CAT/GMAT Quants Flashcards
Arithmetic: Average always take in?
Total
Arithmetic: An operation done on every observation?
Is the operation done on the average
Arithmetic: Average Speed =?
Total Distance / Total Time.
2 Eq Distance = 2 s S/ s + S
Arithmetic: 1/6 =
16.67
Arithmetic: 1/7 and 1/14
14.28 and 7.14
Arithmetic: 1/8 =
12.25
Arithmetic: 1/9 and 1/11
11/11 and 09.09
Arithmetic: 1/12
8.33, 8.25 kisi ka nahi hota, 6.25 hota h 1/16
Arithmetic: 1/13
7.69
Arithmetic: 1/15 and 1/16
6.67 and 6.25
Arithmetic: successive increase ?
+- A +- B +- AB/100
Arithmetic: which formula to use to maintain Rev if exp inc and we have to find how much to decrease cost
Successive formula
Arithmetic: SI mai interest is given on?
Initial P
Arithmetic: SI is which formula and CI is which formula
SI is Interest giving foruma and CI is Amount giving formula
Arithmetic: SI and CI formula
PRT/ 100 and P(1+R/100)*n
Arithmetic: CI change on formula in case of semi annually or quartely
Rate aadha, time double.
Arithmetic: A:B = 2:3, what is the first step you do?
Write 2x and 3x
Arithmetic: 2x = 6y = 9z, find x:y:z process?
Find LCM, here 18. Divide corresponding by LCM and ans uska corresponding ratio. Jitna chota coeff, utna bada ratio.
Arithmetic: what is mixture and what is alligation
Mixture is Q type, allegation is cross multiplying process to find ratio.
Arithmetic: Formula of Pure Liquid remaining?
X ( 1 - y/x)*n
Arithmetic: Golden Equation of Time and Work
Men X Rate = Work (can apply to 2 simultanous Eqs as well)
Arithmetic: Rel b/w Men and Women Questions
Find in like terms. Shortcut = W X D1 - W X D2 = M X D1 - M X D2
Arithmetic: Km se m/s mai krna hai?
chota krna hai literal word wise hence divide by smaller than 1 i.e 5/18
Arithmetic: Speed formula to use
TDS. Time = Distance/ Speed since normally time gap is given and you can get constants on one side and variables i.e D and S on the other
Arithmetic: Relative Speed
Same Direction = S1 - S2
Opposite Direction = S2 + S1
Arithmetic: Trains tsd formula
Time normal formula but take relative speed.
Arithmetic: Boats and Streams, Downsteam and Upstream Speed?
Downstream = X+y
Upstram = X-y
x = boat and y = stream
Arithmetic: Speed of the boat in boats and stream question?
0.5 (Downstream speed + upstream speed)
Arithmetic: Speed of water in boats and streams questions?
0.5 (Downstream - upstream)
Arithmetic: Circular Motion Q1 = First Meeting Key!!
Relative Speed. Total distance / rel speed.
Arithmetic: Circular motion Q2. Meet @ start point
Find T = D/S inidivudal of 2 people and take LCM
Arithmetic: Circumar motion Q3. No if different meeting points?
Same direction = Ratio of speeds minus
Opposite Direction = Ratio of speeds add
Arithmetic: To and Fro Motion, time taken in each meeting?
Same Direction. harr 2D/x+y time k baad and opposite dicrection 1st meeting D/x=y k baad and second onwards 2d/x+y k baad
Arithmetic: Clocks. min hand 1 min degrees?
6
Arithmetic: Hour hand degrees for 12h, 1h, 1 min
360* , 30* and 1/2 *
Arithmetic: Relative speed between hour and min hand?
5.5 * per minute
Arithmetic: To find angle between hour and minute hand at any time?
angle = absolute of 30 Hour - 5.5 Min
Algebra: Domain of Log
R +
Algebra: Log 1 is?
0
Algebra: Log 10 is
1
Algebra: Log 10 sq and log 10 to power x is
2 and x
Algebra: Nth Term of AP?
a + (n-1)D
Algebra: Sum of N terms of AP?
n/2 (a + An) and An = a + (n-1)d
Algebra: Nth Term of Gp
A . R to power of n-1
Algebra: Sum of infinite terms of GP, R is less than 1
A / 1-R , R is less than 1
Algebra: Sum of infinite terms of GP, R is more than 1
Infinity
Algebra: Sum of N terms of GP if R is more than 1
A ( R*n - 1) / R-1
Algebra: Sum of N terms of GP if R is less than 1
A ( 1 - R*n) / 1 - R
Algebra: If A B C are in GP? Then log observation is?
