doomedcat wrote:

Gurdeep is organizing his sunflower seeds, petunia seeds, and daffodil seeds by volume. If the combined volume of all three seeds is 66 cm3, what is the volume of his daffodil seeds?

1) The volume of the petunia seeds is 10 percent of the combined volume of the sunflower and daffodil seeds

2) The volume of the daffodil seeds is 20 percent of the combined volume of the sunflower and petunia seeds

Official Solution (Credit: Manhattan Prep)

Even though the term “volume” is used, this problem is testing Percents, not geometry. Both of the statements reference percents, and you’re also given a total amount. Translate the question:

S + P + D = 66

D = ?

Each statement provides another equation involving these three unknowns. It’s tempting to assume that with three equations and three unknowns, everything is solvable so the answer must be choice (C). However, it can be dangerous to combine the statements too quickly. This question is a disguised Combos problem. It directly asks about only one variable, D, so rearrange the given equation to solve for D:

D = 66 – (S + P)

Solving for the combo (S + P) is also sufficient. C-traps are common in combo problems. Make sure to evaluate each statement individually.

(1) INSUFFICIENT: Translate the statement to solve algebraically:

P = 10/100(S + D)

P = 1/10(S + D) Substitute into equation for the total

S + (1/10(S + D)) + D = 66 Multiply by 10 to eliminate the fraction

10S + (S + D) + 10D = 660

11S + 11D = 660

S + D = 60

The value of D depends on S. You could infer that the volume of petunias is 6, but that gives no information about the volume of daffodils. Statement (1) is INSUFFICIENT. Eliminate choices (A) and (D).

(2) SUFFICIENT: Even though this statement has a similar structure to that given in Statement (1), it separates the volume of daffodils from the other two flower types. That separation may be enough to allow you to solve for the number of daffodils.

D = 20/100(S + P)

D = 1/5(S + P) Rearrange to solve for the combo (S + P)

5D = S + P Substitute (5D) into the equation for the total

(5D) + D = 66

6D = 66

D = 11

Statement (2) is SUFFICIENT. Eliminate choices (C) and (E).

The correct answer is (B).

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