Cheatography

# GMAT Quant Cheat Sheet by amandineguilbault

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 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*51*31-> (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)