Section Format + Strategy
Not publishedof exam
Value, Order, and Factors
Not publishedof exam
Algebra, Equalities, Inequalities
Not publishedof exam
Rates, Ratios, and Percents
Not publishedof exam
Statistics, Sets, Counting, Probability
Not publishedof exam
Quick Facts
- Section
- GMAT Quantitative Reasoning
- Questions
- 21 Problem Solving
- Time
- 45 minutes
- Pace
- About 2:09 per question
- Calculator
- None in Quant
- Section score
- 60-90
- Total score
- 205-805
- Geometry
- Not tested
- Data Sufficiency
- Now in Data Insights
- Answer edits
- Up to 3 per section
- Fee
- $275 center, $300 online
- Score validity
- 5 years
Problem Solving vs Data Sufficiency
Problem Solving
- Quant section only
- Five answer choices
- Solve for a value
Data Sufficiency
- Data Insights section
- Asks if data suffices
- Never fully solve
Quant vs Data Insights
Method Picker
- Variables in the choices→Plug in numbers(Try 2, 10, 100)
- Numbers in the choices→Backsolve(Start at middle)
- Choices far apart→Estimate(Round and bound)
- Choices very close→Compute exactly(No rounding)
- Percent word problem→Assume 100(Simplest base)
- Ratio with no total→Introduce k(Total is a multiple)
- Must be true→Test counterexamples(Try 0, 1, negatives)
- Ugly arithmetic→Factor first(Cancel before multiplying)
- Past three minutes→Guess and bookmark(Edit later)
Section Format
- Questions
- 21 Problem Solving items
- Time
- 45 minutes, no break
- Pace
- About 2:09 each
- Choices
- Five options, one correct
- Adaptive
- Difficulty follows your answers
- Skipping
- Not allowed going forward
- Review & Edit
- Change up to 3Per section
- Calculator
- None; scratch pad only
- Section order
- Choose any order
- Unfinished penalty
- Score reduced significantly
Plug In vs Solve Algebraically
Plug in numbers
- Variables in choices
- Pick simple values
- Check all choices
Solve algebraically
- Numbers in choices
- Cleaner short setups
- Fewer arithmetic slips
Test vs derive
Scoring + Retakes
- Section score
- 60-90, 1-point steps
- Total score
- 205-805
- Weighting
- Quant, Verbal, Data equal
- Pass mark
- None; programs set targets
- Score preview
- Unofficial score shown immediately
- Official report
- Typically 3-5 business days
- Retake wait
- 16 calendar days
- Yearly cap
- 5 per rolling year
- Lifetime cap
- Removed October 2024
- Validity
- 5 years from test
- Free reports
- 5 programs included
Answer Choice Strategy
- Read choices first
- They reveal needed precision
- Spread choices
- Estimate, then eliminate
- Close choices
- Compute exactly
- Backsolving
- Start at middle choice
- Plug in numbers
- Pick easy safe values
- Avoid 0 and 1
- They behave unusually
- Trap answers
- Match partial-step results
- Guess and move
- Past three minutes
- Bookmark
- Flag for later edit
Mental Math Toolkit
- Squares 1-15
- Memorize through 225
- Cubes 1-10
- Memorize through 1,000
- 1/8
- 12.5%
- 1/6
- About 16.67%
- 1/7
- About 14.29%
- 3/8
- 37.5%
- Powers of 2
- 2, 4, 8, 16, 32
- Doubling and halving
- Simplifies awkward products
- Factor before multiplying
- Cancel early, compute less
- Benchmark 10%
- Scale to other percents
Digit Sum Rules
Sum the digits: 3 and 9 both test
3: sum divisible by 39: sum divisible by 9Works at any length
Factor vs Multiple
Factor
- Divides the number
- Never exceeds it
- Finite count
Multiple
- Number times an integer
- Never smaller
- Infinite count
Divides vs divisible
Number Properties Picker
- Asks about remainders→Division algorithm(Remainder below divisor)
- Asks about divisibility→Digit-sum rules(3 and 9)
- Counts the factors→Prime factorization(Add 1 to exponents)
- Units digit of power→Cycle of four(Use exponent remainder)
