Quantitative Aptitude - Arithmetic & Algebra

Monday, June 26, 2006

1. Numbers
   1. Number System
   2. Classification of Numbers
   3. Properties of Numbers
   4. Base System & Base Conversion
   5. Absolute Value
   6. Basic Arithmetic Operations
   7. VBODMAS Rule
       
2. Symbol Based Problems
    
3. Divisibility Test
   1. HCF & LCM
   2. HCF & LCM of Integers
   3. HCF & LCM of Fractions & Decimal numbers
       
4. Surds and Indices
   1. Square numbers
   2. Square roots & Cube roots
   3. Laws of Indices
   4. Rule of cyclicity
   5. Laws of surds
       
5. Averages
   1. Types of averages
   2. Arithmetic mean
   3. Geometric mean
   4. Harmonic mean
   5. Relation between the three means i.e AM, GM, HM
       
6. Percentages
   1. Definition of percentage
   2. Application involving percentage
       
7. Stocks and Shares
    
8. Simple & Compound Interest
   1. SI & CI
   2. Population & Depreciation
       
9. Profit & Loss
   1. Basic terminology in Profit & Loss
   2. Important formulae in Profit & Loss
       
10. Basic Algebraic Operations
    1. Basic concepts of Algebra
    2. Arithmetic operations on algebraic expressions
        
11. Algebraic formula and their applications
    1. Important algebraic formulae
    2. HCF & LCM of polynomials
        
12. Simple Equations
    1. Framing a simple equation
    2. Conversion of verbal statements to simple equation
        
13. Simultaneous Equations
    1. Simultaneous equations
    2. General method of solving simultaneous equations
        
14. Quadratic Equations
    1. Definition of a quadratic equation
    2. Roots of a quadratic equation
    3. Relation between roots and coefficients
    4. Nature of the roots of a quadratic equation
    5. Equation reducible to quadratic equation
        
15. Inequations
    1. Definition of an inequation
    2. Properties of inequalities
    3. Quadratic inequalities
        
16. Ratio, Proportion & Variation
    1. Definition of a ratio
    2. Composition of ratios
    3. Order of ratios
    4. Properties of ratios
    5. Definition of proportion
    6. Continued proportion
    7. Variation
    8. Important results of proportion
        
17. Partnership
    1. Definition of partnership
    2. Simple & Compound Partnership
        
18. Mixtures & Alligations
    1. Types of mixtures
    2. Alligation Rule
    3. Important results based on Alligation rule
        
19. Time, Speed & Distance
    1. Definition of speed
    2. Average speed & proportion related to Average speed
    3. Relative speed & proportion related to Relative speed
        
20. Races
    1. Basic terminology in races
    2. Important formulae related to races
        
21. Work
    1. Definition of work
    2. Important formulae for work related problems
        
22. Pipes & Cisterns
     
23. Calendar
     
24. Clocks
     

What is wrong in the proof? 1 = 0

Tuesday, June 13, 2006

Of course 1 != 0, spot the error.

let x = y and x² = xy

now subtracting y² from both sides, we get

x² - y² = xy - y²

(x + y)(x - y) = y(x - y)

hence x + y = y

Also, x = y then

2y = y

2 = 1

now subtracting 1 from both sides

1 = 0

HCF & LCM - Basics 2

Wednesday, June 07, 2006

I assume the concepts of factors and multiples would be clear till now, if not, don't blame me for it ;), go through my previous posts, I am a bad bad teacher.

Least Common Multiple (LCM): What are the factors of 10? 2 & 5, correct. What if I ask you about a number which is divisible by both 2 and 5, what will be your answer? 10, correct. So, basically 10 is a common multiple of 2 and 5. Now what is a common multiple of 2, 3 & 5? In other words a number which is divisible by 2, 3 and 5? 30, correct. If you understand this concept then you already know what LCM is. Let's officially define LCM. LCM of two or more given numbers is the least number which is exactly divisible by each of the given numbers. Official definitions are scary, aren't they? Of course unless you are a nerd.

