Quantitative

• The Quantitative section measures your basic mathematical skills, concepts and the ability to solve problems in a quantitative setting.

• Problem solving techniques, Short cut methods and formulas

• Basic knowledge of arithmetic, algebra, geometry, Expressions, variables finding

**Question Types**

• Age problems

• Work hours problems

• Clock angles and Sector area

• Algebraic expressions

• Speed distance problems

• Fractions & Percentages

• Range, mean, Mod

• Simple Geometry problems

• Basic Arithmetic

• Probability

• Ratios

• Profit, Discount problems

• Equation solving for Variables

Quantitative Sections Formulas

• **Speed Distance and Time**

**Distance = Speed * Time**

Example:

If a man running at 15 kmph passed a bridge in 9 seconds, what is the length of the bridge?

**Solution**: As S=v*t

Length=(15*1000/ 3600)*9=37. 5m

------------------------------------

• **Mean Value**

• The mean average is not always a whole number.

• The mean is the **total **of the numbers **divided **by how many numbers there are.

• To work out the mean:

• Add up all the numbers.

7 + 9 + 11 +6+13 + 6 + 6 + 3 + 11 = 72

• Divide the answer by how many numbers there are. There are 9 numbers.

72 / 9 = 8

**So the mean value is 8**.

-------------------------------------------

• **Mode Value**

• The mode is the value that appears the **most**.

• 7 9 11 6 13 6 6 3 11

• To work out the mode:

• Put the numbers in order: 3 **6 6 6** 7 9 11 11 13

• Look for the number that appears the most. 6 appears more than any other number.

**So the mode value is 6**.

-----------------------------------------

• **Median value**

• The median is the **middle **value.

• To work out the median:

• Put the numbers in order: 3 6 6 6 **7** 9 11 11 13

• The number in the middle of the list is the median. **So the median value is 7**.

• If there are two middle values, the median is halfway between them. Work out the median for this set of numbers:

• 3 6 6 6 **7** **8** 9 11 11 13

• There are two middle values, 7 and 8.

The median is **halfway **between 7 and 8, so the median is 7.5.

--------------------------------------

• **Range**

• The range is the **difference **between the biggest and the smallest number.

• To work out the range:

• Put the numbers in order:

3 6 6 6 7 9 11 11 13

• Subtract the smallest number from the biggest number:

13 - 3 = 10

**So the range of this set of numbers is 10**.

--------------------------------------

• **Sum of given Series **

Sum = ((First Term+ Last Term) /2 )* Number of Terms

Example:

• .what is the avg of first 20 multiples of 7?

So series for first 20 multiples of 7 is 7,14,21......41

• Sum=((7+140)/2)*20

• Sum=73.5*20

• We have to find avg so

• Avg=73.5*20/20=73.5

--------------------------------------------

• **Probability **

Probability that event A occurs P(A) = n(A) / n(S).

where

n(A) - number of event occurs in A

n(S) - number of possible outcomes

**Example**:

What is the probability of sum 9 on both of two dice when rolled together?

**Solution**:

Total outcomes for two dices=6*6=36

Events whose sum is 9 are (3,6),(6,3),(4,5),(5,4)=4

Probability of sum 9=4/36=1/9

• **Marble Size, Number of Marbles **

Example: • Marble size is 20cm*30cm. How many marbles are required to cover a square with side 3m?

• 3m= 300cm

• Area of Square=300*300

• **No of marbles=Area /Marble size **

• =300*300/ 20*30= 150

------------------------------------------------

• **LOG PROPERTIES **

• 1) Multiplication inside the log can be turned into addition outside the log

• Log(x.y)=log x+logy

• 2) Division inside the log can be turned into subtraction outside the log

• Log(x/y)=logx - logy

• 3) An exponent on everything inside a log can be moved out front as a multiplier

• In x^2=21n x

• In e=1

-------------------------------------------

• **Clock hands and Angles **

• Angle traced by hour hand in 12 hrs = 360°.

• Angle traced by minute hand in 60 min. = 360°.

