📘 Lesson 1.2: Master the Big Three Strategies (Estimation, Backsolving, Plugging In)
🎯 Learning Objectives
By the end of this lesson, you will:
- Master the three most powerful GMAT Quant strategies that can solve 70%+ of problems
- Know exactly when and how to apply each strategy for maximum efficiency
- Develop the strategic mindset that separates 700+ scorers from average test-takers
- Build timing discipline that keeps you on track for all 21 questions
🧠 The Strategic Revolution: Why These Three Matter
The GMAT Focus Edition rewards strategic thinking over computational prowess. While other students get bogged down in complex calculations, you’ll use these three game-changing approaches to solve problems in under 90 seconds.
The Power of Strategic Thinking:
- Traditional Approach: Set up equations, solve algebraically, verify answer
- Strategic Approach: Eliminate wrong answers quickly, find shortcuts, work backwards
- Time Savings: 60-90 seconds per strategic solve vs. 2-3 minutes traditional
- Accuracy Boost: Less calculation = fewer careless errors
🎯 Strategy #1: Strategic Estimation
When to Use: Number-heavy problems, percentage calculations, problems with “approximately” or “closest to”
The Estimation Hierarchy
| Estimation Level | When to Use | Accuracy Target | Time Savings |
|---|---|---|---|
| Rough (±20%) | Eliminate obviously wrong answers | Get within ballpark | 30-45 seconds |
| Refined (±10%) | Narrow to 2-3 choices | Close approximation | 45-60 seconds |
| Precise (±5%) | Final answer selection | Near-exact value | 60-90 seconds |
Master Estimation Techniques
1. Friendly Number Substitution
Replace complex numbers with calculation-friendly alternatives.
Example Problem:
A store increases prices by 18% then offers a 22% discount. What’s the net effect?
Strategic Solution:
- Use 20% instead of 18%: 1.20 × original
- Use 20% instead of 22%: × 0.80 discount
- Net effect: 1.20 × 0.80 = 0.96 = 4% decrease
- Answer range: 3-5% decrease
2. Percentage Anchoring
Use benchmark percentages (10%, 25%, 50%) as reference points.
Power Benchmarks to Memorize:
- 10% ↔ 0.1 ↔ 1/10
- 25% ↔ 0.25 ↔ 1/4
- 33⅓% ↔ 0.333… ↔ 1/3
- 50% ↔ 0.5 ↔ 1/2
- 66⅔% ↔ 0.666… ↔ 2/3
3. Scientific Notation Shortcuts
Handle large/small numbers efficiently.
Quick Powers Reference:
- 10³ = 1,000 (thousand)
- 10⁶ = 1,000,000 (million)
- 10⁹ = 1,000,000,000 (billion)
🔄 Strategy #2: Backsolving (Working Backwards)
When to Use: Word problems with numerical answer choices, especially when setting up equations seems complex
The Backsolving Decision Tree
Is it a word problem with numerical answers?
↓ YES
Are the answer choices in ascending/descending order?
↓ YES
Can you easily test values in the original problem?
↓ YES
→ USE BACKSOLVING
Backsolving Execution Strategy
Step 1: Start Smart
- Always begin with (C) – middle value
- If (C) is too big → try (A) or (B)
- If (C) is too small → try (D) or (E)
- Maximum attempts: Usually 2-3 tests needed
Step 2: Efficient Testing
Create a systematic approach for substituting values back into the original conditions.
Master Example Walkthrough
Problem:
John has 3 times as many apples as oranges. If he gives away 6 apples and 2 oranges, he has twice as many apples as oranges. How many apples did he start with?
- A) 12
- B) 18
- C) 24
- D) 30
- E) 36
Strategic Backsolving Solution:
Test (C) 24 apples:
- If 24 apples, then 24÷3 = 8 oranges initially
- After giving away: 24-6 = 18 apples, 8-2 = 6 oranges
- Check condition: Is 18 = 2×6? ✅ YES!
- Answer: C) 24
Time: 45 seconds vs. 2+ minutes with algebra
Advanced Backsolving Techniques
1. Boundary Testing
When dealing with inequalities, test extreme values first.
2. Pattern Recognition
Look for answer choices that follow arithmetic or geometric patterns.
3. Unit Analysis
Verify that your tested value produces the correct units in the final answer.
🔌 Strategy #3: Strategic Number Plugging
When to Use: Problems with variables in answer choices, abstract algebraic expressions, “must be true” questions
The Number Selection Framework
| Problem Type | Recommended Numbers | Why These Work |
|---|---|---|
| General Cases | 2, 3, 10, 100 | Easy calculation, reveal patterns |
| Even/Odd | 2, 4, 6 vs 1, 3, 5 | Test parity conditions |
| Positive/Negative | 2, -2, 10, -10 | Check sign behavior |
| Fractions | 1/2, 1/3, 2/3 | Between 0 and 1 |
| Special Cases | 0, 1, -1 | Often reveal edge behaviors |
Strategic Plugging Process
Phase 1: Smart Number Selection (20 seconds)
Choose numbers that make calculations simple but test the mathematical relationship.
Phase 2: Systematic Testing (60 seconds)
Test your chosen numbers in both the problem condition and each answer choice.
