GRE Quant : Arithmetic - II

Continuing with our post on Arithmetic, here you will find the remaining concepts related to the Arithmetic section.

The concepts are all followed by questions that you may find in your actual GRE exam. 

We suggest you to make a note of all the formulas mentioned and practice the sample questions. 

PERCENTAGES

Percentage is a number or ratio expressed as a fraction of 100. The percentage is very often denoted with “%” sign or abbreviation “pct.”, or even sometimes “pc”. Percentage is a dimensionless quantity.

Concept of Percentage Change

Absolute value change: It is the actual change in the quantity. For instance, if the sales in a particular year is $3500 and the sales in the consecutive year is $3600, then the absolute value of change is $ 100.

Percentage change: It is the percentage change got by the formula

Percentage change = (Absolute change/Original quantity)*100

Example:

Today the price a table was reduced by 40% from what is was yesterday, and the price of a lamp was reduced by 50% from what it was yesterday.

QUANTITY A	QUANTITY B
The dollar amount of the reduction in the price of the lamp.	The dollar amount of the reduction in the price of the table.

🔘Quantity A is greater.

🔘Quantity B is greater.

🔘The two quantities are equal.

🔘The relationship cannot be determined from the information given.

Answer: The relationship cannot be determined from the information given.

RATIO

A ratio is a comparison between two quantities in the form of a quotient.

Example:

Joy earned $0.85 for every mile he walked in a Walkathon. If he earned a total of $32.3 at that rate, how many miles did he walk?

🔘35

🔘36

🔘37

🔘38

🔘39

Answer: 38

 

PROPORTION

Two varying quantities are said to be in a relation of proportionality, if they are multiplicatively connected to a constant called the coefficient of proportionality or proportionality constant.

A proportion is basically an equation with two fractions, such as 4/x = y/7. You can always solve a proportion by cross-multiplying the numerator of one fraction by the denominator of the other. 4/x = y/7 would become 28 = xy after cross-multiplication.

Example:

In 2004, 2,400 condos sold, 15% of the total housing units sold that year. If 25% of the homes sold in 2004 were four-bedroom houses, then how many four-bedroom homes sold in 2004?

🔘3,600

🔘4,000

🔘4,200

🔘4,800

🔘6,000

Answer: 4,000

PROGRESSIONS

Arithmetic Progression

Arithmetic Progression is a sequence in which the terms increase or decrease by a common difference d.

The series is of the form a, a+d, a+2d, a+3d…

First term is denoted by ‘a’.

Common difference, d=a2-a1 (second term – first term)

nth term of A.P. = a+(n-1)d

Sum of n terms of an A.P. is the addition of first n terms of A.P. It is equal to n/2 times the sum of twice the first term and the product of (n-1) and common difference d.

Sum of n terms of an A.P.= (n/2)[2a+(n-1)d]

Example:

                               2, -3, 5, 2, -3, 5, 2, -3, 5……..

In the above sequence, the first 3 terms repeat without end. What is the sum of the terms of the sequence from the 129^th term to 135^th term?

🔘13

🔘15

🔘17

🔘19

🔘21

Answer: 13

For each integer n>1, let A(n) denote the sum of the integers from 1 to n. For example, A(50)=1+2+3+…..+50 = 1,275. What is the value of A(100)?

🔘10,100

🔘5,050

🔘6,150

🔘20,100

🔘21,500

Answer: 5,050

Geometric Progression

Geometric Progression is a sequence in which the terms increase or decrease by a common factor d.

The series is of the form a, ar, ar², ar³…..  

First term is denoted by ‘a’.

Common difference, r = a2/a1 (second term / first term)

nth term of G.P = ar^n-1

Sum of n terms of an G.P. = a(rⁿ - 1)/(r-1)

Harmonic Progression

The numbers a1, a2, a3…. are said to be in H.P if 1/a1, 1/a2, 1/a3 are in A.P.      

nth term of H.P. = 1/a+ (n-1)d where a=a1, d=(1/a2)-(1/a1).

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