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GMAT QUANTITATIVE SECTION

Algebra

ax2+bx+c
sum roots: -b/a
Δ =b2-4ac
product roots: c/a

Ratios

q1 : q2 = q2-final : q1-final
num<denum so fracti­on<1 so (x+1)/­(y+1) > x/y
num>denum so fracti­on>1 so (x+1)/­(y+1) < x/y
from exerci­se: a-10 + b-20 + c-15 = 11k + 18k + 24k so 1105-4­5=53k (ratios gains)
effica­cy=1/t (inverse propor­tio­nna­lity)
1/t1 : 1/t2 : 1/t3
take LCM = k so you have k/t1 : k/t2 : k/t3
compute to get x : y : z form
then do x + y + z and cross product
Rate of interest = intere­stp­ery­ear­/pr­inc­ipa­lin­vested * 100
When compared, use compared amount as the base
so you have Δ / base * 100
Use quantity as unit of q, the percentage change is
Δ = increased or decrease quantity
Δ/1(or­iginal amount) * 100
To make a profit, take initial price and add the desired profit so that: new price per unit = initial (1+pro­fit)
Always find a 100 that makes the calcul­ation easy = if it's not marked price it's cost price etc.
On Y1, simple and compound interests are the same
Find interest rate w/ difference and interest on interest
Interest = principal * rate * time
discount of marked price = discount / marked price * 100
Usually, these questions include:
1. ratios of shared amounts,
2. time to perform a task,

3. invest­ments and interests
4. price increases or decreases
=> FOR PROFITS
 

Number properties

remainder of sum = sum of remainders
remainder of product = product of remainders
nb of trailing zeros = at least nb of 5s
number of factors = product of each power + 1 [ex: 120 -> 23*­5*­3-> (1+1)­*(1­+1)­*(3+1) = 16]
from exerci­se: If remainder of product to find, can work by pairs
If two expres­sions are equal, the exponents must be equal (if 2n+2m = 23m-1 then n+2m = 3m-1)
AP Sum of arithmetic progre­ssion = (1st + Last / 2) * nb of terms
AP nth term → an = a1 + (n-1) * d (common divisor)
AP sum of the n first terms : n/2 [2a1 + (n-1)d]
GP sum of first n terms = a(rn-1) / r-1where r is common ratio
Number of ways of selecting two distinct integers from the set of first 100 positive integers = 100C2 ways.
i.e., 100C2 = 100 × 992

Sets

P(AUB) = P(A) + P(B) - P(A∩B)
P(AUBUC) = P(A) + P(B) + P(C) + P(A∩B∩C) - [P(A∩B) + P(A∩C) + P(B∩C)]

Statistics and Average

Standard deviation = mean -> (numbe­r-m­ean)2 -> mean -> square root(mean)

From video

Work and Rate
R=J/T
machines identi­ques: nR=J/T
 

Geometry / Coordinate Geometry

air triangle = 1/2 * products of sides * sin (inside angle)
sin 150° = 1/2
sum of interior angles of polygon = (n-2)*180
Pythag­orean triplets (c is odd, at least 2 prime numbers, 1 even number): (3,4,5) / (5,12,13) / (7,24,25) / (8,15,17) / (9,40,41) / (11,60,61) / (12,35,37)
area triangle = r (inserted circle) * semi-p­eri­meter triangle
equation of a circle center (a,b): (x-a)2 + (y-b)2 = r2
equation of a line that crosses two interc­epts: x/value x + y/value y = 1 so (value x)y + (value y)x = (value x)(value y)
       
 

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