GMAT Focus Quant - Formula Sheet
How to calculate the # of trailing zeroes? Ex: What is the # of trailing zeroes for 92x35?
# of trailing zeroes = the number of (5x2) pairs in the prime factorization. Ex: 1 pair of 5x2 = 1 trailing zero
Determine number of multiples divisible by X
((highest # divisible by X) - (lowest # divisible by x)) / X ] +1 Ex: Determine number of 2-digit multiples of 4: [(96-12)/4] +1 = 22
# of ways to arrange a set of items in a circle
(k-1)! where k = the number of objects to be arranged
Combination with repetition formula
(n+r - 1)!/r!(n - 1)!
Square root of 2 = Square root of 3 = Square root of 5 =
1.4 1.7 2.2
# of integers in a consecutive set
= [(highest # - lowest #) / (amount of increment) ] + 1 Ex: (3, 5, 7, 9) = (9-3)/2 + 1 = 4
Compound interest formula
A = P(1+r/n)^nt
Simple interest formula
A = P(1+rt) Interest amount = P x r x t
Formula to find the number of factors: i.e., of 2^51 x 3^2
Add 1 to the value of the exponents, then multiple these results. i.e. number of factors of 2^51 x 3^2 is (51+1) x (2+1) = 52 x 3 = 156
Sum of evenly spaced sets (consecutive integers) formula
Average x number of terms
Difference between combination and permutation
Combination is used for a list where the order does NOT matter. Permutation is used for a list of data where the order DOES matter.
If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M - m ?
For consecutive integers, Mean = Median = (First + Last)/2
How to identify perfect cubes
If exponents of the prime factors are divisible by 3
Determine if Terminating Decimal or note?
If the denominator of reduced fraction (simplest form) has a prime factorization that contains only 2s or 5s or both.
The slope of parallel lines vs perpendicular lines
Parallel lines have same slopes (m) but different y-intercepts A slope of a perpendicular line is the negative reciprocal (-1/x).
Sum of arithmetic sequence formula
Sn=n/2(a1+an)
A number is divisible by 7 if...
The difference between twice the ones digit and the number formed by the remaining digits is a multiple of 7 Ex: 343 Twice the ones digit = 3x2 = 6 34 - 6 = 28 (divisible by 7) Ex: 483 3x2 = 6 48 - 6 = 42
An integer is divisible by 3 if...
The digits add up to a multiple of 3
A number is divisible by 8 if..
The number is even and the last 3 digits is divisible by 8 or the last 3 digits are all 0s
How to find the # of leading zeroes in a decimal? If X is an integer with K digits...
Then 1/X will have K-1 leading zeros *unless X is a perfect power of ten, then it will have K-2 leading zeros
Catch up and pass formula
Time = Change in Distance / Change in Rate
Finding the number of terms in a set of consecutive integers
[(Last - First)/ Increment] + 1
Geometric sequence formula
an=a1(r)^(n-1) where r is the common ratio
Arithmetic sequence formula
an=a1+(n-1)d where d is the common difference
Catch up rate formula
distance 1 = distance 2
Converging/ diverging rate formula
distance object 1 + distance object 2 = total distance
How to identify perfect squares
if exponents of the prime factors are even
Permutation with repetition formula
n!/ x!y! where x and y are the number of repeats of variables x and y
Combination formula
nCr = n!/r!(n-r)!
Permutation formula
nPr = n!/(n-r)!
Distance in a plane formula
square root[(x2-x1)^2 + (y2-y1)^2]
An integer is divisible by 9 if...
the digits add to a multiple of 9
An integer is divisible by 4 if..
the last two digits are a number that's divisible by 4
A number is divisible by 11 if..
the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is 0 or is divisible by 11
Formula for dividend, quotient, divisor, remainder
x = my + r where x = dividend m = quotient y = divisor r = remainder
