How to Solve GRE/GMAT Word Problems: The Complete Strategy Guide

How to Solve GRE/GMAT Word Problems: The Complete Strategy Guide

(1,200+ words, actionable under timed conditions)

Introduction

"Word problems appear 8-10 times per GRE and 6-8 times per GMAT—master them, and you’ll gain 30-50 scaled points in Quant. This isn’t about math; it’s about decision-making under pressure."

WHAT THIS QUESTION TYPE IS ACTUALLY TESTING

The exam isn’t testing your ability to solve equations—it’s testing: 1. Translation speed: Can you convert words into math without errors in under 60 seconds? 2. Variable control: Can you assign variables without overcomplicating (e.g., avoiding 3+ variables when 1 suffices)? 3. Trap detection: Can you spot hidden constraints (e.g., "positive integers," "distinct values") that eliminate answer choices?

ANATOMY OF THE QUESTION

Every word problem has 4 parts:

Representative Example Question

"A bakery sells cupcakes and cookies. Each cupcake costs $2, and each cookie costs $1. If the bakery sold 50 items total and earned $70, how many cupcakes were sold?"

THE DECISION FRAMEWORK (Step-by-Step)

Run this process for every word problem. No exceptions.

Step 1: Assign Variables (10 seconds)

• Rule: Use 1-2 variables max. More = confusion.
• How:
• Let C = # of cupcakes, K = # of cookies (or use x and y if preferred).
• Pro tip: If the question asks for one item (e.g., "cupcakes"), let that be x.

Step 2: Translate Conditions into Equations (20 seconds)

• Rule: Write one equation per condition.
• How:
• Condition 1: "50 items total" → C + K = 50
• Condition 2: "$70 earned" → 2C + 1K = 70

Step 3: Solve the System (30 seconds)

• Rule: Use substitution (not elimination) for speed.
• How:
• From C + K = 50, get K = 50 – C.
• Substitute into 2C + K = 70:
  2C + (50 – C) = 70 → C = 20.

Step 4: Match to Answer Choices (5 seconds)

• Rule: Double-check units and question wording.
• How:
• C = 20 → Answer = (B) 20.

Step 5: Verify (10 seconds, optional)

• Rule: Plug back into both conditions to confirm.
• How:
• C = 20, K = 30 → 20 + 30 = 50 items ✔️
• 2(20) + 1(30) = $70 ✔️

Total time: ~75 seconds.

Worked Examples

Example 1: Straightforward (GRE/GMAT Easy-Medium)

"A farmer has chickens and rabbits. There are 30 heads and 80 legs in total. How many rabbits are there?"

Step 1: Assign Variables

• Let C = chickens, R = rabbits.

Step 2: Translate Conditions

• Heads: C + R = 30
• Legs: 2C + 4R = 80 (chickens = 2 legs, rabbits = 4 legs)

Step 3: Solve

• From C + R = 30, get C = 30 – R.
• Substitute into 2C + 4R = 80: 2(30 – R) + 4R = 80 → 60 – 2R + 4R = 80 → 2R = 20 → R = 10.

Step 4: Match Answer

• R = 10 → Answer = (B) 10.

Step 5: Verify

• C = 20, R = 10 → 20 + 10 = 30 heads ✔️
• 2(20) + 4(10) = 80 legs ✔️

Example 2: Common Trap (GMAT Medium-Hard)

"A store sells pens and pencils. Pens cost $3 each, and pencils cost $1 each. If the store sold 100 items and earned $180, how many pens were sold?"

Step 1: Assign Variables

• Let P = pens, C = pencils.

Step 2: Translate Conditions

• Items: P + C = 100
• Revenue: 3P + 1C = 180

Step 3: Solve

• From P + C = 100, get C = 100 – P.
• Substitute into 3P + C = 180: 3P + (100 – P) = 180 → 2P = 80 → P = 40.

Step 4: Match Answer

• P = 40 → Answer = (D) 40.

Trap Detection

• Wrong answer (C) 30: Comes from misreading the question as "pencils sold."
• Wrong answer (E) 60: Comes from reversing the variables (3C + P = 180).

Example 3: Hard Variant (GMAT 700+)

"A train travels from City A to City B at 60 mph. On the return trip, it travels at 40 mph. If the total travel time is 5 hours, what is the distance between the cities?"

Step 1: Assign Variables

• Let D = distance (one way).

Step 2: Translate Conditions

• Time to B: D/60
• Time back to A: D/40
• Total time: D/60 + D/40 = 5

Step 3: Solve

• Find common denominator (120): (2D + 3D)/120 = 5 → 5D = 600 → D = 120.

Step 4: Match Answer

• D = 120 miles → Answer = (C) 120.

Trap Detection

• Wrong answer (A) 100: Comes from averaging speeds (60 + 40)/2 = 50 mph, then 50 5 = 250 → 250/2 = 125 (close but wrong).
• Wrong answer (E) 240: Comes from adding distances (D + D = 240) without considering time.

WRONG ANSWER PATTERNS

Common Mistakes

TIME STRATEGY

BACKSOLVING AND SHORTCUTS

1. Backsolving (Answer Choices First)

• When to use: When the question asks for a specific value (e.g., "how many cupcakes?").
• How:
• Start with B or D (middle values).
• Plug into the easier condition first (e.g., total items = 50).
• If it works, check the second condition (e.g., revenue = $70).
• If not, eliminate and move to the next choice.

Example (Bakery Problem): - Try B) 20 cupcakes: - 20 cupcakes + 30 cookies = 50 items ✔️ - 2(20) + 1(30) = $70 ✔️ → Correct.

2. Number Substitution

• When to use: When the question has variables in answer choices (e.g., "Which of the following could be the value of x?").
• How:
• Pick easy numbers (e.g., x = 2, y = 3).
• Solve the problem with those numbers.
• Plug the same numbers into the answer choices to find a match.

3. Elimination First

• When to use: When the question has obvious traps (e.g., unit mismatches, partial answers).
• How:
• Scan answer choices for:
  • Units that don’t match (e.g., hours vs. minutes).
  • Values that violate constraints (e.g., "positive integers" but answer is negative).
• Eliminate 2-3 choices before solving.

1-Minute Recap

"Here’s your 60-second word problem battle plan:

1. Assign variables fast—one for what the question asks. No more than two.
2. Write two equations—one for each condition. If you can’t, you missed a constraint.
3. Solve with substitution—plug one equation into the other. No fancy elimination.
4. Match the answer—double-check units and question wording. No autopilot.
5. Verify if time—plug back into both conditions. If it doesn’t work, you messed up.

Traps to watch for: - Partial answers—they match one condition but not both. - Unit mismatches—hours vs. minutes, miles vs. km. - Variable reversal—pens vs. pencils, trains vs. buses.

If you’re stuck after 90 seconds, eliminate the worst two answers and guess. Move on. This isn’t about perfection—it’s about points per minute.

Now go practice. Your next word problem is waiting."