## Time and Work

In this post, we shall discuss about the Time and Work. Lets start with some basic formulas.

Work = Strength X Time
=>   Strength X Time = Work
=>   (Strength X Time ) / Work = 1   :)

So, For every Case
(Strenth X Time) / Work = 1      [ No matter the values]

So, (SxT)/W will be same for all the cases.

I mean   st/w  =  ST/W

Keep this point in your mind.

Now lets see some more important formulas

### If Days are Given :

• If A can do some work in n days, then he can do 1/n work in One day

### If Work is Given :

• If A can do 1/n work in One day, he can finish it in n days

### If A is TWICE as good a work man as B, then

• The ratio of work done by A and B = 2:1
• The ratio of time taken by A and B to finish the work = 1:2 (Please Dont be confused)

## Articles - The

The Usage of the "THE"     :P

Ok, first of all sorry for the confusing title. In this blog we shall discuss where we should use the article "The". Some of these statements are really make you confuse and seems they are opposing each other. Please try to read this for two or three times. so that you can understand THE concept easily.

• Before superlative forms
• Ex :
• The Tallest
• The Best
• The most beautiful
• Before double comparatives
• Ex:
• ✔ The higher you go, the colder you gets
• ✔ The harder you work, the better rank you get in Bank Exams
• ✔The more you earn, the more you want
• When the comparison is between the two and either of the subjects is Highlighted
• Ex:
• ✔ Sachin is the greater of the two cricketers
• ✔ Of the two cricketers sachin is the greater
• Note :
•  Sachin is the greater than  lara
• Now whats the difference between the first statement and the third? why the first one is correct and third one is wrong? because in the 3rd statement, we have mentioned the Person's name. But in the first statement we didnt.
• Before positive form in apposition
• EX:
• Alexander, the great
• Manmohan Singh, the prime minister etc
• Before musical instruments
• The Guitar
• The Tabla
• The voilin etc
• Before a Proper noun when used as a Common noun
• Nelson mandela is The Gandhi of South Africa
• Kalidasa is The Shakespeare of India
• Before some adjectives to make them nouns
• Ex:
• The Blind
• The Rich
• The Poor
• Usage :
• The doctor restored sight to the blind (Here there is no need to mention "The Blind Person" because, the term Blind itself represents the Blind person, so its the adjective which is used as the noun.)
• The rich should not mock at the poor
• ✔ Jesus rose from the Dead
• Before some Languages, to make them PEOPLE.
•  English ruled over India for many Years
• ✔ The English Ruled over India for Many Years
• ☓  French are good at heart
• ✔ The French are good at heart
• When a noun's quality is STRESSED
•  We cannot remove warrior in him
• ✔ We cannot remove the warrior in him
• Mother in her aroused when she saw a Crying Baby
• ✔ The mother in her aroused when she saw a Crying Baby
• Before Ordinal numbers
• The First
• The Third
• The Tenth, etc
• Ex:
• The first and the second posts of this blog
• Note : Little clarification for those people who have no idea about Ordinal numbers
• One, Two, Three, Four  →  Cardinal Numbers
• First, Second, Third  →  Ordinal Numbers
• Before the names of Oceans, Seas, Rivers, Canals, Deserts, Groups of Mountains and Groups of Islands
•  Note :  Dont use "The" for single mountain or single Island (Thats the reason why we've underlined these two statements)
• Ex :
• The Pacific
• ✔ The Red Sea
• ✔ The Sahara
• ✔ The Himalayas
• Usage :
• ✔ Kolkata is on the banks of the Hoogli
• ☓ Kolkata is on the banks of the River Hoogli
• ✔ Kolkata is on the banks of river Hoogli
• ✔ Kolkata is on the banks of the Hoogli river
• Dont be confued, please read the above sentences properly and understand them
• Before Holy Books
• The Ramayana
• The Quran
• The Bible
• Usage:
• My father reads the Bible everyday
• Before the names of the Things, which are unique in nature
• The Sun
• The moon
• The Sky
• Before the names of Planets and  Satellites
•  The Mars
• The Earth
• Note :  Little clarification for those people who confuses between the words Planet and Satellites
• Planets rotates around the Sun
• Satellites rotates around Planets
• In apposition, when name precedes the position (Important)
• Manmohan singh, the prime minister is on a two day tour to srilanka
• In correction of sentences, they've given this model for a number of times. The above sentence means, Manmohan singh, who is the prime minister is on a two day tour to srilanka.
• Some time they will give like this
• The X, the Y is on a two day tour to srilanka
• Whats wrong with this sentence? You can remove THE at the begining or, just put ARE in the place of IS, so that the sentence tells about TWO different persons one is X and the second one is Y
• Before the names of News Papers
•  The Indian Express
• The Hindu etc
• Before the names of some countries
•  The U.S.A
• The UAE
• The Netherlands
• The Congo etc
Thats all for now Friends. Tomorrow we shall discuss "Where shouldn't we use the article THE" .