Q) Why should I learn LCM? Can I do without it?
A) Previously while we were looking into HCF, we planted some trees, now that the trees are grown and its Mango season, I want to send some Mangoes (hafus) to my siblings and relatives, I sent each one same amount of mangoes, dint exceed 150 dozens each, just that the cartoons didn't contain equal number of mangoes. I sent few cartoons each containing 6 dozens to my sister, I shipped few cartoons each containing 8 dozens to my brother and I shipped few cartoons each containing 10 dozens of mangoes to my aunty, who stays in Alibaug. How many cartoons were in each shipment?

Since I am fair to everyone, each receives equal number of mangoes, say X, then X has to be a multiple of 6, 8 and 10. In other words X is a common multiple of 6, 8 and 10. To find out common multiple which is not greater than 150, I did some math, you don't need to worry about that right now.

6 = 2 x 3
8 = 2^3
10 = 2 x 5

LCM = 2^3 x 3 x 5 = 120.

Each one received 120 dozens of mangoes, that's hell lot of mangoes. Hence my sister received 120 / 6 = 20 cartoons, my brother received 120 / 8 = 14 cartoons and my aunt who is in Alibaug received 120 / 10 = 12 cartoons, so total 20 + 14 + 12 = 46 cartoons.

So can I do without LCM? No. LCM also comes handy for arithmetic of fractions, which I will cover later.

Methods to find LCM:

Factorization method 1: Express the given numbers in prime factors, then pick all the highest powers of the primes and multiply it. Voila! you got your LCM.

Example: LCM of 60 and 150
60 = 2² x 3 x 5
150 = 2 x 3 x 5²
LCM = 2² x 3 x 5²

In the above example the highest powers of 2, 3 and 5 are 2, 1 and 2 respectively, hence I picked 2², 3 & 5².

Factorization method 2: Start with a small prime, divide all the numbers possible, leave alone which are not divisible, repeat until you are left with only prime numbers.

Example: Find the LCM of 26, 18, 28, 39

LCM = 2 x 2 x 3 x 3 x 7 x 13 = 3276

*TIP: After practice you will be able to find out the common factors by just looking at the numbers, only consider the highest power of that factor and continue.

Dont's: Don't mistake LCM for HCF, if you are finding the lingo little confusing, try to say LCM as "common multiple which is least" for LCM and "common factor which is highest" for HCF. You will get used to it.

Reading Comprehension - 1

Monday, June 05, 2006

Surreal, not Saral

Income tax lawyers can rejoice. Government has just made filing tax returns considerably more complicated. Instead of the earlier one-page Saral form, the IT department is set to introduce Form 2F.

The latter is a four-page form and promises to make life far more complicated for salaried taxpayers. They will now have to provide a slew of details, including household expenses, cash balance, bank balance and receipt of gifts.

This would in effect involve totting up income and expenditure just as in a company balance sheet. The revenue secretary has justified the new form on the grounds that it would reduce the likelihood of 'intrusive investigation'.

But, unfortunately, replacing Saral does just the opposite - it smacks of economic policing. There is absolutely no rationale for finding out how people have spent their money as long as they are paying income tax.

It also goes against the worldwide trend of simplifying filing of tax returns. The logic for this is that the easier it is for an individual to file returns, greater the likelihood of tax compliance.

The revenue department, it seems, has learnt none of these lessons. The new form is a throwback to an earlier age. It is more likely to be an impedi-ment in widening the tax net.

It also has the potential to further increase the already bloated babudom of the IT department thereby increasing the cost of collecting taxes. The finance ministry should be worried that total tax revenue collection in India is around 16 per cent of the national income.

This is not only much lower than the US, which has a tax-GDP ratio of over 25 per cent, and western European nations with a ratio of over 30 per cent, but also lower than developing countries like Mexico.

Government should be putting its mind to raising the tax-GDP ratio by measures such as bringing agricultural income into the tax net and targeting the black economy.

