What This Episode Covers
In Episode 12 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 substitution question asking for the value of $-3x^2$ when $x = -3$, a fraction with $29^2 + 29$ in the numerator, and a system of equations asking for the value of $t$ that makes $x = y$. The thread running through all three is execution: the math is middle school familiar, and the wrong answers exist because execution slips, not because knowledge does.
The episode builds the habit set one problem at a time. Parentheses around everything plugged in for a variable, demonstrated on a substitution question where the two wrong answers (27 and 81) are both un-parenthesized readings of the same expression. The two legal routes through a fraction with a sum on top, splitting it apart or factoring the numerator first, and the illegal one-term cancellation that produces 58. And the scratch-work layout of writing every operation under both sides of an equation, the habit that protects the last line of an algebra solve, introduced alongside the story of how that habit got built: by missing questions like these until the pain of changing the behavior beat the pain of changing the outcome.
Problems Covered
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"If $x = -3$, what is the value of $-3x^2$?" Parentheses around the substitution make the base of the exponent the full negative three, so $(-3)^2 = 9$ and $-3 \times 9 = -27$. The answer is (A). Dropping the parentheses produces 27 (choice D), and executing left to right produces 81 (choice E), which about 7% of test takers pick.
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"What is the value of $\frac{29^2 + 29}{29}$?" Two correct rearrangements: split the fraction into $\frac{29^2}{29} + \frac{29}{29} = 29 + 1$, or factor the numerator into $29(29 + 1)$ and cancel. Both give 30, the answer (E). Canceling the denominator against just the $29^2$ gives $29 + 29 = 58$ (choice C), picked by about 4%.
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"If $x = 1 - 3t$ and $y = 2t - 1$, for what value of $t$ does $x = y$?" Set the expressions equal ($1 - 3t = 2t - 1$), add $3t$ and then 1 to both sides, then divide by 5: $t = \frac{2}{5}$. The answer is (D). Inverting the fraction on the final line gives $\frac{5}{2}$ (choice A), picked by about 3%.
Key Takeaways
Parentheses around every substitution. The parentheses say the base of the exponent is the full negative three, and both wrong answers on the first problem come from un-parenthesized readings of it.
Split or factor before you cancel. Canceling is division, and division reaches every term. The split ($\frac{29^2}{29} + \frac{29}{29}$) and the factoring ($29(29 + 1)$) are the two legal routes through a sum on top, and both arrive at 30.
Write every operation under both sides. The inverted-fraction error survives because everything before it was right. A written $\div 5$ under each side makes the final line a recorded, checkable step.
Easy questions cost more when missed. The scoring algorithm weighs a question's difficulty, so the questions that feel like free points are the ones the habits need to protect.
Knowledge and execution are different skills. Over 90% of test takers solve the third problem's algebra correctly, and about 3% still submit an inverted fraction, so knowing the method doesn't guarantee executing it.
Related Reading
- GMAT® Execution Habits: The Scratch-Work System for Easy Questions
- "If x = -3, What Is the Value of -3x²?"
- "What Is the Value of (29² + 29)/29?"
- "If x = 1 - 3t and y = 2t - 1, for What Value of t Does x = y?"
- How Writing Down More Improves Your GMAT® Score
- Be Accurate to Improve Your GMAT® Score: Why Precision Comes Before Speed