Liked this Post? Read more English Shortcut Tips and Tricks Here

## Articles

Articles are of TWO types. They are
1. Indefinite article  ----      A / An
2. Definite article   ----      The
What's the difference?
If you want to say about ANY item, you should use the articles A / An. If you want to say about a SPECIFIC item, you should use the article THE.

Confused? Lets see an example. Assume that you've selected for a Bank Exam. You have a stupid friend like me. So obviously She will ask you a party.
Suppose if She says
• Lets go to a Restaurant, that means She doesn't have any specific restaurant in Her mind. So you can give her party in ANY cheap restaurant.  But,
• If she says Lets go to THE restaurant, that means She has some SPECIFICATIONS. I mean she have a specific restaurant in her mind. So you cant escape ;)
Well, this is the basic difference between A/An and The. There are so many differences and usages of these articles. We shall discuss them later.

Ok, lets discuss about the Indefinite articles first.

Indefinite Articles :

A : The indefinite article 'a' is used before singular countable nouns that start with a Consonant sound.
An : The indefinite article 'an" is used before singular countable nouns that start with a Vowel sound.

Wow, Nice definitions. No?

Have a look at some examples,

A :
• A Bat
• A Cat
• A Rat
• A Jug
An :
• An Apple
• An Egg
• AN Ink-Bottle
• An Orange
• An Umbrella
Great,

Now tell me, what should I use before the words European, One-Eyed Beggar, University, Useful Website?

Can I say, Guide4BankExams is an Useful site to know about Banking Exams?

NO

why ?

Please Re-Read the definitions. Here we are talking about Vowel and Consonant SOUNDS. Not the Letters. People often confuse with this. They blindly put A before a word, if it starts with a Vowel letter (A, E, I, O, U) and put An before the word which starts with the consonant letter.

Consider the SOUND, not the LETTER.

Confusing?  Lets see a short cut for this.
• If a word starts with a SWAR (Any of the Indian Language) sound, then we should use An before it.
• If a word starts with a Vyanjan (An of the Indian Language) sound, then we should use A before it.
Have a look at this picture,

so, now see these examples,

A :
• A European
• A One-Eyed beggar
• A University
• A Useful Website

An:
• An hour
• An Honest Man
• An honourable person
Thats it.

Now lets see some more TRICKY examples in English.

Suppose , if you want to say about the Member of Parliament, you can say a Member of Parliament, But if you use shorter form as M.P, Then you should say, He is an M.P

Lets see another example, He is an NRI but He is a Non Resident Indian

Thats all for now friends, tomorrow we shall discuss about the article THE.

