Three2Tango » Aptitude Questions & Challenges

Speed Maths-Fractions

Sam — Tue, 24 Nov 2009 12:33:28 +0000

Comparison Of Fractions:

Fractions is an important area where most people have problems, and this is a portion which is very much necessary in Quatitative Ability and Data Interpretation area of most competitive exams, like CAT,XAT,SNAP,MAT etc.So Lets discuss a few methods of identifying the largest or smallest fractions from a given set of fractions.

CASE-1: When numerators are same & denominators are different,The fraction with the largest denominator is the smallest, and the fraction with smallest denominator is the largest.

CASE-2: Different Numerator & Same Denominator, the fraction with largest numerator is the Largest, and one with smallest numerator is the Smallest.

CASE-3: In a set of fractions,one with largest Numerator and smallest denominator is the largest in the set.

CASE-4: For a fraction less than one and difference between numerator & denominator are same then fraction with largest values of numerator & denominator will be the largest.Vice Versa also, fraction with smallest value of numerator & denominator will be smallest.

CASE-5: For a fraction greater than one and difference between numerator & denominator are same,then the fraction with smaller values of numerator & denominator will be the largest and vice versa also.

Numbers & Multiplications PART-2

Lloyd — Sat, 08 Aug 2009 06:14:58 +0000

Some of you will be having difficulties when multiplication of 9 comes.So here are some tricks with “NINE”.

MULTIPLICATION of TWO NUMBERs between 90-100

The trick is very simple,but again i stress on practice because if you dont practice, the technique won’t come to you when it is required.And knowledge is absolutely worthless if it didnt help in need.

STEP:1 Find the difference of each number with 100,their product will give the last two digits of the final ANSWER.

STEP:2 Now to get the first two digits of the ANSWER you can either subtract the difference of the 2nd number and 100 from the 1st number or the vice versa.This method is called COUNTER DIFFERENCE method.Because both will give you same answer.

Eg.
96*95=?
STEP:1 4* 5=20 (Product of difference with 100)
STEP:2 96-5=95-4=91
ANSWER =9120

__________________________________________________________

MULTIPLICATION of TWO numbers of which one is full of 9’s.

Eg:
26*99 = (26-1)(100-26)=2574
42*99 = (42-1)(100-42)=4158
I think the 2 examples are self explanatory.

Notes:1

If the number which has only 9’s has more digits than the other then there is a small variation.Here is an example.

Eg:
64*999=?
The number minus ONE will give 63 and 100-64=36 but answer is not 6336.Between 63 and 36 you have to insert as many 9 as the difference between number of digits of both numbers.
64 is two digit number,999 is 3 digit number,So difference is 3-2 =1
Hence add a NINE betweenn 63 and 36 to get the ANSWER,63936.
64*999=63936.

Eg.
76*9999=?
Difference between number of digits is 4-2=2.
Hence 76*9999=(76-1)insert TWO 9(24)=759924

NUMBERS & MULTIPLICATION-CAT RELATED

Lloyd — Fri, 07 Aug 2009 06:08:42 +0000

Numbers & Multiplication
Experts say numbers are very vast.From a CAT, XAT, MAT, or from any competative exam point of view numbers is got prime importance.When we talk about numbers the very basic things that we need to know are 4 operations “addition,subtraction,division,multiplication“.Of these the last one is bit time consuming compared to first two.So lets think of steps to reduce time in multiplication .

Finding SQUARES with ease
I have mentioned a few tips in the same topic before,but here are a few more tricks.First of all certain things you need to keep in mind.
1.While finding a square you must have an idea on how many digits the answer consists of.
For Eg:- its 2 digit till squares of 9,3 digits till squares of 31,from 32-99 it is 4 digits.

SQUARES in the range 40-50-60
Take 50 as the BASE number.Think about number of digits in the answer(Till 99 its 4 digit).

Now an Example will do the explaining job.

Take 56 as the number whose square is to be found.
Find the difference with the BASE(50),here it is 6.
Square of 6 will give last 2 digits of your 4 digit answer.
For the first 2 digits add the difference 6 to the first 2 digits of the square of the BASE number.
So first 2 digits are 25+6=31(First 2 digits of the square of BASE number(50*50=2500) =25).
and answer of 56*56 = 3136

Another Eg:-
59*59= (25+9)(81)=3481.
52*52=2704.