Log A Log B and Log C are in AP
Algebra: AMean = Average, what is Geometric Mean?
GM = Product and power mai 1/no of terms
if a b are in GP
GM = a b to the power of 1/2.
Algebra: AM GM and HM formula?
AM = a+b/2, GM = root ab, HM = 2ab/a+b
Algebra: AM GM HM relationship and comparision of size?
AM X HM = Square of GM
A>G>H
Algebra: Sigma N?
n(n+1) diviided by 2
Algebra: Sigma N square?
n(n+1)(2n+1) divided by 6
Algebra: Sigma N cube
Square of Sigma N
Algebra: Sum of special serires jismai terms are in AP and harr denominator mai ek ek AP term badta rehta h but no of terms is constant. for example. 1/a1a2a3 +1/a2a3a4 +….+1/anan1an2.
denom wali = 1/ek kam D ( 1/ ek kam start se minus 1/ek kam last se)
Algebra: sum of special serires jismai terms are in Ap and harr numerator only mai ek ek Ap serires aage badhti h but no of terms is constant for example = a1a2 +a2a3 + …. +anan1
1/ek zada D ( end wale plus ek aur - start wale ek aur)
Algebra: What is domain and what is range?
Domain is the values a function can take. The Input i.e Root function cannot take negative and 0. Range is Output, for example xsq function cant give negative output
Algebra: Vertical line test for a function?
If you draw a verticial line in a graph of a function. for it to be a function it should only ineresect it once.
Algebra: Domain and Range via Graph?
Move left to right (x axis ki values) for Domain and Move Top to Bottom (y axis ki values) for Range.
Algebra: Log is used when?
When there is X in power. a = b^x
Algebra: Log b base a. =
Log b / log a
Algebra: log ab =
log a + log b
Algebra: log abc =
log a + log b + log c
Algebra: a to the power log b =
b to the power log a
Algebra: a to the power of log x base a =
x
Algebra: log a to the power x =
x log a
Algebra: when is a quad equition minimum?
at x = -b/2a
Algebra: for a squad eqution formula of roots?
x = num = -b +- root b square - 4ac divided by 2a
Algebra: quad roots. sum of roots?
alpha + beta = - b / a
Algebra: Quad roots product of roots =
c / a
Algebra: 1 / root 1 + 1 / root 2 =
- B / C
Algebra: what is discriminat and its significant in types of rotos
D = b square - 4ac .
D > 0 = Real and unequal roots
D = 0, real and equal roots
D < 0 = no roots, no real roots, only complex and conjucate roots
Algebra: Quad eq using sum of roots and product of rotos.
coeff of x square has to be 1. and then equation is x sq - (sum) x + product = 0
Algebra: Polynomials. sum of roots, prod of roots taken 2 at a time and prod of roots taken all 3
-b/a , c/a , -d/a
Algebra: equation of a polynomial using sum of roots, prod of roots tkaen 2 at a time adn prod of roots taken 3 at a time
x cube - prod xsquare + prod 2 at a time X + prod all 3 = 0
Algebra: inequaltiy modulus way to write |x| <= a
-a <= x <= a
Algebra: inequality ranges of |x| => a and |x| =<a
if a is bigger than - a se a mai sab mai and if a is smaller than modulus than - a to a k ilava sab mai including infinity
Algebra: Total values of a modulus function |x| <= a
2a + 1
Probability: what is the POV rule in probability
POV = plus OR Unionion are same i.e counterly multiply and interesction teeno same
Probability: total sample space ?
outcomes possible to the power of item no. for example. sample space for 2 dice will be 6 to the power of 2. ismai n c r ka n wala part jayega and you read n c r as n mai se r. so for example there are 3 coins and we need one tail. sample space will be outcome to the power of dice. i.e 2 to the power of 3. since 3 mai se 1 tail. 3 is the n part.