Good Day

Read more English Shortcuts Here >>

## Aptitude Questions with Answers - Average

Before going to solve the below problems, first read the basics of Average here

1.  What is the average of first 21 multiples of 7 ?
1.  49
2. 147
3. 77
4. Cant be determined
5. None of these
2.  In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
1. 12.5 Yrs
2. 14.2 Yrs
3. 12.3 Yrs
4. 12.6 Yrs
5. None of these
3.  The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
1. 42
2. 57
3. 27
4. Cant be determined
5. None of these
4.  The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
1. 49
2. 46
3. 48
4. Cant say
5. NOne of these
5.  The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?
1. 67.4kg
2. 58.85kg
3. 57.75kg
4. 49.4kg
5. None of these
6.  The average weight of 8 persons increases by 1.5kg when a person weighting 65kg is replaced by a new person. What could be the weight of the new person?
1. 53kg
2. 58.85kg
3. 75kg
4. 77kg
5. None of these
7.  The average temperature for Monday, Tuesday and Wednsday is 36.3 degrees C. The average temperature for Tuesday, Wednesday and Thursday is 36.7 degrees C. if Monday's temperature recorded as 39 degrees c, find the Thursday's temperature ?
1. 40.2 degrees C
2. 39.2 degrees C
3. 41.4 degrees C
4. 40.4 degrees C
5. None of these
8.  A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
1. Rs. 2050
2. Rs. 210
3. Rs. 1950
4. Rs. 2200
5. None of these
9.  There were 45 students in a hostel, if the numbers of students increased by 7, the expenses of the mess were increased by Rs. 39 per day while the average expenditure per head diminished by Re.1. What is the original expenditure of the mess?
1. Rs. 624
2. Rs. 562
3. Rs. 585
4. Rs. 598
5. None of these
10.  The average age of father and his two sons is 27 Years. Five years ago, the average age of the two sons was 12 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?
1. 42
2. 48
3. 44
4. 47
5. None of these

1.  Required average  = 7(1+2+....+21) / 21
=  (7/21)X ( (21x22) / 2 )  (because sum of first 21 natural numbers)
=  77

2.  Total age of 50 students
=  (30X 13+20 X 12) = 630
Average =  630/50 = 12.6 Years

3.  The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27

4.  Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems :
Teacher's age is 16+(33X1) = 49 Years :)

5.  Actual total weight is (20X 58.4 - 56 + 65) = 1177 Kgs
Actual average weight is 1177/20 = 58.85kgs

6.  Let the average weight of 8 persons be 'x'
years and the age of the new person be 'y'   years
so, (8x - 65 + y) / 8  = x+1.5
so, y = 77kgs                   Shortcut : 65 + 8X1.5 = 77kgs

7.  MOn + Tue + wed Temperature  =  3X36.3 = 108.9
Tue + wed Temperature = 108.9 - 39 = 69.9
Tue + wed + Thu temperature = 3X36.7 = 110.1
So, Thursday's temperature = 110.1 - 69.9 = 40.2 degrees C

8.  Total expenditure for the first 3 months = 3X1600 = 4800
Total expenditure for 4 months = 4X1550 = 6200
Total expenditure for 5 months = 5X1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 5200 = Rs. 25200
So, Average monthly income = 25200/12  =  Rs. 2100

9.  Let the original expenditure be Rs.x
Original average expenditure = X/45
New average expenditure = (x+39)/52
So (x/45) - ((x+39) / 52) = 1  so x = 585
so, original expenditure is Rs 585

10.  The total present age of father and two sons is 3S27 = 81 yrs
The total present age of sons is (12+5) X 2 = 34Years
so, present age of father is 81 - 34 = 47 yrs

Liked this Post? Read more Shortcut Techniques of Aptitude Here

## Problems on LCM and HCF

Read Basics of LCM and HCF Here, Before starting Practice

1. Find the least number which when increased by 4 is exactly divisible by 8, 16, 24, 30 and 32 ?
a)   480
b)   484
c)   476
d)   472
e)   None of these

2. What is the greatest number of five digits which when 3769 is added to it will be exactly divisible by 5, 6 , 10, 12, 15 and 18 ?
a)   4309
b)   99459
c)   100539
d)   99911
e)   None of These

3. Find the minimum number of square tiles required to pave the floor of a room of 2m 50cm long and 1m 50cm broad ?
a)    50
b)   750
c)   45
d)   15
e)   None of these

4. Five bells toll together at the intervals of 5, 6, 8, 12 and 20 seconds respectively. Find the number of times they toll together in one hour's time (Inclusive of the toll at the beginning)
a)   120
b)   31
c)   30
d)   5
e)   None of These