- Terminating or repeating→Check denominator primes(Only 2s and 5s)
- Even or odd result→Parity rules(Signs do not matter)
- Largest common divisor→GCF(Lowest shared powers)
Divisibility Rules
- 2
- Last digit is even
- 3
- Digit sum divisible by 3
- 4
- Last two digits divisible
- 5
- Ends in 0 or 5
- 6
- Passes 2 and 3
- 8
- Last three digits divisible
- 9
- Digit sum divisible by 9
- 10
- Ends in 0
- 11
- Alternating digit sum works
- 12
- Passes 3 and 4
Units Digit Cycles
Powers cycle every four; divide the exponent by 4
2: 2, 4, 8, 63: 3, 9, 7, 17: 7, 9, 3, 1Remainder 0 means last
Primes + Factors
- Primes under 50
- Fifteen of them2 to 47
- Only even prime
- 2
- 1 is not prime
- Needs exactly two divisors
- Prime test
- Trial-divide to sqrt n
- Factor count
- Add 1 to exponents
- 72
- 2^3 x 3^2 gives 12
- GCF
- Lowest shared prime powers
- LCM
- Highest prime powers
- GCF x LCM
- Equals product of numbers
- Perfect square
- All exponents are even
Exponents + Roots
- a^m x a^n
- a^(m+n)
- a^m / a^n
- a^(m-n)
- (a^m)^n
- a^(mn)
- (ab)^n
- a^n x b^n
- a^0
- 1 for nonzero a
- a^(-n)
- 1/a^n
- a^(1/2)
- sqrt a
- sqrt(ab)
- sqrt a x sqrt b
- sqrt(a^2)
- |a|, not always a
- Negative base
- Even power gives positive
- 0 < x < 1
- Squaring makes it smaller
Number Line + Signs
- Even + even
- Even
- Odd + odd
- Even
- Even x odd
- Even
- Odd x odd
- Odd
- Negative x negative
- Positive
- Zero
- Even, neither positive nor negative
- Zero product
- Some factor equals zero
- Consecutive integers
- Product divisible by n!
- Remainder range
- 0 <= r < divisor
- Division algorithm
- dividend = divisor x quotient + remainder
- Absolute value
- Distance from zero
Decimals + Place Value
- Terminating decimal
- Denominator only 2s, 5s
- Repeating decimal
- Denominator has other primes
- Rounding
- Look one digit right
- Scientific notation
- One digit before point
- Multiply by 10^n
- Shift point right
- Place value
- Tenths, hundredths, thousandths
- Percent to decimal
- Divide by 100
Order of Operations
PEMDAS: parentheses, exponents, multiply, divide, add, subtract
Work left to rightMultiply and divide tieAdd and subtract tie
Algebra Move Picker
- Equation equals zero→Factor it(Zero product property)
- Two equations, two unknowns→Substitute or eliminate(Check for parallel)
- Squared binomial appears→Use the identity((a+b)^2)
- One square minus another→Difference of squares(Fast factoring)
- Inequality times negative→Flip the sign(Adding never flips)
- Absolute value equation→Split into cases(Check both roots)
- Asks for root sum→Use -b/a(Skip the formula)
Factoring Patterns
- Difference of squares
- a^2 - b^2 = (a+b)(a-b)
- Perfect square
- (a+b)^2 = a^2+2ab+b^2
- Negative square
- (a-b)^2 = a^2-2ab+b^2
- Common factor
- Pull out shared term
- Trinomial
- Find two factors of c
- 79 x 81
- 80^2 - 1 = 6,399
- FOIL
- First, outer, inner, last
- Zero product
- Set each factor zero
Quadratics
- Standard form
- ax^2 + bx + c = 0
- Quadratic formula
- -b +/- sqrt D over 2a
- Discriminant
- b^2 - 4ac decides roots
- D > 0
- Two real roots
- D = 0
- One repeated root
- D < 0
- No real roots
- Root sum
- -b/a
- Root product
- c/a
Inequalities + Absolute Value
- Negative multiply
- Flip the sign
- Adding
- Never flips the sign
- Unknown divisor
- Never divide by variable
- |x| < a
- -a < x < a
- |x| > a
- Two separate intervals
- |x-3| < 2
- 1 < x < 5
- Squaring an inequality
- Safe only when positive
- Reciprocal
- Positive terms reverse order
- Compound inequality
- Operate on all parts
Functions + Sequences
- f(x)
- A rule, not multiplication
- f(g(x))
- Inner function first
- Domain
- Allowed input values
- Undefined
- Zero denominator, negative root
- Arithmetic term
- a_1 + (n-1)d
- Arithmetic sum
