 ## Arithmetic Ability

Theory

Questions on Arithmetic form a major chunk of the Quant section in all Banking Entrance exams. It is very important to get the basics right in this topic.

Theory

BODMAS

When an expression contains all the mathematical operations, there is an order in which those operations have to be performed. BODMAS is an acronym for Brackets, Order, Division, Multiplication, Addition, Subtraction. The operations have to be performed in this order: 1. Brackets 2. Order (Power or Index) 3. Division 4. Multiplication 5. Addition 6. Subtraction

Solved Example

What is the value of $$(2+3)^2 * 5 + 9/3 – 8$$ = ?

The first operation is brackets: 2+3 = 5
The second operation is order: $$5^2 = 25$$
The third operation is division: 9/3 = 3
The fourth operation is multiplication: 25*5 = 125
The next operation is addition: 125 + 3 = 128
The next operation is subtraction: 128 – 8 = 120

Tip

The order of division and multiplication can be interchanged. Similarly, the order of addition and subtraction can be interchanged.

Theory

Percentages

Many questions in Arithmetic are on Percentages. It is important to keep the following percentage – fraction conversions in mind.
½ = 50%
1/3 = 33.33%
¼ = 25%
1/5 = 20%
1/6 = 16.67%
1/7 = 14.28%
1/8 = 12.5%
1/9 = 11.11%

Formula

1. LCM of fractions = $$\frac{LCM of numerators}{HCF of denominators}$$

2. HCF of fractions = $$\frac{HCF of numerators}{LCM of denominators}$$

Theory

A few questions are asked on inequalities. It is important to know the following inequalities:

1. For any positive real number x, x+1/x >= 2

2. For any three real numbers x, y and z, if x > y, then x + z > y + z

Theory

If x > y and

1. If z is positive, then xz > yz
2. If z is negative, then xz < yz
3. If x and y are of the same sign, then $$\frac{1}{x}$$ < $$\frac{1}{y}$$
4. If x and y are of different signs, then $$\frac{1}{x}$$ > $$\frac{1}{y}$$
Theory

1. The modulus of x, |x| = maximum of (x, -x)

2. For any two real numbers ‘a’ and ‘b’, |a| + |b| >= |a+b|

3. For any real number ‘a’, $$a^2 = |a|^2$$

Solved Example

In a two-digit number, the difference between the digits is 5 and the sum of the digits is 13. What is the number?

Solution: Let the number be xy. So, x – y = 5 and x + y = 13
=> x = 9 and y = 4
So, the number is 94. The number can also be 49.

Solved Example

What is the greatest number that divides 1265 and 1070 and leaves remainders 4 and 3 respectively?

Solution: Since the number leaves a remainder of 4 when dividing 1265, it is a factor of 1261. Similarly, the number is a factor of 1067. So, the number is a factor of both 1067 and 1261. Since we need the highest such number, the required number is the HCF of 1067 and 1261.
The prime factors of 1067 = 11*97
The prime factors of 1261 = 13*97
Hence, HCF of these two numbers is 97.