10.2 Multiple-Choice — Select One Answer

10.2 Multiple-Choice - Select One Answer

Quick Answer: 5 choices, exactly one correct. Solve first, then match (predict-then-match). If choices are numeric and ordered, backsolve from the middle. For NOT/EXCEPT, use POE. Target 60-90 seconds per question.

Format Basics

Multiple-Choice - Select One Answer (MC-Single) presents 5 answer choices labeled (A) through (E) with exactly one correct response. This format appears roughly 12-15 times per scored Quant section and is the format most students recognize from other standardized tests. You must select exactly one bubble; selecting more than one forfeits the question, even if one of your selections is correct.

Strategy 1: Predict-Then-Match

The single most reliable MC-Single strategy is to solve the problem first (without looking at the choices), then scan the choices for your value. This protects you from well-designed distractors engineered to catch a partial calculation or a common mistake.

Worked Example 1

If 3x + 7 = 22, what is x?

• Solve: 3x = 15, x = 5.
• Now scan the choices: (A) 3, (B) 5, (C) 7, (D) 15, (E) 22.
• Match: (B) 5.

Had you looked at choices first, distractor (D) 15 catches students who stop after 3x = 15, and distractor (E) 22 catches students who subtract 7 from the wrong side. Predict-then-match sidesteps both traps.

Strategy 2: Backsolving

When the answer choices are numeric and (especially) ordered from smallest to largest, plug the MIDDLE choice into the problem first. Based on whether the result is too big or too small, move to a higher or lower choice. This turns algebra into arithmetic and eliminates the risk of setting up the wrong equation.

Worked Example 2

A shirt is on sale for 40% off. The sale price is $36. What was the original price?

Choices: (A) $21.60, (B) $50, (C) $60, (D) $72, (E) $90.

• Test the middle, (C) $60: 60 - 0.40(60) = 60 - 24 = 36. That matches the sale price exactly.
• Answer: (C) $60.

If (C) had given a sale price too high, you would move to (D) or (E); too low, move to (A) or (B). At most two tests are needed for 5 ordered choices.

Strategy 3: Estimation

When the choices are far apart, estimate aggressively. The on-screen calculator's failure to respect order of operations makes exact computation error-prone; estimation is often faster and safer.

Worked Example 3

Estimate (498 x 51) / 99.

• 498 is about 500, 51 is about 50, 99 is about 100.
• 500 x 50 = 25,000; 25,000 / 100 = 250.
• Choices: (A) 25, (B) 250, (C) 2,500, (D) 25,000, (E) 250,000.
• Answer: (B) 250.

Estimation also exposes magnitude errors. If your computed answer is 2,500 but the choices are clustered near 250, you likely misplaced a decimal.

Strategy 4: Process of Elimination (POE)

Eliminate choices you can prove wrong quickly. POE is especially powerful on:

• NOT/EXCEPT questions: three of four statements are true; eliminate the three true ones to find the false one.
• Word problems with unrealistic distractors: if a question about a person's age has choices including 250 and -3, eliminate those immediately.
• Geometry with impossible values: a triangle's angle sum is 180 degrees; any choice implying a single angle of 200 degrees is out.

Worked Example 4 (NOT/EXCEPT)

Which of the following is NOT a factor of 60?

(A) 4, (B) 6, (C) 8, (D) 10, (E) 12.

• 60 / 4 = 15 (integer) - 4 is a factor, eliminate (A).
• 60 / 6 = 10 (integer) - 6 is a factor, eliminate (B).
• 60 / 8 = 7.5 (not integer) - 8 is NOT a factor.
• Answer: (C) 8.

NOT/EXCEPT framing is rare on the GRE compared to tests like the SAT, but when it appears it is usually in number theory or data interpretation. Read the question stem carefully - missing the word "NOT" is the most common error on this question type.

Strategy 5: Watch for "No Solution" and Identity Cases

Occasionally the GRE frames a question so that no listed choice matches the true answer. This is rare but does happen, typically in:

• Inequalities with no solution (e.g., |x - 3| < -1).
• Equations that reduce to a tautology (e.g., 2x + 4 = 2(x + 2) - true for all x).
• "None of the above" framings, which the GRE uses sparingly but does appear.

If your computed answer matches none of the choices, re-read the question for a missed constraint or sign error. If still no match, choose "none" if it is offered; if not, you likely made an error - recompute carefully.

Pacing and Mark-and-Review

Target 60-90 seconds per MC-Single question. If a question still resists at 90 seconds:

1. Mark it for review (the GRE interface has a mark button; marked questions appear in the review screen at the end).
2. Pick a strategic guess - eliminate what you can and choose among the rest.
3. Move on. A single hard question is not worth sacrificing two easier ones later.

Within the Quant section, you CAN move forward and back within the current section. Use the review screen at the end to revisit marked questions with fresh eyes - often the second look reveals a simplification you missed the first time.

Calculator Caution

The on-screen calculator does NOT respect order of operations. If you type 2 + 3 x 4, it computes (2 + 3) x 4 = 20, not 2 + 12 = 14. Use parentheses liberally or compute intermediate results and re-enter them. For MC-Single, where a single arithmetic slip selects a distractor, treat the calculator as a last resort - estimation and mental math are often faster and less error-prone for arithmetic that fits in your head.