Probability: shortcut to baye’s theorm?
pehle box a ki akeli, then box b ki akeli, then que ne pucha what is the chance wo box a ka tha, then use box a / box a + box b
PnC: what is permutation and what is comibation
permutation is arrangement and combination is selection ( n c r) n mai se r
PnC: what is permutation formula and what is combination formula?
npr = n! / (n-r)! , combination mai bass jitna chaiye uska average bhi leleta h. ncr = n! / (n-r)! r! hence naturally npr is greater than ncr
PnC: what is nc0 nc1 and ncn
1 , n , 1
PnC: seat a b c d e f such that a b c are together?
4! since a b c r one unit but multiple by 3! kyunki a b c ki apas ki arrangement
PnC: no of permutation of n things if p are alike and rest are unique is?
n ! divided by p!
PnC: there are 3 letters and 4 letter boxes, no of arrangments?
4 to the power of 3. jo chez distrubute hogi wo power mai jayegi
PnC: circular permutatiion formula?
(n-1)! and in case of beads flowers where identifical stuff so anticlockwise and clockwise wont matter so half of above formula
PnC: n c r will be max at?
middle. n c n/2 or n c (n+1)/2 for odd
PnC: sum of full series of nc0 nc1 nc2 …. ncn ? and sum of only odd and even?
sum of full is 2 to the power of n, and sum of odd and even is equal which is 2 to the power of n-1
PnC: derrangement of 1 2 3 4 5 6 items?
0 1 2 9 44 265
PnC: no of rectanges possible from h horizontal lines and v vertical lines and no of square also?
h c 2 X v c 2 for recetange. and for square. ek ek kam krke multiply. for example. if lines are 6X3. then 1x1 square are 6x3, 2x2 sqaure are 5x2, 3x3 square are 4x1. stop since next will be 0.
PnC: n straight lines are drawn, no 2 are parallel and no 3 are concurrent. what is the total no of parts, unbounded parts and bounded only.
1 +sigmaN ,
2n ,
1+sigma N - 2n
PnC: out of n non concurrent and non parallel lines, points of intersection are?
n c 2
PnC: out of n points how many straight lines?
n c 2
PnC: out of n points how many straight lines if m are colinier
n c 2 - m c 2 + 1. plus 1 is m ki apas ki ek line
PnC: no of traingles from n points
n c 3. and nc3 - mc3 if m are coolinear
PnC: no of circles from n points
n c 3
Sets: what are the 2 equations?
a + b + c + x + y + z + k = TOTAL
(a+b+c) + 2(x+y+z) + 3k = bahr k totals
Geometry: Sum upto 180* what are those?
Supplementary angles and make a straight line
Geometry: taking one exterior angel per vertex, sum of traignle exterior angles is?
360 degree
Geometry: enxterial angel is equal to?
sum of opposite interior angels
Geometry: Scalene traingle and iscoles traignle?
Scalene = scale use so all unequal sides, iscoles 2 sides r equal
Geometry: area of iscocles right angel triangle?
Leg square by 2
Geometry: ratio of sides of a 45 45 90 right angle traingle?
1:1: root 2
Geometry: ratio of sides of a 30 60 90 right angel triangle?
1: root 3 : 2
x : root 3 X : 2x
Geometry: Height of a eq. traingle and area?
height is A root 3 by 2
area = root 3 by 4 . side square
Geometry: dropping an altitutde from top vertex of equi traingle makes?
2 triangles of 30 60 90 dimensions
Geometry: what are similar triangles>
if 2 traingles are merely an enlargement of one and another
Geometry: what are the 3 properties of similarity traingles>
- all angels same
- all side same ratio
- 2 sides same ratio and angel between them is same.
point 2 means. s/s = S/S
Geometry: reln between squares, rectangles and parallelgoram
all squares are rectangles and all rectangles are parallelogram
Geometry: in parallelogram opposite sdes and opposite angels??
opposite sides are requal and opposite angels are equal
Geometry: diagnols of a parallogram bisect each other?
YES
Geometry: area of a parallelogram
base into height
Geometry: how can I find len of diagnol of rectangle>
use pythogores theorm and reach root len square + wid square
Geometry: 2 properties of diagnols of rectangle
diagnols are equal and bisect each other
Geometry: are the diagnols of parallelogram equal
NO
Geometry: do the diagnols of a rectangle instrect each other at 90 degree?
