Estimation & Pacing

Strategy/Review

The Estimation Decision Rule

When you see answer choices, ask: "How far apart are they?"

• Far apart (at least 20-30% difference, or separated by orders of magnitude, or clearly distinct): ESTIMATE. Round numbers, use benchmarks, get the answer in 15-20 seconds, and move on.
• Close together (within 5-10% of each other, or differing only in the last digit): CALCULATE ACCURATELY. Estimation could push you to the wrong choice.

Example — Estimate: Question: 48 × 52 = ? Answers: (A) 496, (B) 996, (C) 2,496, (D) 24,996

Round: 48 ≈ 50, 52 ≈ 50. 50 × 50 = 2,500. The answer must be near 2,500. (C) 2,496 is the only plausible choice. Done in 10 seconds — no calculator needed.

But if the choices were: (A) 2,486, (B) 2,496, (C) 2,506, (D) 2,516, then estimation won't cut it — you need the calculator.

Example — Calculate: Question: √185 = ? Answers: (A) 12.8, (B) 13.2, (C) 13.6, (D) 14.0

Estimation: 13² = 169, 14² = 196. √185 is between 13 and 14, closer to 13.6? Actually 185 − 169 = 16, and 196 − 185 = 11, so it's closer to 14 than to 13. Rough interpolation: ~13.6. But with choices so close (0.4 apart), use the calculator for precision. √185 = 13.601... → (C).

Estimation Techniques

Rounding:

• Round to one or two significant figures.
• 4,876 × 31 ≈ 5,000 × 30 = 150,000 (actual: 151,156 — within 1%).
• Compensate: if you rounded one number up and one down, the errors partially cancel.

Order of Magnitude:

• What power of 10 is the answer? Is it in the hundreds, thousands, or millions?
• 0.0042 × 0.031 ≈ 4 × 10⁻³ × 3 × 10⁻² = 12 × 10⁻⁵ = 0.00012
• Eliminate any choices in the wrong order of magnitude immediately.

Fraction Benchmarks:

• 1/2 = 0.5, 1/3 ≈ 0.33, 2/3 ≈ 0.67, 1/4 = 0.25, 3/4 = 0.75
• 33/98 ≈ ? Slightly more than 33/99 = 1/3 ≈ 0.333. Maybe ~0.337.
• Use these instead of long division when choices permit.

Square Root Benchmarks:

• √2 ≈ 1.41, √3 ≈ 1.73, √5 ≈ 2.24
• √50 = √(25 × 2) = 5√2 ≈ 5 × 1.41 = 7.05
• √75 = √(25 × 3) = 5√3 ≈ 5 × 1.73 = 8.65

Percentage Benchmarks:

• 10% = move decimal one place left.
• 5% = half of 10%.
• 15% = 10% + 5%.
• 1% = move decimal two places left.
• 17.5% of 80: 10% = 8, 5% = 4, 2.5% = 2 → 8+4+2 = 14.

Calculator Strategy

When to Use the Calculator:

• Multi-digit multiplication or division where choices are close.
• Square roots of non-perfect squares.
• Decimal arithmetic with more than 2-3 digits.
• Verifying an estimation when you're unsure.

When NOT to Use the Calculator:

• Simple arithmetic (7 × 8, 36/6, 25% of 200). Using the calculator for these wastes 5-10 seconds of button-pressing.
• When estimation gets you the answer faster and choices are far apart.
• For algebraic manipulation — you can't type variables into the basic calculator.
• For fraction simplification — do it by hand.

Calculator pitfalls:

• Order of operations: The basic calculator may not respect PEMDAS automatically. Use memory or write intermediate results.
• Mis-keying: It's extremely easy to hit a wrong digit. Glance at the display after every operation to catch errors.
• Over-reliance: The calculator slows you down. Each operation costs 2-5 seconds of hunting and pecking. A strong mental math student can solve many QR questions faster WITHOUT the calculator.

Pacing Strategy

The 67-Second Rule: 40 questions in 45 minutes = 67.5 seconds per question. This is your budget. Track yourself ruthlessly.

The Three-Pass Pacing System:

Pass 1 (Minutes 0-35) — Answer Everything Answerable:

• Work through all 40 questions in order.
• Target 45-60 seconds per question.
• If you know how to solve it, solve it. If it's taking more than 60 seconds without clear progress, flag and move.
• For flagged items, eliminate obvious wrong answers and make your best guess. Write the question number on scratch paper.

Pass 2 (Minutes 35-42) — Return to Flagged Questions:

• Review your scratch paper list. Attack the flagged questions you're most confident about first.
• You now have fresh eyes and less time pressure (most questions are already answered).
• For questions where you're still stuck after 90 seconds of this pass, commit to your best guess.

Pass 3 (Minutes 42-45) — Final Sweep:

• Verify no questions are blank (no penalty for guessing!).
• Review any answers you marked with a "?" for uncertainty.
• Trust your first instinct on questions you already answered — don't second-guess without a specific reason.

Which Questions to Flag (Skip Aggressively)

• Multi-step word problems where you can't set up the equation in 30 seconds.
• Complex geometry requiring construction of auxiliary lines or multi-step area/volume calculations.
• Probability with combinatorics that requires computing multiple nCr values.
• Quantitative comparison where you've tested 3 cases and they all agree but you're not sure about edge cases.
• Any question where you find yourself re-reading for the third time.

Which Questions to Bank Time On (Solve Quickly)

• Simple algebra: "Solve for x: 3x + 7 = 22." Done in 15 seconds.
• Straightforward arithmetic with far-apart choices: Estimate and move.
• Direct formula application: "Area of a circle with radius 5." A = 25π. Done.
• Data interpretation questions where the answer is directly visible in the chart/table.
• Quantitative comparison where simplification reveals an obvious equality or inequality.

Time-Saving Mental Math Accelerators

• Difference of squares: a² − b² = (a+b)(a−b). 97 × 103 = (100−3)(100+3) = 10000−9 = 9991. Done in 5 seconds.
• Percent change shortcut: New/Old − 1. 75 → 90: 90/75 = 1.2 → 20% increase.
• Divisibility rules: A number is divisible by 3 if sum of digits is divisible by 3. By 4 if last two digits divisible by 4. By 9 if sum of digits divisible by 9.

Common Traps

Trap 1 — Calculator Dependency. Reaching for the calculator for 12 × 15 when you know it's 180. Every unnecessary calculator interaction costs time and breaks your mental flow.

Trap 2 — Precision When Approximation Works. Computing √37 to three decimal places when the answer choices are 4, 5, 6, and 7. √37 is between 6 (36) and 7 (49), much closer to 6. Answer is 6. Done.

Trap 3 — Perfectionism on Flagged Questions. Returning to a flagged question and spending 4 minutes on it. If you didn't get it in 60 seconds the first time, you're unlikely to get it in 4 minutes. Guess, move on, protect the rest of your test.

Trap 4 — Not Checking the Clock. Students get absorbed in a geometry problem and look up to find 8 minutes have passed. Check the timer after every 10 questions. At Q10: ~11 minutes elapsed. At Q20: ~22 minutes. At Q30: ~33 minutes. At Q40: done.

Trap 5 — Leaving Questions Blank. The DAT has no penalty for wrong answers. In the final 30 seconds, fill in ALL remaining blanks. If you have 3 blanks and 30 seconds, pick one letter (e.g., all "B") and fill them in. You'll get ~1 correct by chance — that's a free point.