Now if the number is greater than 40 and less than 50.Same rules apply,but here we will subtract the difference with 50, from the first two digits of the BASE number’s square(2500).
Eg:-
46*46 = (25-4)(16) =2116.
47*47 = (25-3)(09)=2209.

By now i hope you understood what i intended, one very important thing is practice, without which you cannot apply or use these tips, at the right time.

2. SQUARES of numbers greater than 100 till 200.

This can be done in three steps.I will explain steps first and then elaborate with an example.
STEP:1 Number + Last 2 digits of the number
STEP:2 Find square of last two digits.
STEP:3 Write down STEP2 below result of STEP:1 such that it starts from unit place of the STEP:1’s answer.Add to get the answer.

E.g:-

113*113

STEP1: 113+13=126 +
STEP2: 13*13 = 169
STEP3: 12769

With these techniques we can considerably reduce time taken.I am telling you all again, workout using some problems.
Eg:-124*124=?
124+24=148 +
24*24 = 576
Answer= 15376

NOTE:1(Important)
153*153=?
153+53=206 +
53*53 = 2809(53 square can be found easily with the other method)
Answer=23409

Here you can see a slight difference,instead of writing the step2 at the unit place, we put it at 10th place or else number of digits in answer will be error.

NOTE:2(Important)
109*109=?
109+09=118 +
9*9 = 81
Answer=11881
See in NOTE:1 & 2 ,knowing the number of digits in the answer comes to play.

Speed Maths

Lloyd — Mon, 27 Jul 2009 18:24:53 +0000

I have posted some speed maths posts before,here are a few more tips and tricks.These are the things i forgot to mention in the other post,these few things are very simple and basic but they will help you gain some time in your quatitative sections.

1.Squares upto 25.
2.Cubes upto 12.
3.Powers of 2 upto 10.
4.Powers of 3 upto 6.
5.Multiplication tables upto 20.
6.Reciprocals of integers upto 12.

Making all these through will surely help you.All these should be in both ways like,when we see 529 in a question 23 should come to our mind automatically.Similarly when we see when we see 144,two things must come to your mind 12 x 12 and 18 x 8.

Multiplication by 11 ( just throw a look, it is very simple)

The trick is simple, start from unit place add the number in the right hand side to each digit and write it as the result in the corresponding place.To avoid confusion add a zero in the beginning and end of the number.

Eg:- Let “873421″ be the number to be multiplied with “11″.

Add zero at both ends,0-873421-0

Answer = (0+8+1)(8+7+1)(7+3)(3+4)(4+2)(2+1)(1+0)

=9607631

Hope you understood the trick.When the sum of adding the right hand digit is a two digit number put the unit place digit in the result and take tenth place digit as carry.

Multiplication by 12.

If you understood the previous multiplication then this also is simple,a small variation is there,DOUBLE each digit before adding the right digit.

Eg:- 879 x 12=?

0-879-0

Answer:=start from unit place

(9×2+0) :CARRY = 1 ANSWER=8

(7×2+9+1) :CARRY = 2 ANSWER=48

(8×2+7+2) :CARRY = 2 ANSWER=548

(0×2+8+2) :CARRY = 0 ANSWER=10548

There are tricks for multiplication by 13 also,slightly complicated yet interesting.

Here is a set of excercise problems

“Simple” Multiplication Challenge

Lloyd — Mon, 27 Jul 2009 18:16:39 +0000

Set your stop watch and check how much time you take to do these multiplications.

397 x 11 =

8598 x 11 =

59784 x 11 =

287986 x 11 =

8894357 x 11 =

157 x 12 =

2189 x 12 =

45876 x 12 =

914785 x 12 =

8237694 x 12 =

Now make a note of your time,and Read This
Check your time again with these figures and see the difference

Quatitative Challenge

PARTS of SPEECH

Lloyd — Tue, 14 Jul 2009 18:57:12 +0000

When one starts thinking about English grammar,the first thing he/she must look into is the parts of speech.Just like studying alphabets when we start studying a language,studying parts of speech is the first step we should take when we start with English grammar.

Just look at the set of words given below and pic the odd one.

