Arithmetic from the CAT QA section is one of the important topics. Around 10 questions are from this topic every year. Since CAT Exam Pattern has been revised and the total number of questions from CAT QA has been reduced to 26, therefore, candidates can expect around 6-7 questions based on arithmetic in CAT Question Paper 2021. 

Arithmetic consists of topics such as Percentages, Simple Interest, Compound Interest, Profit and Loss, etc. The questions are usually not very difficult if candidates have their basics covered. Candidates can refer to NCERT Mathematics, as well as books by RS Agarwal and Arun Sharma for CAT Preparation. Check CAT Preparation Tips​

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CAT Arithmetic Important Topics

Here are all the major topics for CAT Arithmetic: 

CAT 2021 Arithmetics: Important Formulas

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CAT Arithmetic: Percentages

Here is all the basic information about percentages: 

• Denoted by the symbol %, percentage can be calculated through the following formula: 

Percentage = (Given Value ⁄ Total Value) × 100

• Percentage Change: it can be calculated by: 

Actual Change/Original Value x 100

• Percentage vs Fraction Form
  • 100% - 1
  • 50% - 1/2
  • 331⁄3% or 33.33 - 1/3
  • 25% - 1/4
  • 162⁄3% or 16.66% - 1/6
  • 142⁄7% or 14.28% - 1/7
  • 121⁄2% or 12.5%; - 1/8
  • 111⁄9% or 11.11% - 1/9
  • 10% - 1/10
  • 91⁄11% or 9.09% - 1/11
  • 81⁄3% - 1/12

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CAT Arithmetic: Simple Interest

• Simple interest is a quick and easy method of calculating the interest charge on a loan. 
• It is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
• Formula for Simple Interest is as follows: 

A = P(1+rt)

Where
A - Final Amount
P - Initial Principal Interest
r - Annual Interest Rate 
t - Time Period of the Loan/Deposit in years.

• Formula for Principal:

P = (100 x A/R x T)

• Formula for Rate of Interest:

R = (100 x P/P x T)

• Formula for Time:

t = (100 x A/R x T)

• Formula for Net Amount:

A - P+I

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CAT Arithmetic: Compound Interest

• Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. 
• The total initial amount of the loan is then subtracted from the resulting value
• Compound interest = total amount of principal and interest in future (or future value) less principal amount at present (or present value)

= [P (1 + i)n] – P
= P [(1 + i)n – 1]

Where:
P = principal
i = nominal annual interest rate in percentage terms
n = number of compounding periods

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CAT Arithmetic: Averages

• Averages or central tendency includes mean, median and mode. 
• They are essentially the central value of a data set and provide information about the data in a glance. 
• Formula for Mean:
  Sum of all the values/Number of Values
• Median: Median is the central most value in a data set. 
• Formula for Median:
  {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.
• To find the median, first order the numbers from smallest to largest. Then find the middle number.
• Mode: The mode is the most frequently occurring value of a data set/Sample. 

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CAT Arithmetic: Profit and Loss

• Important formulas for Profit and Loss: 
  • Profit = Selling Price – Cost Price
  • Loss = Cost Price – Selling Price
  • Profit % = (profit/ Cost price) *100
  • profit % = {(selling price – cost price)/ Cost price} *100
  • Loss % = (loss/ Cost price) *100 
  • Loss % = {(Cost price – selling price)/ Cost price} *100A is x% more than B and is x% of the sum of A and B. What is the value of x?

Check CAT Quant Paper Analysis

CAT 2021 Arithmetics: Tricks and shortcuts to increase speed

• Memorize important Squares and Square Roots – Certain squares and Square Roots are commonly repeated in the CAT examination and of that matter in any other examination. So it's best to memorize the results to speed up the calculation. Try to at least memorize squares and square roots till 20 as they are an important part of CAT Arithmetic Questions.
• Memorize Percentage Tables – Common percentage fractions like 33.33%, 87.50% 8.33%, and others are also an inseparable part of CAT Arithmetic Questions. So, aspirants should memorize import fractional conversions of the percentages.

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CAT Arithmetic Sample Questions

Ques 1. A: B: C is in a 3: 2: 5 ratio. How much C earns out of Rs 1260?

1. 252
2. 125
3. 503
4. None of these

Solution: 4

Ques 2. If 15 men can build a wall on the border in 28 days. The wall is destroyed by a mortar and 10 men are killed, in how many days would the remaining men be able to build the wall again. (Assuming that the wall would need rebuilding from scratch)?

1. 50 days
2. 60 days
3. 84 days
4. 9.333 days

Solution: 3

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