"In a Horticultural Experiment, 200 Seeds Were Planted in Plot I..." — GMAT® Worked Solution

Source: Official Guide for GMAT® Review, 11th Edition

In a horticultural experiment, 200 seeds were planted in plot I and 300 were planted in plot II. If 57 percent of the seeds in plot I germinated and 42 percent of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?

(A) 45.5%

(B) 46.5%

(C) 48.0%

(D) 49.5%

(E) 51.0%

Try it before reading on.

Step 1: Translate the Question Into an Equation

The percent translations run the setup here, one word at a time. The full walkthrough lives in "What Percent of 30 Is 12?" — GMAT® Worked Solution; the short version:

• what introduces a variable, $P$, that nothing else in the problem uses
• percent puts it over 100, so $\frac{P}{100}$
• of the total number of planted seeds multiplies by 500, because $200 + 300 = 500$
• germinated is the count on the other side of the equal sign, call it $G$

The equal sign gets inferred here: "what percent of the total" and "the number that germinated" are the same quantity written two ways, which produces:

$\frac{P}{100} \times 500 = G$

If the fraction $\frac{G}{500}$ appeared intuitively instead, that route works too; it's the same equation rearranged. The translation is the version to have ready for the questions where intuition stalls.

Step 2: Count the Germinated Seeds in Each Plot

Plot I holds 200 seeds at 57%. Setting the percent up as a fraction keeps the canceling visible:

$\frac{57}{100} \times \frac{200}{1} = 57 \times 2 = 114$

Two zeros cancel between the 200 and the 100, and the multiplication shrinks to $57 \times 2$.

Plot II holds 300 seeds at 42%:

$\frac{42}{100} \times \frac{300}{1} = 42 \times 3 = 126$

Same move: cancel two zeros, multiply by 3.

Step 3: Add and Solve for P

The two plots germinated $114 + 126 = 240$ seeds in total, which is the value of $G$:

$\frac{P}{100} \times 500 = 240$

On the left side, $\frac{500}{100}$ cancels to 5:

$5P = 240$

Divide both sides by 5:

$P = \frac{240}{5} = 48$

The answer is (C).

Where the Wrong Answers Come From

The stocked wrong answer is choice (D) at 49.5%, which is the simple average of 57 and 42. Averaging the two percents treats both plots as the same size, and they aren't: 300 seeds at 42% contribute 126 germinated seeds against 114 from the 200 seeds at 57%. The blended rate should sit closer to 42 than to 57, below the midpoint of 49.5, and 48.0 does. The weighting check doubles as the trap check.

Choice (E) at 51.0% comes from swapping the plots: 57% of 300 plus 42% of 200 is $171 + 84 = 255$, and $\frac{255}{500} = 51\%$. The arithmetic runs cleanly to a wrong answer because the error happened at setup, before any computation.

Both wrong answers are setup errors rather than computation errors, which is the case for writing the translation down before computing: the equation on the page keeps the percents attached to the right plots, and keeps the blend honest about plot size.

Why This Problem Matters

Structurally, the approach is fixed: count the germinated seeds in each plot, add the counts, and divide by the 500 seeds planted. Plenty of computational routes can get there, but the structure stays the same, and the misses happen at setup. A percent attached to the wrong plot, or the two rates averaged without weighting, produces a wrong answer as cleanly as the right one.

An inconsistent translation has a specific cost. The wrong fraction produces a wrong number, the number isn't among the choices, and the question gets solved twice, once wrong and once right. The translations cost a few seconds up front. The reboot costs a question's worth of time.

Want the full strategy? Read: GMAT® Setup Habits: The Question-First System

From Episode 13 of Real GMAT® Problems (The GMAT® Strategy Podcast).