India,Srilanka,Pakistan,Orange

Here one can easily pic orange as the odd one,its because of the categorization of the words,all except orange are names of different countries.Similarly the parts of speech are categories used to organize or classify words according to their usage.We use parts of speech as a way to make it easier to talk about language.

Now consider the sentence “A man surreptitiously entered the room”.Even if the word “surreptitiously” is alien to you,if you are familiar with Parts of Speech(POS) you can simply make out that it is an adverb.Similarly when we look into dictionary we can find the POS of the word with its meaning.

The eight PARTS OF SPEECH used to describe English words are

1)Nouns

2)Pronouns

3)Adjectives

4)Verbs

5)Adverbs

6)Prepositions

7)Conjunctions

8)Interjunctions

NOUNS

A noun is often defined as a word which names a person, place or thing.Examples:-boy,girl,India,Gandhiji,Ganga,Thames,movie,Newdelhi.Nouns can be classified into 2 mainly

a) PROPER NOUNS

These are usually names and start with capital letters even in the middle of sentences.Like name of a person,place etc

b)COMMON NOUNS

Can be name of objects(concrete noun),quality,feelings,ideas(abstract nouns),or group names like pride,clan,herd etc(collective nouns).

PRONOUNS

a) Personal Pronouns

I,You,He,She,It,They,We

b) Possessive Pronouns

my,mine,us,our,ours,them,their,your,yours

c) Emphatic Pronouns

myself,ourself,herself,himself

d) Demonstrative Pronouns

this,that,these,those

e) Relative Pronouns

which,who

ADJECTIVES

Adjectives describes a noun or a pronoun.It has different degrees of comparison.

Always use “THE” before a superlative degree.

Eg:- Good teacher, better teacher, best teacher

VERBS

Actions, state of an object.Verbs have VOICE.

ACTIVE VOICE & PASSIVE VOICE.In an active voice subject is the doer of the action.

Verbs can be TRANSITIVE & INTRANSITIVE.

TRANSITIVE verbs has objects.

Eg:-He writes essays.

Whereas INTRANSITIVE verbs don’t have objects

Eg:- Birds fly.

SUBJECT – Is the doer of the action.

OBJECT- Is the receiver.

ADVERBS

An adverb is usually defined as a word that gives more information about a verb, an adjective or another adverb.Adverbs are of different types,

Adverbs

of TIME,tells us WHEN E.g:- always late.

of MANNER E.g:-Smith runs fast.Here fast is the adverb

of FREQUENCY,tells HOW OFTEN

of PLACE,

of REASON.

PREPOSITION

Show relationship between nouns,pronouns.The relationships include direction, place, time, cause, manner and amount.

Eg:- He went to the store.Here “to” gives direction

Other prepositions are by,with,in,on,under,between etc

CONJUNCTION

A conjunction is a word that connects other words or groups of words.Conjunctions are mainly 3 types.

Coordinating conjunctions are conjunctions which connect two equal parts of a sentence.Most common ones are AND,OR,BUT,SO.

Subordinating conjunctions connect two parts of a sentence that are not equal.

ALTHOUGH,INSPITE OF,WHILE,WHEN,IF,SINCE etc are a few examples

Correlative conjunctions are pairs of conjunctions that work together.Common ones are

both..and,either..or,neither..nor,not only..but also etc

INTER JUNCTIONS

These are words that show strong feelings,these are very scarcely used from a grammarian point of view.

E.g:-wow,alas

One Step to Tackle “Competitive English”-CAT Verbal

NUMBERS:An important QUAT topic

Lloyd — Mon, 06 Jul 2009 18:59:46 +0000

SQUARES
1. Square of a number ending with 5
Let y5 be the number then
square is :- y*(y+1)25
Eg :-
35 * 35 = 1225
3*(3+1)25=1225

2. Square of a number near to a known square
This is real simple you just need to look around ,the formula is very familiar.
(n+1)^2 = n^2 +2*n +1
Eg:-
35^2 can be found easily,so 34^2 = 1225-2*34-1=1156
———————————————————————————–
To find the digit in the unit place of a number given in powers???

Have a look at the pattern below,here the case is with “powers of 2″
2^1 = 2
2^2 =4
2^3 =8
2^4=16
2^5=32
2^6=64
If you have carefully look at the above table you can find that the digits in the unit place forms a pattern(2,4,8,6 ) which is repeating.From this we can deduce that 2^8 will end with unit place as 6.Similarly 2^10 will end with unit place as 4.