But instead of finding ways to increase tax collection, government has made it more difficult for genuine taxpayers to file returns. Tinkering around with income tax return forms typifies the mindset of the Indian state.

It usually, and often willfully, misses the wood for the trees. Instead of tackling issues vital to the health of the economy, government has chosen a soft target: The salaried middle class. Instead of making life simpler for law-abiding citizens, the state has chosen to harass them.

Questions:

1. Is the author happy about the change in filling tax returns?

2. According to the author, the government should pay more attention to..?

3. What is the tax revenue collection in US?

4. Is India's total tax revenue collection higher than Mexico's?

Word power:

1. surreal - adj. dream like, strange

2. totting - v. add, total

3. impediment - n. a hindrance or obstruction

4. bloated - adj. excessively large or wealthy

5. tinkering - v. path, fix, tamper with

Vocabulary Set 3 - A

Sunday, June 04, 2006

1. abstract
   adj. [more abstract; most abstract] theoretical; not concrete
   To him, hunger was an abstract concept; he had never missed a meal.
   


2. abusive
   adj. coarsely insulting; physically harmful
   An abusive parent damages a child both mentally and physically.
   


3. abut
   v. [abutted; abutted; abutting] border upon; adjoin
   Where our estates abut, we must build a fence.
   


4. abysmal
   adj. bottomless
   His arrogance is exceeded only by his abysmal ignorance.
   


5. accede
   v. [acceded; acceded; acceding] agree
   If I accede to this demand for blackmail, I am afraid that I will be the victim of future demands.
   


6. accelerate
   v. [accelerated; accelerated; accelerating] move faster
   In our science class, we learn how falling bodies accelerate.
   


7. accessible
   adj. easy to approach; obtainable
   We asked our guide whether the ruins were accessible on foot.
   


8. accessory
   n. [accessories] additional object; useful but not essential thing
   She bought an attractive handbag as an accessory for her dress.
   


9. acclimate
   v. [acclimated; acclimated; acclimating] adjust to climate or environment
   One of the difficulties of our present air age is the need of travelers to acclimate themselves to their new and often strange environments.
   


10. acclivity
    n. [acclivities] sharp upslope of a hill
    The car could not go up the acclivity in high gear.
    

<< Vocabulary #2- A || Table of Contents || Vocabulary #4 - A >>

Vocabulary Set 2 - A

1. ablution
   n. washing
   His daily ablutions were accompanied by loud noises that he humorously labeled "Opera in the Bath."
   


2. abnegation
   n. renunciation; self-sacrifice
   Though Rudolph and Duchess Flavia loved one another, their love was doomed, for she had to wed the king; their act of abnegation was necessary to preserve the kingdom.
   


3. abominate
   v. [abominated; abominated; abominating] loathe; hate
   Moses scolded the idol worshipers in the tribe because he abominated the custom.
   


4. abortive
   adj. unsuccessful; fruitless
   We had to abandon our abortive attempts.
   


5. abrasive
   adj. rubbing away; tending to grind down
   Just as abrasive cleaning powders can wear away a shiny finish, abrasive remarks can wear away a listener's patience.
   


6. abrogate
   v. [abrogated; abrogated; abrogating] abolish
   He intended to abrogate the decree issued by his predecessor.
   


7. abscond
   v. [absconded; absconded; absconding] depart secretly and hide
   The teller absconded with the bonds and was not found.
   


8. absolute
   adj. complete; totally unlimited
   Although the King of Siam was an absolute monarch, he did not want to behead his unfaithful wife without absolute evidence of her infidelity.
   


9. absolve
   v. [absolved; absolved; absolving] pardon (an offense)
   The father confessor absolved him of his sins.
   


10. abstain
    v. [abstained; abstained; abstaining] refrain; withhold from participation
    After considering the effect of alcohol on his athletic performance, he decided to abstain from drinking while he trained for the race.

<< Vocabulary #1- A || Table of Contents || Vocabulary #3 - A >>