turn words in the question stem and statements into math expressions before further evaluating them.