No, unless it is a square, for a square diagnols cut each other at 90* since ratio of len to wid is same.
Geometry: what are the properties of diagnols of a square and len. 2 properties
are equal and bisect each other at 90* and form 45 45 90 triangles. length is root 2 x
Geometry: when is the area of a rectangle max?
when it is square. given rectangle and a square with same perimeter. square area will be more. almost equal multiplied togeher always gives you max.
Geometry: when does a rectangle has a minimum perimeter
when it is square. and max when one side is equal to the area and one side is1.
Geometry: what is a trapezium
one pair of opposite side is parallel and unequal, other pair is not parallel may or may not be equal. if they are equal it is called an isocoles trapezium.
Geometry: what are the bases of trapezium
the parallel sides. and never ever equal in length
Geometry: area of a trapezium
(add the len of parallel sides ) X Height
Divide the entire thing by 2
Geometry: sum of all interior angels of a polygon
(n - 2) * 180
Geometry: area of a hexagon and approximation?
(3 root 3 by 2 )(side square).
approx . 2.6 into side square
Geometry: what is the area of a hexagon when distance between any 2 parallel sides is given and side is given
1.5 X DISTANCE X SIDE
Geometry: sum of exterior angels of a polygon?
always 360 degrees
Geometry: 3 ratios of a cricle?
center angel / 360 = arc length / circumference = area of sector / area of circle
Geometry: angel subtended by 2 chords at the center and at the circumfrence relationship?
center angel is double of circumference angel
Geometry: when a triangle is subtended in a circle, if one side of the traingle is the diamtere then?
it is a right triangle
Geometry: if a right triangle is with in a cricle and i break the triangle into 2 triangle forming a line to centr from 90 degree vertex then the angels of 2 traignles are?
one triangle is 60 60 60
other is 30 30 120
Geometry: if a perpendicular is drawn from the center of a circle to a chord
it will bisect the chord
Geometry: if an equilateral traingle is inscribed in a triangle and i drop a perpendicular from the center of a triangle to one of the side of the equi triangle and close the triangle by joining it at the vertex, ratio of angels?
30 60 90.
90 at the point perpendicular is drawn bsectiong the side
60 at the center
Geometry: when a circle is inscribed inside a equialteral triangle. and circle will touch each equilateral triangle at midpoint and side will act a tangent. if i draw a perpendicular from circle center to one of the sides and complete the triangle. angle ratio is.
30 60 90.
90 at the point perpendicular is drawn bsectiong the side
60 at the center
Geometry: square inside a circle. diamter?
diameter is the diagnol of square
Geometry: circle inide a square then side of a square is?
the diameter of the circle.
Geometry: when a square is inscribe in another square
if vertex of smaller square touches larger square at mid points then area of small square is half of large square.
Geometry: rectangle inside a semi circle.
if rectangle side touches diameter then the rectangle is symetrical u can divide it into 2 parts. and if u join center to top vertex u get right angel triangle.
Geometry: area of a circular ring formed by 2 concentric circles
normal is pi r square
here is Pi ( R square - r sqare)
individual squares
Geometry: area of a circular ring formed by 2 concentric circles
normal is pi r square
here is Pi ( R square - r sqare)
individual squares
Geometry: volume of cube and cuboid
side cube
base X width X height
Geometry: diagnol of a cuboid and cube
cuboid is underoot L sq + W sq + H sq
cube is S root 3
Geometry: in general volume is? and use it for volume of cylinder
height X base area. base kitni height tak gya
cylinder volume = pi r square H
Geometry: lateral surface area of a cylinder and total surface area?
2 pi R H
2 pi r square + 2 pi R H
Geometry: formula of volume and rate
Time = Distance / Rate
Geometry: it is imporant to know dimensions of a figure to find how fast will it fill the 3d fig?
yes, we must know the rate at which liquid flows into the figure and exact dimension. same is with if we want to fit smaller objects into larger objects. since a 6x6 box can fit into a 100x1 box even tho volume of 100x1 box is more.
Geometry: Diagnols are equal for which of parellogram, rectangle, square
only rectangle and square
Geometry: diagnols bisect each other for which
all 3 of parallelogram, rectangle and square
Geometry: dignols bisect at 90* for which?
Only square in all 3 of parallogram, rectangle and square.
