Quant Flashcards
What to do with large number of order magnitude 5 -00000
i.e: 99998
Try and see whether they can be turned into multiple of 10 such as 10^5
99998 = 10^5 - 2
What to do when you have number with roots ?
1) First try and simplify by removing from under the root when dealing with integers number
2) If having x or letter (k) under the root, think of raising the power to square
What to do when you have number with roots as denominator ?
Always try and rationalise to see what happens before moving on
How to deal with geometric progression?
Geo Progression
= ar^(n-1)
Then get value of „r“
a : number of elements
n : the order of the item (8th)
If K is a two digit positive integer with tens digit x and units digit y then k^2 -(x+y)^2 must be divisible by which factors ?
Define as follow
Tens factor = 10x
Units factor = y
Hence
K= 10x+y
Try and raise it to the power then
K^2 = (10x+y)^2 = 100x^2 + 20xy+ 2y^2
What to do when dealing numbers that are very small such as 0.0025 or 0.00025
?
First convert them into the power of 10
I.e.: 0.0025 = 25*10^(-4)
or 0.00025 = 25*-10^(-5)
Turn them into power of 10 before computing
When faced with an arithmetic question of average
Let say a class -average is 70, of the boy‘s’ average is 65 and that of the girls‘ is 80, what could be the number of boys and girls
Define the variables
Girls —-> g : 80g
Boys—->b : 65b
Total score of the class is:
80g + 65b
Given average = 70
Hence
80g + 65b = 70(g+b) = 70g+70b
80g-70g+65b-70b=0
10g=5b
b/g =10/5 or 2/1
General rule
Total number of all element characteristic combine / total number of elements = average
How to approach questions defined by speed and time
1) define the speed and time
T=distance/speed
So the change in time will correspond to change in speed
Let say distance is 900
T1 = 900/ S1
T2 = 900/ S2 + 10
The difference should help you with finding the speed
Simple Interest rate ?
PRT/100
Principal, Rate, Time
Use the absolute value for interest rate given they are divide by 100.
Make sure you follow the formula to define who does what
Increase of 100%
Let say the quantity doubles every year for 3 years
X(1+1)^n
X(1+1)^3
Shortcut recognisable identity
X^2 + 1
X^2 + 1 = (X-1)^2 + 2X
Number of ways of picking 2 black balls out of a pack of 11 black balls and 11 white balls
% = number of way of picking 2 black balls out of 11 / number of ball of picking any two balls
%= (1110 / 2) / (2221/2)
%= 110/ 462
%= 10/42 or 5/21
Median question 1
How to find the median of 4 numbers ?
Estimate the median of the min
Estimate the median of the max
The median of the range is in between
Property between 2 digit numbers and numbers obtained from interchanging them
The difference between 2 digit numbers is Always 9 times the difference between the number
Assume the difference is 54
So the digit can be reverse only by 6-6
Hence 93-39
System of equations with 3 variables
Always render one of the equations variable equal by multiplying
Generally chose the z as we want to arrive at x and y
Assume x and y are positive integers
2x+3y+xy=12
A way to solve is :
2x+3y+xy=12
Add the smallest multiple of the factor to both side of the equation
2x+3y+xy+6 = 18
(2x+6) + (3y+xy) = 18
2(x+3) + y(3+x) = 18
(2+y) (x+3) = 18
Perimeter of rectangles
Length = x
Width = y
Perimeter = 2(x+y)
A straight line in the plane XY- plane has a slope of 3 and a Y-intercept of 4. on this line, what is the X-Coordinate of the point whose Y-coordinate is 10?
Equation of a line is given by
Y=mx +c where m is the slope and c is the intercept
The equation of the line is
Y=3x + 4
Let’s the required point on the above line be (a, 10)
Thus we have
10 = 3a + 4
a = 2
So the point is (2,10)
In a plane XY, a line l passes through the origin and has a slope of 3.
If points (1, a) and (b, 2)
What is the value of a/b
Equation of line passing through a point (p,q) and a slope m is given as
y-q=m(x-p)
Thus the equation of the line that passes through the origin and has slope 3 is
y-0=3(x-0)
y=3x
Since (1,a) is on the line we have
a= 3(1)= 3
b==> 2=3a= a= 2/3
a/b = 3/2/3 = 9/2
If the points (a,0) (0,b) and (1,1) are collinear, what is the value of a in term of b
The slope of lines joining 2 points must be equal
Get the slope of the line using the difference of points then compare both.
Adding a solution to get to a target or threshold, how to proceed
Content / total solution >= target
What can be the divider of 0.2151515151
Among intergers
1) define x
2) multiply by 100
3) Substrat x from both side of the equation
4) determine x
Number of ways in which 3 elements can be selected from n elements in a set
3Cn = n(n-1)(n-2) / 321
3Cn = n(n-1)(n-2) / 6
What is the relationship between the median and the mean in normal distribution?
In normal distribution, the mean and the median are the same