- n(a_1 + a_n)/2
- Geometric term
- a_1 x r^(n-1)
- Evenly spaced mean
- (first + last)/2
- Off-by-one
- Mind the n-1
Coordinate Plane
- Slope
- (y2-y1)/(x2-x1)
- Slope-intercept
- y = mx + b
- y-intercept
- Set x = 0
- x-intercept
- Set y = 0
- Parallel lines
- Same slope, different intercept
- Perpendicular
- Slopes multiply to -1
- Distance
- sqrt of squared differences
- Midpoint
- Average both coordinates
- Quadrant I
- Both coordinates positive
Translation Keywords
- is
- equals
- of
- multiply
- per
- divide
- sum, more than
- add
- difference, less than
- subtract
- 5 less than y
- y - 5
- twice
- multiply by 2
- consecutive
- n, n+1, n+2
- what percent
- x/100 times
Rate Time Distance
D = R x T; cover one, read the rest
R = D/TT = D/RRates add, times do not
Simple vs Compound Interest
Simple
- P x r x t
- Interest on principal
- Linear growth
Compound
- P(1 + r/n)^(nt)
- Interest on interest
- Exponential growth
Principal vs balance
Word Problem Picker
- Two objects moving→Relative speed(Add or subtract)
- Two workers together→Add the rates(1/T = 1/a + 1/b)
- Round trip speeds→Total distance over time(Never average speeds)
- Solutions being mixed→Track the solute(volume x concentration)
- Price then discount→Multiply the factors(Order does not matter)
- Interest over years→Compound formula(P(1+r)^t)
- Cost versus selling price→Check markup or margin(Different denominators)
- Units do not match→Convert first(Cancel the units)
Percent Formulas
- Percent change
- (new - old)/old x 100
- Base of percent
- Always the original value
- Increase 25%
- Multiply by 1.25
- Decrease 20%
- Multiply by 0.80
- Successive changes
- Multiply factors, never add
- +15% then -20%
- Net 8% decrease
- Percent to fraction
- Divide by 100
- Reverse a percent
- Divide, do not subtract
Percent Change Base
Change over original; the original is always the base
40 to 50 is 25%50 to 40 is 20%Denominator never switches
Percent Of vs More Than
20% of y
- x = 0.2y
- A fraction of y
- Smaller than y
20% more than y
- x = 1.2y
- Added on top
- Larger than y
Multiply vs add
Ratios + Proportion
- Ratio a : b
- Quantities ak and bk
- Total parts
- (a + b)k
- Ratios hide totals
- Need one actual value
- a/b = c/d
- Cross multiply: ad = bc
- Direct variation
- y = kx
- Inverse variation
- xy = k
- Scaling a recipe
- Multiply every part equally
- Three-term ratio
- Match shared term first
Markup vs Margin
Markup
- Profit over cost
- Cost is denominator
- $20/$80 = 25%
Margin
- Profit over price
- Price is denominator
- $20/$100 = 20%
Cost vs selling price
Rate, Work, Distance
- Distance
- rate x time
- Time
- distance / rate
- Average speed
- total distance / total time
- Never average speeds
- Weight by time spent
- Combined work
- 1/T = 1/a + 1/b
- Two workers
- T = ab/(a+b)
- Rates add
- Times never add
- Opposite directions
- Add the speeds
- Same direction
- Subtract the speeds
- Downstream
- boat + current
- Upstream
- boat - current
Mixtures + Interest
- Solute amount
- volume x concentration
- Mixing
- Solute amounts add
- Weighted average
- Falls between component values
- Simple interest
- P x r x t
- Compound interest
- P(1 + r/n)^(nt)
- Annual compounding
- P x (1+r)^t
- Doubling estimate
- Rule of 72
- Profit
- revenue - cost
Unit Conversion
- Conversion fraction
- Equals 1, cancels units
- km/h to m/s
- Multiply by 5/18
- m/s to km/h
- Multiply by 18/5
- Check units
- Units must cancel cleanly
- Mixed units
- Convert before computing
- Rate units
- Numerator over denominator
Order Test
Order matters? Permute. Order ignored? Combine.
Ranking: permutationCommittee: combinationHandshake: combination
Permutation vs Combination
Permutation
- Order matters
- n!/(n-r)!