5. A milk man has three different kinds of milk 493liters, 551 liters and 435 liters. Find the minimum number of equal size containers required to store all the milk without mixing.
a)   29
b)   51
c)   58
d)   49
e)    None of these

6. The circumference of the front and back wheels of a vehicle are 6 3/14 m and 8 1/18 m respectively. At any given moment, a chalk mark is put on the point of contact of each wheel with the ground. Find the distance traveled by the vehicle so that both the chalk marks are again on the ground at the same time
a)   217.5 m
b)   435 m
c)    412m
d)   419m
e)   None of these

7. The LCM of two numbers is 28 times of their HCF. The sum of their LCM and HCF is 1740. If one of the numbers is 420, the other number is
a)   150
b)   225
c)   180
d)   240
e)   None of these

8. Two persons A and B walk around a circular track whose radius is 1.4 km. A walks at a speed of 176 meters per minute while B walks at a speed of 110 meters per minute. if they both start at the same time, from the same point and walk in the same direction, at what interval of time would they both be at the same starting point again? (in Hours)
a)   6 2/3
b)   2 1/3
c)   5 1/4
d)   3 2/3
e) None of these

9. Find the least number which when divided by 8, 9, 15, 24, 32 and 36 leaves remainders 3, 4, 10, 19, 27 and 31 respectively?
a)   2880
b)   2885
c)   2974
d)   2875
e)   None of these

10. Find the greatest number which when divide 357, 192 and 252 leaves same remainder in each case
a)   45
b)   1
c)   15
d)   Cant be determinde
e)    None of these

Solutions :

1.  LCM of 8, 16, 24, 30 and 32 is 480
So, Required number is 480 - 4  =  476

2.  LCM of 5, 6, 10, 12 and 18 is 540
On dividing  (99999 + 3769)  by 540, the remainder is  88
So, the required number is 99999 - 88 = 99911

3.  HCF of 250 cm and 150 cm is 50 cm, which is the side of the tile

So, the required number of tiles  =  (250 X 150) / (50X50)  =  15

4.  Time after which all the bells tol together is the LCM of 5, 6, 8, 12 and 20.
i.e., 120 seconds = 20   minutes
The number of times they toll together in one hour =  60/2  = 30 + 1 (beginning tone)

5.  As minimum number of containers are required, the size of the container should be maximum and the size is also equal. so size of the container will be HCF of 493, 551 and 435 i.e., 29
So, required number of containers is =  (493+551+435) / 29  =  51

6.  The required distance is the LCM of 6 3/14  and 8 1/18
LCM of 6 3/14 and 8 1/18 =  LCM (87/14, 145/18)
=>  LCM(87,145) / HCF (14,18)  =  435/2  =  217.5m
7.  LCM =  28 HCF
LCM + HCF = 1740
=>  28  HCF + HCF = 1740
HCF =  1740/29  =  60 and LCM = 28X60
if a and b are two numbers, then
LCM of (a & b) X HCF of (a & b) = aXb
28X60X60 = x X 420  = >  x = 240
So, the other number is 240

8.   Circumference of the track is 2Ï€r
= 2 X (22/7) X 1400m = 8800 m

Time taken by A to complete one round
=  (8800m) / (176m/min)  =  (8800X60)/(176) =  3000 sec

Time taken by B to complete one round
= (8800) / (110m/min)  =  (8800X60) / (110)  =  4800 sec

Time they meet together at the starting point is LCM of 3000 and 4800 sec
i.e., 24000 sec   =  6 2/3 hours
So, they meet at the starting point after 6 2/3 hours

9.   We can observe that the difference between the numbers and their remainders is same
i.e., 8-3  =  9-4  =  15-10  =  24-19  =  32-27  =  36-31  =  5

LCM (8, 9, 15, 24, 32, 36) - 5
= > 2880 - 5 = 2875

HCF (357-192, 192-252, 357-252)
= > HCF (165, 60, 105) = 15

## LCM and HCF Shortcuts

• Factor : A number is said to be a factor of other when it EXACTLY divides the other.
• Ex : 6 and 7 are Factors of 42.
• Multiple : A number is said to be a multiple of another, when it is Exactly divisible by the other
• Ex : 42 is a multiple of 6 and 7
Please re - read these definitions. So that you can get the difference between Factor and Multiple.