Similarly for every numbers by checking the pattern we can easily find the unit place digit.
Eg:-What will be the unit place digit of 3^46.
3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
3,9,7,1 is the reapeating pattern.
So 3^46 will end with “9″.If you didn’t understand then read more.At multiples of “4″ the power of three will give 1 as unit place digit.
So 3^44 will give “one” at unit place.Therefore 3^46 will give “9″.
———————————————————————————–
Sum of all factors of a number “N”
Represent the number “N” as a product of prime numbers.
(a^p) *( b^q)*(c^r)
Formula for sum is given below.

————————————————————————————
What is a CO-PRIME??
Two numbers are said to be Co-Primes if they DONT have any common factors other than one.

Number of ways 2 numbers can be written as product of Co-Primes
is 2^(n-1),where n is a distinct prime number.
Eg:-Question:-How many ways 48 can be written as a product Co-Primes??
Solution:- Write 48 as a product of prime powers
2^4 * 3^1=16*3=48
We can write 48 as product of two prime powers,therefore n=2.
No: of ways=2^(2-1)=2

————————————————————————————
Find number of Co-Primes to N that are less than N.
Represent N as (a^p)*(b^q)*(c^r),where a,b,c are prime numbers.

No of Co-Primes less than N = N*[1-1/a]*[1-1/b]*[1-1/c]

Eg: Question : find no: of Co-Primes till 165
165=3*5*11
Therefore answer = 165*{1-1/3}{1-1/5}{1-1/11}=80
————————————————————————————
The sum of Co-Primes less than N =(N/2)*No of Co-Primes less than N
Eg:Sum of Co-Primes till 165??
(165/2)*80=6600

One Step to Tackle “Competitive English”-CAT Verbal

Lloyd — Wed, 01 Jul 2009 18:50:39 +0000

English one of the most widely used languages is so deep, that it is very difficult to search for its roots.British have navigated the globe many times so ENGLISH has in it influences from many others languages or almost every other languages.Because of this significance of ENGLISH most of the competitive exams test your skills in the language.Exams like TOEFL,IELTS etc test your communicative skills,understanding skills,your grammer, your accent etc.But when it comes to CAT,XAT,MAT etc they test mainly you reading and writing skills only.And when it comes to CAT we need to concentrate in 3 main sections-Vocabulary,Grammer,Reading Comprehensions.

Here i would like to share a few things about RC(reading comprehensions).Every B-school entrance exams have VERBAL sections.And every verbal ability exam will surely constitute a RC portion,which most students consider as a difficult one.But it actually is not very tough provided you do some preparations.Firstly you need to do one thing start reading articles,magazines,newpapers,books etc.This should go in parallel with the preparations.So first approach to an RC is reading. By reading i meant two things mainly to perceive & comprehend. Perceiving means just going through the passage ,just seeing the words.Comprehension means you need to understand the essence of it.

There are certain simple things we need to be taken care of while attempting an RC.Increase your reading speed.The average reading speed of a literate person is expected to be 250 words a minute.But for effective time management in a CAT exam or in any other competitive exams,we need a reading speed of atleast 450 words/minute.But we must comprehend also as much as 450 words/minute.First i will start with techniques to enhance your reading speed.

Reduce Regression

Regression means going back to a previously read sentence.Reducing regression will increase your reading speed considerably.

Avoid lipping

Usually speaking needs more effort and time than mentally reciting something.So if you use your lips then it will take more of your time.So better learn to read in your mind without moving your lips.

Framing the text

This technique will help you to concentrate more on your passage.This can be done using two methods,first method is underlying hand motion in which your finger tip follows every word you read.Secondly vertical hand motion where your both hand will follow a sentence from both sides of the paper.This 2 method will help you to concentrate more.

Now another important things you should keep in mind SQ3R-SURVEY,QUESTION,READ,REVIEW,RESTATE.

SURVEY means go through the passage in 2 or 3 seconds,just to induce a curiosity in ourselves which will surely enhance your reading speed.QUESTIONS also will do the same job for you.Three R’s will help you understand the essence of the essay.

Now things you should remember in the second phase of the reading(comprehend).

Skim keywords

This will help you in your second reading where by just looking at keywords you will get some idea.Thus sparing time.And this method of checking keywords only is called scanning.

