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Question 1

What to do with large number of order magnitude 5 -00000

i.e: 99998

Answer 1

Try and see whether they can be turned into multiple of 10 such as 10^5

99998 = 10^5 - 2

Question 2

What to do when you have number with roots ?

Answer 2

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

Question 3

What to do when you have number with roots as denominator ?

Answer 3

Always try and rationalise to see what happens before moving on

Question 4

How to deal with geometric progression?

Answer 4

Geo Progression
= ar^(n-1)

Then get value of „r“

a : number of elements
n : the order of the item (8th)

Question 5

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 ?

Answer 5

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

Question 6

What to do when dealing numbers that are very small such as 0.0025 or 0.00025
?

Answer 6

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

Question 7

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

Answer 7

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

Question 8

How to approach questions defined by speed and time

Answer 8

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

Question 9

Simple Interest rate ?

Answer 9

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

Question 10

Increase of 100%

Answer 10

Let say the quantity doubles every year for 3 years

X(1+1)^n
X(1+1)^3

Question 11

Shortcut recognisable identity

X^2 + 1

Answer 11

X^2 + 1 = (X-1)^2 + 2X

Question 12

Number of ways of picking 2 black balls out of a pack of 11 black balls and 11 white balls

Answer 12

% = 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

Question 13

Median question 1

How to find the median of 4 numbers ?

Answer 13

Estimate the median of the min
Estimate the median of the max

The median of the range is in between

Question 14

Property between 2 digit numbers and numbers obtained from interchanging them

Answer 14

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

Question 15

System of equations with 3 variables

Answer 15

Always render one of the equations variable equal by multiplying
Generally chose the z as we want to arrive at x and y

Question 16

Assume x and y are positive integers

2x+3y+xy=12

Answer 16

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

Question 17

Perimeter of rectangles

Answer 17

Length = x
Width = y

Perimeter = 2(x+y)

Question 18

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?

Answer 18

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)

Question 19

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

Answer 19

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

Question 20

If the points (a,0) (0,b) and (1,1) are collinear, what is the value of a in term of b

Answer 20

The slope of lines joining 2 points must be equal

Get the slope of the line using the difference of points then compare both.

Question 21

Adding a solution to get to a target or threshold, how to proceed

Answer 21

Content / total solution >= target

Question 22

What can be the divider of 0.2151515151
Among intergers

Answer 22

1) define x
2) multiply by 100
3) Substrat x from both side of the equation
4) determine x

Question 23

Number of ways in which 3 elements can be selected from n elements in a set

Answer 23

3Cn = n(n-1)(n-2) / 321
3Cn = n(n-1)(n-2) / 6

Question 24

What is the relationship between the median and the mean in normal distribution?

Answer 24

In normal distribution, the mean and the median are the same

Question 25

A truck traveled 336 miles per full tank of diesel on the national highway and 224 miles per full
tank of diesel on the state highway. If the truck traveled 4 fewer miles per gallon on the state
highway than on the national highway, how many miles per gallon did the truck travel on the
state highway?

Answer 25

Truck travelled 4 miles less on the state highway compared to the national highway

1- define the distances
1.1 the distance on national highway
1.2 the distance on state highway

The ratio of the gallons consumed over the distance for both highways should be equal

hence
let’ consider
x: distance on national highway
x-4: distance on state highway

hence
336/(x) = 224/(x-4)
3/(x) = 2/(x-4) —> x=12

Question 26

Andrew borrows two equal sums of money under simple interest at 5% and 4% rate of interest.
He finds that if he repays the former sum on a date six months before the latter, he will have to
pay the same amount of $1,100 in each case. What is the total sum that he had borrowed?

Answer 26

Okay, so the two sums are equal
let label them “x”

define the time (the variable that differs)
time for sum a = t
time for sum b = t-1/2

The amount to be repaid is principal + interest

simple interest formula = PRT/100

let’s equal the two final sum payments

5x(t-1/2) / 100 = 4xt / 100
t= 5/2

since the amount to be repaid is principal + interest

x + [x5(t-1/2)]/100 = 1100, replace t by 5/2
remember t=5/2

then we have
x+10x/100 = 1100
(10x+x)/10 = 1100
x= 1000

Question 27

if 3C5 = 3Cx and X=/=3, what is the value of x

Answer 27

value of 3C5 = 5-3C5
hence 3C5 = 2C5
x=2

Question 28

In the XY-plane, a line l passes through the origin and has a slope 3. If points (1; a) and (b; 2) are on the line l, what is the value of
a / b ?

Answer 28

Equation of a line passing through (p,q) and slope m is given as
[y-q= m(x-p)]
Thus the equation that passes through origin (0;0) and has a slope of 3 is
y-0=3(x-0) —-> y=3x
since (1; a) is on the line
y = 3 (1) = 3 , a = 3
since (b; 2)
2 = 3 (x) = x =2/3 b=2/3

from that
a/b = 3/ (2/3) = 9/2

Question 29

In the XY-plane, the point (3; 2) is the center of a circle. The point (1;2) lies inside the circle
and the point (3;4) lies outside the circle. Which of the following could be the value of r?

