"If x = -3, What Is the Value of -3x²?" — GMAT® Worked Solution

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

If $x = -3$, what is the value of $-3x^2$?

(A) $-27$

(B) $-18$

(C) $18$

(D) $27$

(E) $81$

Try it before reading on.

Step 1: Plug In With Parentheses

The problem hands over the value of $x$, so the work is substitution, and the habit worth building starts here: parentheses around whatever gets plugged in. Since $x = -3$, the expression $-3x^2$ becomes

$-3(-3)^2$

The parentheses carry information. They say the base of the exponent is negative three, all of it, and that detail decides the answer.

Step 2: Exponents Before Multiplication

Order of operations puts the exponent first, and the parenthesized base makes the exponent's scope unambiguous:

$(-3)^2 = 9$

Two negatives multiplied together make a positive, so the square of negative three is positive nine. Multiplication comes last:

$-3 \times 9 = -27$

The answer is (A).

Step 3: Where the Wrong Answers Come From

Both major wrong answers come from a version of this problem with the parentheses left out.

Drop the parentheses and the substitution reads $-3 \times -3^2$. By the standard convention, an exponent attaches to the number directly under it, so $-3^2$ means $-(3^2)$, which is $-9$. That path produces $-3 \times -9 = 27$, and there's choice (D) waiting.

The other wrong turn executes left to right: $-3 \times -3$ first, which makes $9$, and then squaring at the end, which makes $81$. That's choice (E), and about 7% of test takers pick it.

Why This Problem Matters

The math underneath fits in two lines, and that's the point of the episode it comes from: on easy questions, execution can decide the outcome. About 7% of test takers pick (E), and another few percent pick (D), which puts roughly one person in ten on a wrong answer here. The scoring algorithm factors a question's difficulty into the score, so misses on questions like this one cost more than misses on hard ones.

The parent article calls the parentheses habit the first execution habit in the set, and this question shows why: without the parentheses, two of the five choices come into play; with them, neither can. It's a habit worth using on every substitution, including the ones that seem to go fine without it.

Ready for the next one? "What Is the Value of (29² + 29)/29?" — GMAT® Worked Solution.

Want the full strategy? Read: GMAT® Execution Habits: The Scratch-Work System for Easy Questions

From Episode 12 of Real GMAT® Problems (The GMAT® Strategy Podcast).