• Prime Number : Prime number is a number which has no factors except itself and Unity.
• Ex  :2, 3, 5, 7, 11, 13, 17 etc are prime numbers
• Composite Number :  Composite number is a number which has other factors besides itself and Unity.
• Ex : 14, 15, 16, 18 etc
• Co-Prime : Two numbers are said to be Co-Prime (Prime-To-Each Other) when they have no common factors except Unity.
• Note : The Co-Primes need not necessarily be Primes.
• 15 and 19
• 15, 17 and 22          are        Co-Primes
• Common Multiple : A Common Multiple of two or more numbers is a number which is exactly divisible by each of them.
• Ex : 12 is a common multiple of 2, 3, 4 and 6
• Least Common Multiple  (LCM) : The LCM of two or more given numbers is the Least Number which is exactly divisible by each of them.
• Ex  :
• 20 is the Common Multiple of 2, 4, 5 and 10
• 40 is the Common Multiple of 2, 4, 5 and 10
• 80 is the Common Multiple of 2, 4, 5 and 10,          But
• Here 20 is the Least Common Multiple of 2, 4, 5, and 10
• Highest Common Factor (HCF) : The HCF of two or more numbers is the Greatest Number which divides each of them Exactly.
• It is also Called Greatest Common Divisor (GCD)
• Ex : Find the HCF of 18, 24
• Factors of 18 --> 1, 2, 3, 6, 9, 18
• Factors of 24 --> 1, 2, 3, 4, 6, 8, 12, 24
• Here the Greatest number, which divides them exactly is 6. So 6 is the H.C.F of 18, 24
In the above example they have given very small numbers. So it was easy for us to find the HCF. What if they ask you to find the HCF for 84 and 540 ? Will you write the factors to both of them and then find out the Highest number? If you are planning to do that , please erase that thought from your mind :) Because there are several methods to make the process simple

Methods of finding HCF :
• HCF by factorization :
1. Express each of the given number as the product of Prime Factors
2. Choose common factors
3. Find the Product of Lowest Power of these Factors.
• This Product  is the required HCF of the given Numbers
Ex : Find the HCF of 84, 540

If you find this method lil confusing, dont worry. There is another method to find HCF.

• HCF by Method of Division :
• Consider two different numbers.
• Divide the longer number by the smaller one.
• Now divide the divisor by the reminder.
• Repeat this process of dividing the preceding divisor by the last reminder obtained, till you get the reminder "0"
• The LAST DIVISOR is the HCF of the given TWO numbers
Ex : Find the HCF of 42, 70

Thats it. Now the answer is 14 :)

## Problems on Alpha - Numeric Symbol Test

-> Study the following information carefully to answer these questions

A 8 B 6 # 7 H U % 3 \$ F V R 2 I @ 1 4 1 W E 9 ^ L 5

1. If all the symbols are dropped from the above arrangement which of the following will be eigth from the left end ?
1. 3         2. \$       3. F        4. U         5. None of These

Ans. 1) 3

Explanation : The element  Highlighted  in the Red Color in the following sequence is the 8th element from the left end after dropping all the symbols (#, %, \$, @, 1 and ^)

A  8  B  6  7  H  U  3  F  V  R  2  I  4  1  W  E  9  L  5

2. Which of the following is Seventh to the right of fifteenth from the right end?
1.4   2. T   3. 1   4. w   5. None of These

Ans. 1) 4

Explanation : 7th right of the 15th from the right end ---> (15-7) right --> 8th right element. (Please read our Tutorial here)
The element Highlighted in the red color in the following sequence is the 8th element from the right end.

A  8  B  6  #  7  H  U  %  3  \$  F  V  R  2  I  @  1  !  4  1  W  E  9  ^  L  5

3. Four of the following five are alike in a certain way on the basis of their positions in the above arrangement and so form a group. Which is one that does not belong to the group?
1.  95L    2. I41  3. F2R  4. B73   5. None of These

Ans. 5. None of These

Explanation : Four Groups belong to the same group. So, there is no group which is the odd man out.

