Multiple Choice
Single Answer Strategy
Master the strategic techniques that top GRE scorers use to solve quantitative multiple choice problems faster and more accurately.
GRE Quantitative
What is a Single Answer MC Question?
On the GRE Quantitative section, Multiple Choice (Single Answer) questions present you with a problem and exactly five answer choices labeled (A) through (E). You must select one and only one correct answer.
Why Strategy Matters
The GRE is a timed test: you have roughly 1.75 minutes per question. Brute-force algebra wastes precious time. Strategic approaches let you find the answer in half the time or rescue a problem you'd otherwise skip.
Speed
Back-solving and estimation can cut solve time from 3 minutes to under 1 minute.
Accuracy
Plugging in values avoids algebraic errors that trap careless solvers.
Rescue
Even if you forget a formula, elimination and estimation can identify the answer.
Anatomy of an MC Question
The Five Core Strategies
1
Back-Solving. Plug answer choices into the problem. Start with (C) to bracket.
2
Plugging In Numbers. Replace variables with concrete values to simplify algebra.
3
Estimation and Approximation. Use rounding and magnitude checks to eliminate choices.
4
Strategic Elimination. Remove impossible answers using number properties (sign, parity, magnitude).
5
Direct Solve. When the math is straightforward, solve directly: don't over-strategize.
Back-Solving vs Plugging In
| Back-Solving | Plugging In | |
|---|---|---|
| When to use | Choices are specific numbers | Problem uses variables or "must be true" |
| How it works | Test choices in the equation | Choose your own numbers for variables |
| Start with | Choice (C) (middle value) | Simple numbers: \(2, 3, 5, 10\) |
| Best for | "What is the value of \(x\)?" | "Which expression equals...?" |
| Risk | Time if no clear bracket | Accidental match with wrong choice |
The Decision Flowchart
Step-by-Step Approach
1
Read carefully. Identify what's being asked. Circle the key constraint or "find" statement.
2
Glance at choices. Are they numbers, expressions, or ranges? This tells you which strategy to use.
3
Eliminate first. Cross out any choice that violates obvious constraints (wrong sign, too big, not an integer).
4
Apply your strategy. Back-solve, plug in, estimate, or solve directly.
5
Verify once. Plug your chosen answer back into the original conditions to confirm.
Example 1: Back-Solving
1
Start with (C): Test \(x = 5\). Compute \(3(5) + 7 = 15 + 7 = 22\). ✓
2
It works! The left side equals 22, which matches the right side.
3
Answer: (C). We solved it in one test: no algebra needed.
Example 2: Plugging In Numbers
1
Choose \(n = 4\). A positive even integer: simple and concrete.
2
Evaluate each choice: (A) \(4+2=6\) (even). (B) \(2(4)+1=9\) (odd ✓). (C) \(4^2=16\) (even). (D) \(3(4)=12\) (even). (E) \(\frac{4}{2}=2\) (even).
3
Verify with \(n = 2\): (B) gives \(2(2)+1 = 5\), still odd. Confirmed: Answer is (B).
Example 3: Estimation
1
Benchmark: \(12^2 = 144\) and \(13^2 = 169\). So \(\sqrt{150}\) is between 12 and 13.
2
Refine: \(150\) is much closer to \(144\) than to \(169\), so the answer is closer to 12.
3
Only (B) 12.2 falls in the range \([12, 13]\). Eliminate all others instantly.
Elimination Techniques
Sign Check
If the answer must be positive, eliminate all negative choices immediately.
Parity Check
If \(x\) is even, then \(x + 1\) is odd. Eliminate choices with wrong parity.
Magnitude Check
A 10% discount on $80 can't be $60. Quick mental math rules out extreme values.
Units Digit
The product of two numbers ending in 3 and 7 ends in 1. Check last digits to eliminate.
When to Solve Directly
Not every problem needs a trick. Direct solving is the fastest path when the math is clean and familiar. Recognize these patterns:
Simple Equations
One-step or two-step linear equations: just solve. Example: \(2x - 5 = 11\).
Known Formulas
Area, perimeter, percent change: plug values into the formula you know.
Clean Factoring
If you spot \(x^2 - 9 = (x-3)(x+3)\), factor immediately.
Common Mistakes to Avoid
Not Reading All Choices
Jumping to the first choice that "looks right" without checking the rest. A closer answer may be hiding in (D) or (E).
Solving Every Problem Algebraically
Spending 3 minutes on algebra when back-solving would take 30 seconds. Always check if the choices offer a shortcut.
Forgetting to Verify
Choosing an answer without plugging it back in. Trap answers are designed to catch arithmetic slips.
Picking the Trap Answer
The GRE includes a "partial solve" distractor: the value you'd get if you solved only half the problem. Always finish the full calculation.
Strategy Summary
| Strategy | Best When | Time Saved |
|---|---|---|
| Back-Solve | Numerical choices, "find \(x\)" | High |
| Plug In Numbers | Variable expressions, "must be true" | High |
| Estimation | Spread-out choices, square roots, percents | Medium |
| Elimination | Always: use as first pass on every problem | Medium |
| Direct Solve | Simple algebra, known formulas | Varies |
Question 1 of 5
If \(x^2 - 5x + 6 = 0\), which of the following is a possible value of \(x\)?
The equation factors as \((x-2)(x-3)=0\), giving \(x=2\) or \(x=3\). Using back-solving: plug in \(x=2\) to get \(2^2 - 5(2) + 6 = 4-10+6=0\) ✓. Answer: (B).
Question 2 of 5
A store marks up the wholesale price of an item by 40% and then offers a 20% discount on the marked price. The final price is what percent of the wholesale price?
Plug in: Let wholesale = $100. Marked up 40%: $140. Then 20% off: \(\$140 \times 0.80 = \$112\). That's 112% of wholesale. The trap answer (D) 120% comes from incorrectly subtracting the percentages (\(40\% - 20\% = 20\%\)): a common error.
Question 3 of 5
If \(n\) is a positive integer, which of the following must be divisible by 3?
Plug in strategy: Try \(n=1\): (A) 2, (B) 2, (C) 2, (D) \(1(2)(3) = 6\), (E) 0. Try \(n=2\): (A) 3 ✓, (B) 4, (D) \(2(3)(4) = 24\) ✓. Try \(n=4\): (A) 5. Only (D) works every time because three consecutive integers always include a multiple of 3.
Question 4 of 5
Which strategy is most appropriate when the answer choices are algebraic expressions involving a variable \(k\)?
Plugging in numbers is ideal when choices contain variables. Choose a concrete value for \(k\) (like \(k = 3\)), compute the question's target value, then evaluate each expression to find the match. Back-solving requires numerical choices, so it doesn't apply here.
Question 5 of 5
A train travels at 60 mph for the first half of a journey (by distance) and 40 mph for the second half. What is the train's average speed for the entire journey?
Elimination first: The average of 60 and 40 is 50, but that's only true for equal times. Since the train spends more time at the slower speed, the average must be below 50. Eliminate (C), (D), (E). Now plug in: let total distance = 120 miles. First half: 60 mi at 60 mph = 1 hr. Second half: 60 mi at 40 mph = 1.5 hr. Average = \(\frac{120 \text{ miles}}{2.5 \text{ hours}} = 48\) mph. Answer: (B).