What This Episode Covers
In Episode 13 of the Real GMAT® Problems series, Isaac works through three real GMAT® problems from the 11th edition of the Official Guide for GMAT® Review: a circular region with two unshaded sections ($\frac{3}{7}$ and $\frac{1}{3}$) asking for the shaded fraction, the expression $\frac{(0.3)^5}{(0.3)^3}$, and a horticultural experiment where 200 seeds in plot I and 300 in plot II germinate at 57% and 42%. The thread running through all three is setup: the math is grade-school familiar, and the wrong answers come from solving a slightly different problem than the one on the screen.
The episode builds the case for one habit above all: write what the question asks before any math. The circle problem stocks a wrong answer for combining the labeled fractions instead of subtracting them from the whole, and about 3% of test takers pick it. The seeds problem stocks wrong answers for averaging the two percents (49.5) and for swapping the plots (51.0). The exponent problem's most popular wrong answer (0.9) is the correct multiplication with the decimal moved one place instead of two. Along the way: what geometry looks like on the current exam, why the exponent shortcut counts surviving factors, and the full percent translations, word by word.
Problems Covered
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"The shaded section comprises what fractional part of the area of the circular region?" Subtract the unshaded sections from one whole: $\frac{21}{21} - \frac{9}{21} - \frac{7}{21} = \frac{5}{21}$. The answer is (D). Choice (E), $\frac{16}{21}$, is the sum of the two labeled fractions, the unshaded area, picked by about 3% of test takers.
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"$\frac{(0.3)^5}{(0.3)^3}$?" Same base means subtract exponents: $(0.3)^2 = 0.09$. The answer is (C). Choice (D), 0.9, is the most common incorrect answer: the right multiplication with the decimal moved one place instead of two. Choice (E) comes from canceling the bases outright.
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"In a horticultural experiment, 200 seeds were planted in plot I and 300 were planted in plot II..." Plot I germinates $0.57 \times 200 = 114$ seeds, plot II germinates $0.42 \times 300 = 126$, and $\frac{240}{500} = 48%$. The answer is (C). Averaging 57% and 42% gives 49.5% (choice D), and swapping the plots gives 51.0% (choice E).
Key Takeaways
Write the question before the math. The first line of scratch work is what the question asks: shaded = ?, or the translated percent equation. It costs two seconds and prevents the most expensive mistake pattern on easy questions, answering a question the problem didn't ask.
One consistent translation per pattern. "What" introduces a variable, "percent" means divided by 100, "of" means multiply, "is" means equals. A method used every time is still available under time pressure; an improvised one is only as good as the improvisation.
Keep the computation on the page. Decimal placement and exponent canceling are exactly the steps mental math leaves unrecorded. The written version takes seconds longer and can be checked; the mental version can only be re-done.
Geometry on the current exam is usually one step. The circle problem wears geometry as a costume and solves like fractions. Volume and surface area still appear; the multi-step constructions from older editions mostly don't.