- Rankings, passwords
Combination
- Order ignored
- n!/(r!(n-r)!)
- Committees, handshakes
Arrange vs choose
Counting Picker
- Order changes the outcome→Permutation(n!/(n-r)!)
- Order is irrelevant→Combination(n!/(r!(n-r)!))
- Independent stages→Multiply outcomes(Counting principle)
- Repeated identical items→Divide by factorials(Remove duplicates)
- Asks at least one→Complement(1 - P(none))
- Two overlapping groups→Venn formula(Subtract the overlap)
- Seats in a circle→Fix one seat((n-1)! arrangements)
Average + Spread
- Mean
- Sum divided by count
- Sum
- mean x count
- Median
- Middle of ordered list
- Even count median
- Average two middle values
- Mode
- Most frequent value
- Range
- Largest minus smallest
- Standard deviation
- Spread about the mean
- Add a constant
- Deviation unchanged
- Multiply by k
- Deviation scales by k
- Identical values
- Standard deviation is 0
- Symmetric set
- Mean equals median
Mean vs Median
Mean
- Sum over count
- Outliers pull it
- Recovers the total
Median
- Middle ordered value
- Outlier resistant
- Better for skew
Average vs middle
Sets + Venn
- Two-set total
- A + B - Both + Neither
- Union
- |A| + |B| - overlap
- Double counted
- Subtract the overlap once
- Neither
- Outside both circles
- Maximum overlap
- Size of smaller set
- Minimum overlap
- A + B - Total
- Three sets
- Add back triple overlap
Range vs Standard Deviation
Range
- Largest minus smallest
- Only two values
- Ignores the middle
Standard deviation
- Spread about mean
- Uses every value
- Shifting changes nothing
Endpoints vs spread
Counting Methods
- Counting principle
- Multiply stage outcomes
- Arrangements
- n! orderings
- 0!
- Equals 1
- Permutation
- n!/(n-r)!
- Combination
- n!/(r!(n-r)!)
- Order matters
- Use a permutation
- Order ignored
- Use a combination
- Identical items
- Divide by repeat factorials
- Circular seating
- (n-1)! arrangements
- Handshakes
- C(n, 2)
Probability Rules
- Basic probability
- favorable / total outcomes
- Range
- Between 0 and 1
- Complement
- 1 - P(E)
- At least one
- Use 1 minus none
- Or rule
- P(A) + P(B) - both
- Mutually exclusive
- Overlap term is zero
- And, independent
- P(A) x P(B)
- Dependent events
- Adjust after first draw
- Without replacement
- Denominator shrinks each draw
Series + Estimation
- Consecutive sum
- n(first + last)/2
- First n integers
- n(n+1)/2
- Evenly spaced count
- (last - first)/step + 1
- Geometric ratio
- Each term times r
- Choices spread out
- Round and bound
- Choices close together
- Exact arithmetic needed
- Rounding both up
- Overstates the product
- Keep one exact
- Bound the error direction
Common Traps
Average speed
Weight by time ≠ Not average of speeds
Successive percents
Multiply the factors ≠ Never add the percents
Squares and roots
sqrt(x^2) is |x| ≠ Not always x
Zero and one
Zero is even ≠ One is not prime
Inequality sign
Negative multiply flips ≠ Adding never flips
Ratio is not a total
3 : 5 means 3k, 5k ≠ Actual amounts need k
Rates versus times
Rates add directly ≠ Times never add
Median is not mean
Median ignores outliers ≠ Mean follows them
No calculator
Quant forbids calculators ≠ Data Insights allows one
Geometry removed
No triangles or circles ≠ Coordinate lines still tested
Last Minute
- 1.21 questions, 45 minutes, no calculator
- 2.Pace about 2:09 per question
- 3.Only Problem Solving; no Data Sufficiency
- 4.Geometry gone; coordinate lines stay
- 5.Section scored 60-90; total 205-805
- 6.Edit up to 3 answers
- 7.Percent change uses the original
- 8.Average speed uses total time
- 9.Rates add; times do not
- 10.Order matters means permutation
- 11.Negative multiply flips the inequality
- 12.Factor count: add 1 to exponents
- 13.At least one = 1 minus none
- 14.Sum = mean x count
- 15.sqrt of a square is absolute
- 16.Never leave a question blank
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