Visualize & Mind Map

By visualizing your essay you wil have a small idea where your particular keyword in placed.So that while reading the questions it will be easy for you to find respective portions of the passage.

Try sticking to all these things and i am sure you can gain some advantage.And keep reading to enhance your vocabulary and taste in the language.Time is very precious in these type of exams.

PARTS of SPEECH

Basic Maths made easy-Speed Enhancing Tips

Lloyd — Mon, 29 Jun 2009 17:54:39 +0000

Mathematics the base every engineering branch,is used not only by engineers,but by economists,historians,teachers…infact everyone need maths in there everyday life.And because of this importance of arithmetics almost every competitive exams test your maths skills.In most cases they test not only your skill but also your ability to use right thing at the right place.In big exams like CAT,XAT, GMAT etc if we try answering the quatitative questions after the exam it will look easier to us.So the key in such exam is SWIFT thinking,and small tricks.Conventional maths is a bit time consuming.So here are a few simple tricks which may help you in simple addition and multiplications.

Multiplication

Usually multiplication is considered a tough job as the number of digits goes high but here we will do this in single step whether the number is 2 or 3 or 4 digit. Its better I explain with an example or else it will be confusing.

Two digit numbers:

a b *

x y

**a * x+$, a * y+b * x+$, b * y**

Let ab and xy are the two numbers to be multiplied. It’s a three step process which is explained below. You will get the answer by removing the commas. “$” symbol indicates a carry over from previous position, which can be zero also. This equation may sound weird but just throw a look at the example below.

E.g.:-

28*

Start from the unit place (b*y) place 8*7=56. (6 goes towards answer and $=5)

Now (a*y+b*x+$) means 2*7 + 8*6 + 5 = 67

(Here 7 moves to answer and $ = 6 now).

Final step (a*x+$) means 2*6 + 6 = 18

So the answer is 1876.

The whole thing may look very disturbing to you but let me tell you this trick is worth trying. Give it a few minutes, it will be surely useful.

Three digit numbers:

In 3 digit numbers it is a 5 step process. An example will do the explanation job.

abc*

xyz

a*x+$, a*y+b*x+$, a*z+c*x+b*y+$, b*z+c*y+$, c*z

If you understood previous trick of 2digit multiplication then you will surely understand this one also. Anyway I will explain with an example.

E.g.:-

123*

789

I will simply write down the procedure.

Step1: Start from unit place 9*3=27, CARRY=2 ANS=7

Step2: 2*9+3*8 + CARRY =44, CARRY=4 ANS=47

Step3: 1*9+3*7+2*8+ CARRY=50, CARRY=5 ANS=047

Step4: 1*8+2*7+ CARRY=27, CARRY=2 ANS=7047

Step5: 1*7+ CARRY=9 ANSWER=97047

Another Multiplication technique(Reference Number )

This is used when the numbers to be multiplied is in a closer range.

E.g.:-

17*

Let “10” be your ref. Number.

7 & 4 are the deviation from the ref number. Add any one of this two the other number. Like 17+4 or 14+7, both will give you same result 21.Now this sum * ref. number + product of deviations will give you the result.

21*10+ (7*4) =238

E.g.:-

25*17=?

Take 20 as ref number. So deviations are 5,-3.

(17+5)*20+ (5*-3) =440-15=425.

Multiplication

Two digit numbers:

a b *

x y

a*x+$, a*y+b*x+$, b*y

E.g.:-

28*

Start from the unit (b*y) place 8*7=56. (6 goes towards answer and $=5)

Now (a*y+b*x+$) means 2*7 + 8*6 + 5 = 67

(Here 7 moves to answer and $ = 6 now).

Final step (a*x+$) means 2*6 + 6 = 18

So the answer is 1876.

The whole thing may look very disturbing to you but let me tell you this trick is worth trying. Give it a few minutes, it will be surely useful.

Quatitative Challenge-4

Lloyd — Wed, 03 Jun 2009 09:27:32 +0000

Solve the Questions to enrich your Quant Skills….
Question of the week

The L.C.M. of two numbers is 45 times to their H.C.F.If one of the numbers is 125 and sum of L.C.M. and H.C.F. is 1150, the other number is???
a) 200
b) 275
c) 250
d) 500
e) None of these

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