Mental Math Shortcuts for GMAT and GRE Quantitative Sections

The GMAT and GRE Quantitative sections are not primarily memory tests — they reward reasoning speed and number sense. Students who master mental arithmetic save 30–60 seconds per problem, which on a timed test translates to a dramatically better score.

Here are the shortcuts that matter most.

Multiplication Tricks

The "close to round number" technique

When numbers are near round numbers, adjust:

• 47 × 8 → 50 × 8 − 3 × 8 = 400 − 24 = 376
• 98 × 7 → 100 × 7 − 2 × 7 = 700 − 14 = 686
• 203 × 6 → 200 × 6 + 3 × 6 = 1,200 + 18 = 1,218

FOIL in your head for near-equal numbers

• 52 × 48 = (50 + 2)(50 − 2) = 50² − 4 = 2,500 − 4 = 2,496
• 63 × 57 = (60 + 3)(60 − 3) = 3,600 − 9 = 3,591

This is the difference-of-squares pattern: (a + b)(a − b) = a² − b².

Multiply by 5, 25, 125

• × 5 → divide by 2, multiply by 10
• × 25 → divide by 4, multiply by 100
• × 125 → divide by 8, multiply by 1,000

Example: 84 × 25 → 84/4 = 21 → 21 × 100 = 2,100

Percentage Shortcuts

The GMAT loves percentages. Know these cold:

Fraction	Decimal	Percentage
1/8	0.125	12.5%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%
1/6	0.1667	16.7%
1/3	0.333	33.3%
2/3	0.667	66.7%

Quick percentage calculations:

• 15% of X: take 10% (move decimal one left), then add half of that
• 7.5% of X: take 15% and halve it
• 33% of X: divide by 3

Example: 15% of 280 → 28 + 14 = 42

Division Tricks

Dividing by 7

7 has a pattern: 1/7 = 0.142857... (cycles: 1, 4, 2, 8, 5, 7). Know the first 4 digits and the rest follows.

"Is it divisible by X?" checks

• 2: last digit even
• 3: sum of digits divisible by 3 (243: 2+4+3=9 ✓)
• 4: last two digits divisible by 4
• 6: divisible by both 2 and 3
• 9: sum of digits divisible by 9
• 11: alternating sum of digits (253: 3−5+2=0 ✓)

GRE vs. GMAT: What's Different

GMAT Data Sufficiency is unique — you don't compute the answer, you determine if there's enough information to compute it. Mental math plays a smaller role here than logical reasoning.

GRE Quantitative Comparison asks "which quantity is larger?" You often don't need to compute either side fully — just determine which is bigger.

The shared skill is number sense: knowing that 3⁵ = 243, that √200 ≈ 14.1, that log₂(1000) ≈ 10. These appear on both exams.

The Estimation Skill Both Exams Test

Both the GMAT and GRE include problems where exact computation takes too long. The trick is to estimate:

"Approximately what percent of 48 is 19?"

Rather than computing 19/48 exactly: 19/48 ≈ 20/50 = 40%. Exact answer: 39.6%. Close enough.

Estimation rule of thumb: Round to the nearest number that divides cleanly, then correct direction.

Practice

Building these reflexes takes repetition. Fermiq's Math and Probability categories include estimation and arithmetic problems similar to what appears on standardized tests:

• Practice math questions
• Probability questions
• 60-second blitz mode for speed building

The GMAT typically rewards students who have 6 months of consistent practice. The GRE is more forgiving but still rewards number sense heavily.

Build the habit. Ten minutes a day compounds faster than you'd expect.