Phase 3: Pattern Recognition (30 seconds)
Look for which answer choice consistently matches your calculated results.
Master Example Walkthrough
Problem:
If x and y are positive integers and x > y, which expression is always greater than 1?
- A) x/y
- B) (x+1)/(y+1)
- C) x/(y+1)
- D) (x+1)/y
- E) (x-1)/y
Strategic Plugging Solution:
Test Case 1: x = 3, y = 2
- (A) 3/2 = 1.5 ✓
- (B) 4/3 ≈ 1.33 ✓
- (C) 3/3 = 1 ✗
- (D) 4/2 = 2 ✓
- (E) 2/2 = 1 ✗
Test Case 2: x = 2, y = 1
- (A) 2/1 = 2 ✓
- (B) 3/2 = 1.5 ✓
- (D) 3/1 = 3 ✓
Test Case 3: x = 10, y = 9 (close values)
- (A) 10/9 ≈ 1.11 ✓
- (B) 11/10 = 1.1 ✓
- (D) 11/9 ≈ 1.22 ✓
Answer: Need to test edge cases, but (D) consistently produces the largest values. (Note: A more rigorous approach might be needed to definitively prove it’s *always* greater than 1, but plugging helps narrow down quickly.)
⚡ Strategy Integration: The Decision Matrix
Quick Strategy Selection Guide
| Problem Characteristics | First Choice | Backup Strategy | Avoid |
|---|---|---|---|
| Numerical answers, word problem | Backsolving | Estimation | Plugging |
| Variables in answers | Plugging | Algebra | Backsolving |
| “Approximately” in question | Estimation | Calculation | Complex algebra |
| Time pressure (<90 sec left) | Estimation | Educated guess | Any lengthy method |
The 30-Second Decision Protocol
Within 30 seconds of reading, ask:
- Are the answer choices numerical and ordered? → Backsolving
- Are there variables in the answer choices? → Plugging
- Can I estimate to eliminate obviously wrong answers? → Estimation
- None of the above? → Traditional algebraic approach
🚨 Common Strategy Mistakes & Solutions
Mistake #1: Strategy Overuse
- Problem: Using backsolving on every problem, even when algebra is faster
- Solution: Master the decision matrix above – some problems are faster with direct calculation
Mistake #2: Poor Number Choice in Plugging
- Problem: Choosing numbers that make calculations complex (like 7, 13, 17)
- Solution: Stick to the recommended number sets unless testing specific conditions
Mistake #3: Incomplete Estimation
- Problem: Stopping after eliminating 2-3 choices instead of finding the answer
- Solution: Use estimation hierarchy – start rough, then refine as needed
Mistake #4: No Time Awareness
- Problem: Spending 3+ minutes on strategic approaches that should save time
- Solution: Set 90-second maximum per problem, then guess and move on
📊 Strategy Efficiency Analysis
Time Investment vs. Payoff
| Strategy | Learning Time | Per-Problem Time Savings | Accuracy Boost | Problems Applicable |
|---|---|---|---|---|
| Estimation | 2-3 hours | 30-60 seconds | +15% | 40-50% of problems |
| Backsolving | 3-4 hours | 60-90 seconds | +20% | 25-30% of problems |
| Plugging | 4-5 hours | 45-75 seconds | +25% | 30-35% of problems |
ROI Ranking for Study Time:
- Estimation (fastest to learn, broadly applicable)
- Backsolving (moderate learning curve, high impact)
- Plugging (longer learning curve, very powerful for specific problems)
🎯 Practice Integration Protocol
Week 1: Foundation Building
- Day 1-2: Master estimation techniques with 20 practice problems
- Day 3-4: Learn backsolving with 15 practice problems
- Day 5-7: Strategic number plugging with 15 practice problems
Week 2: Integration & Speed
- Day 1-3: Mixed strategy practice (30 problems)
- Day 4-5: Timed strategy selection (21-question sets)
- Day 6-7: Full-length practice tests with strategy tracking
Ongoing Mastery
- Track which strategies you use most successfully
- Identify personal pattern preferences (visual vs. numerical learner)
- Refine timing on your strongest strategic approaches
🏆 Advanced Strategy Combinations
The Estimation-Backsolving Combo
- Use estimation to eliminate 2-3 obviously wrong answers
- Backsolve only the remaining plausible choices
- Result: Faster backsolving with higher accuracy
The Plugging-Verification Combo
- Use strategic plugging to identify the likely answer
- Verify with one additional test case or quick algebra
- Result: Confidence in complex abstract problems
📋 Strategy Mastery Checklist
✅ Estimation Mastery:
✅ Backsolving Mastery:
✅ Strategic Plugging Mastery:
🚀 Ready for Lesson 1.3?
You now possess the three most powerful weapons in the GMAT Quant arsenal. These strategies alone can boost your score by 50-100 points when applied consistently.
Coming up in Lesson 1.3: Learn how to recognize the specific problem patterns that signal which strategy to use, plus advanced timing techniques that ensure you never run out of time.
💡 Pro Tip: Print out the Strategy Decision Matrix and keep it handy during your first 50 practice problems. After that, the decision process becomes automatic and takes just 5-10 seconds per problem.