Answer 29

The equation of the circle having center (p;q) and radius r is
(x-p)^2 + (y-q)^2=r^2
Since the center of the circle is at (3; 2), the equation of the circle is:
(x-3)^2 + (y-2)^2=r^2
If a point (m,n) lies inside the circle then,
(m-p)^2 + (n-q)^2 < r^2

since (-1;2) lies inside the circle,
it must satisfy
(-1-3)^2 + (2-2)^2 < r^2
16 < r^2 ——> 4<r

Question 30

A straight line in the 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?

Answer 30

Equation of the line y = mx + c where m is the slope and c is the y intercept
the equation of the line is
y=3x+4
let’s the required pont on the above line be (a,10)
10=3a+4
a=2
hence the point is (2;10)

Question 31

If the points (a; 0) ; (0; b) and (1; 1) are collinear, what is the value of a in terms of b?

Answer 31

Since the points are collinear, their slopes must be equal.

so derive the slope of the line by subtracting the y and x coordinates of the first 2 points and get the result.

the compare this result against the slope derived using two other different points.

From there you can pull a or b

(X1;Y1) and (X2;Y2)

Question 32

A bag contains 3 white and n red marbles, n > 3. Two marbles are drawn from the bag. If the
probability that one marble is white and the other is red is greater than the probability that
both the marbles are red, what could be value of n?

Answer 32

The probability would be
the number of counting possibilities of picking 1 out of 3 marble times picking 1 out of n possibilities

(1C3 * 1Cn)/ 2C(3+n) =
(3n)/ [(3+n)(2+n)/2*1]= 6n/(3+n)(2+n)

Question 33

If the number of three-element subsets of (1, 2, 3, 4, 5, . . .n), where n is a positive integer, that
do not contain both the elements 2 and 4 simultaneously is less than 35, what could be the
value of n?

Answer 33

Number of ways 3 elements can be selected from n elements is a set

3Cn = n(n-1)(n-2)/321
3Cn= n(n-1)(n-2)/6

Cases whereby 3 elements are selected but number 4 and 2 are not simultaneously selected : 1Cn-2 = n-2

total cases - cases excluding 4 & 2
n(n-1)(n-2)/6 - (n-2)
(n+2)(n-3)(n-2)/6

Question 34

Kris and David work with n other workers. Two of the workers are to be chosen to work on a
new project. What is the expression that gives the probability that both Kris and David will be
chosen?

Answer 34

Proba of the event
# of favorable cases/Total number of cases

favorable case = 2C2

total # of cases
2C(n+2) = (n+2)(n+2-1)/2*1

hence
=2C2/ [(n+2)(n+2-1)/2]
=2/n^2+3n+2

Question 34

General probability formula

Answer 34

2Cn = [n(n-1)]/2*1

Question 35

Machine P produces parts twice as fast as machine Q does. Machine Q produces 100 parts of product K in n minutes. If each machine produces parts at a constant rate, how many parts of product R does machine P produce in t minutes, if each part of product R takes
3/2 times of the
time taken to produce each part of product K?

Answer 35

Machine Q produces 100 parts of product k in N minute
since machine P Produces parts twice as fast as machine Q does, time taken by machine P to produce 100 parts of product K is N/2 minutes

Since each part of product R takes 3/2 times the time taken to produce each part of product K, the time taken by machine P to produce 100 parts of product R is

N/2 * 3/2 = 3N/4

hence th number of part of product R produced by machine P in 3n/4 minutes = 100

The number of part in t is

number of object/time *t

100/[3n/4] *t = 400/3n *t

t / 0.0075n

Question 36

Number of diagonals based on number of sides (n)

Answer 36

Number of diagonal = n(n-3)/2

Question 37

Every person in a certain group is either a Dodgers fan or a Yankees fan, but not both. The ratio of Yankees fans to Dodgers fans is 5 to 3. If 22 Yankees fans change teams to become Dodgers fans, the ratio of Dodgers fans to Yankees fans will be 1 to 1. How many people are in the group?

Answer 37

5/3 could be described as 5x/3x –>
removing 22 from one group and adding them to the other group changes the ration 1/1
5x-22/3x+22 = 1/1 —-> do the math

Question 38

What to consider when dealing with a number with a denominator?

Answer 38

Always be mindful that a denominator CANNOT be equal to zero

Question 39

A certain school in Dec 2013 had 6 teachers and 200 students. On January 2, 2014, 1 teacher and 35 students joined the school, no one left the school.
Quantity A : ratio teacher student Dec 2013
Quantity B : ratio teacher student January 2014

Answer 39

Use fraction pull and push to solve the problem
here we have 6/200 or 3/100 or ~1/33.3
the new addition is 1/35 which is lower than 1/33.3 so the new ratio is lower
hence Quantity A is bigger

Question 40

The sum of the pre-tax costs of Item A and Item B is $300. In Alumba, each item would be charged a flat 7%. In Aplandia, Item A is subject to 5% tax and Item B is subject to 10% tax. If the tax in Aplandia on the purchase of both items is exactly $3 more than it is in Alumba, then what is the pre-tax price of Item A?

Answer 40

Let designate item A as X
X= item A
Given item A is 5% taxed,
0.05X + (300 -X) 0.1 = 24
0.05X + 30 - 0.1X = 24
-0.05X = -6
X=120
Item A = 120
Item B = 180