**Example**:

• 5:35 express hour hand in degree?

• As 12 Sectors on clock=360 degree

• 5*30+30*35/60=150+17.5=167.5 degrees

-------------------------------------------

• **WORK SHARE **

• Amount of Work/Time=Output(Rate)

**Example**:

• A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

• A=1/4

• B+C=1/3

• A+C=1/2

• C=1/2 - 1/4=1/4

• B=1/3 - 1/4=1/12

• **So B alone will do in 12 hours**.

----------------------------------------------

• **AGE PROBLEM **

• **Example**:

• If father is double the age of his son. 20 years ago he was 12 times that of son. What is the age of father now?

• F=2S

• F-20=12(S-20)

• 2S-20=12S-240

• 10S=220

• S=22

• F=2S=44

------------------------------------------------

• **Percentage % SHARE **

• A company sell three types of mobiles worth 100, 125, and 225. It sold equal no. of all mobiles. What is the percent share of cheapest mobile?

• Total=100+125+225=450

Share of cheapest mobile= 100*100/450=22.22%

-----------------------------------------------

• **Consumer math formulas**:

Discount = list price * discount rate

Sale price = list price - discount

Discount rate = discount - list price

Sales tax = price of item * tax rate

Interest = principal * rate of interest * time

Commission = cost of service * commission rate

• Loss = C.P — S.P

• Gain% = Gain* 100 / C.P

• Loss % = Lost* 1 00 / C. P

---------------------------------------------

• **Sector Area **

• Sector Area=pi* r^2*angle

**Example**:

A clock's minute hand is 10cm long. What area it will cover from 9:00am to 9:35am?

• **Solution**:

r=10 cm

Area=pi* r^2* angle

Area=3.14*10*10*(7/12)

Area=183.3 cm^2

**Note**: for 35 minute, minute hand position will be at 7 angle with position as 7/12 or angle= 210/360

-------------------------------------------------

• **Solving Expressions **

**Example**:

What is the value of x? If 3^ (1+x) + 5*3^x -8=0

**Solution**:

3 * 3^x +5 * 3^x=8

3^x (3+5)=8

3^x=1

3^x=3^0

Hence x=0

--------------------------------------------------

• **AREA & CIRCUMFERENCE OF CIRCLE **

• Area= pi*r^2

• C=2*pi*r

• **AREA OF SQUARE, Triangle,Rectangle **

• Area of square= s^2

• Perimeter=4s

• Area of triangle= b*h/ 2

• Perimeter= sum of all sides

• Area of Equilateral triangle=sqrt3 *s^2 /4

• Perimeter=3s

• Area of rectangle= L*W

• Perimeter=2(L+W)

• Volume of cylinder = pi*r^2*h

-----------------------------------------------------

• **Cube** :

• Let each edge of a cube be of length a. Then,

• 1. Volume = a^3 cubic units.

• 2. Surface area = 6a^2 sq. units.

• 3. Diagonal =sqrt 3a units.

**Example**:

What is the volume of a cube whose surface area is 294?

A.125

b.216

c.294

d.343

• **SOLUTION**:

Surface Area of Cube= 6*a^2=294

a^2=49

So a=7

Volume of Cube= a^3

a^3=7^3=**343**

-----------------------------------------------

• **Cylinder** :

• Let radius of base = r and Height (or length) = h. Then,

• 1. Volume = (π * r^2 * h) cubic units.

• 2. Curved surface area = (2*π * r * h) sq. units.

• 3. Total surface area = 2*π * r*(h + r) sq. units.

--------------------------------------------------

• **i values**

• I=sqrt of -1

• I^2=-1

• I^4=1

------------------------------------------------

• **Average formula: **

Let a1, a2,a3,........an be a set numbers, average = (a1 + a2 + a3 + ....... +an)/n

• Average= sum of elements/no of elements

-------------------------------------------------

• **RATIO **

• 3:b=x:c

• X=?

• 3c=bx

• X=3c/b

-------------------------------------------------- GOOD LUCK