4. How many such numbers are there in the above arrangement each of which is immediately followed by a vowel but not immediately preceded by a number ?

1.  None   2.  One   3. Two   4. Three   5. More than Three

Ans. 2) One

Explanation :  Not a Number - Number - Vowel  --- >  NNV  The elements in Highlighted in the Red color are such numbers

A   8   B   6   3   7   H   U   %   3   \$   F   V   R   2   I   @   1   4   1   W   E   9   ^   L   5

5. How many such symbols are there in the above arrangement, each of which is immediately followed by a consonant and also immediately preceded by a number?
1.  None   2. One  3. Two  4. Three  5. More than Three

Ans. 3 ) Two

Explanation :   Smbol - Consonant ----- >  SC

The elements Highlighted in Red color in the following sequence are such symbols

A   8   B   6   #   7   H   U   %  3   \$   F   V   R   2   I   @   1   4   1   W   E   9   ^   L   5

HOPE THESE QUESTIONS HELPED YOU FOR YOUR PRACTICE. WE SHALL DISCUSS SOME MORE QUESTIONS TOMORROW. GOOD DAY

## ALPHA-NUMERIC-SYMBOL TEST (Part - II)

• Now Let Us discuss about the Sides:
• Left of Left  ( - ) Left
• Left of Right   (+) Right
• Right  of Right   ( - )  Right
• Right  of Left   (+)  Left
• NOTE :  If opposite sides (Left - Right) are given add up the numbers. If same sides (Left -Left or Right - Right) are given deduct Small number from the Big one.
• Ex : Check the following Alphabetical Series
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

• What is the 7th alphabet to the left of the 10th alphabet from the right end in the above series?
• Ans : 7th left - 10th right  (7+10) right  17th right. i.e., "J" (10th alphabet from the right end is Q and 7th alphabet to the left of 'Q' is 'J')
• What is the 5th alphabet to the left of the 6th alphabet from the left end in the above series?
• 5th left - 6th left   (6-5) left   1st left   'A'
• What is the 2nd alphabet to the right of the 5th alphabet from the left end in the above series?
• 2nd right - 5th left   (2+5) left  7th left 'G'
• What is the 13th alphabet to the left of the 13th alphabet from the right end in the above series?
• 13th left - 13th right    (13+13) right   26th right   'A'
• What is the 3rd alphabet to the right of the 16th alphabet from the right end in the above series?
• 3rd right - 16th right   (16-3) right    13th right   'N'

## ALPHA-NUMERIC-SYMBOL TEST (Part-I)

In this topic, a JUMBLED SEQUENCE of some Alphabets / Letters / Numbers / Symbols are given, followed by Certain Questions based on It.

Now Lets See the BASICs of It.

BASICS :
• Before starting with this topics lemme clear some Meanings of the words "Following, Followed by, Preceding and Preceded by" Let me start with an example.
• Take Two consecutive alphabets (say A B), Here
• A is Preceding B <=> B is Preceded by A
• B is Following A <=> A is Followed by B
• Take One more Example. Now take 3 consecutive alphabets (say ABC), Here
• A is followed by B and C, But
• A is immediately followed by B,
• A is not immediately followed by C      (Or We can say)
• A is not immediately followed by C
• A is followed by C, but NOT immediately.
• C is preceded by A and B, But
• C is immediately preceded by B,
• C is not immediately preceded by A   (Or We can say)
• C is preceded by A but not Immediately
Now Lets see some EXAMPLES
• How many such Numbers are there in the arrangement each of which is immediately followed by a Symbol and also immediately preceded by a Consonant?
• Sol : Check for the sequence of Consonant-Number-Symbol (Shortcut : just write the first letters CNS above the question and check for that arrangement)
• How many such Consonants are there in the arrangement each of which is immediately preceded by a Number and also immediately followed by another Consonant?
• Sol : Check for the sequence of Number - Consonant - Consonant (Shortcut : Same as above. write NCC n check)
• How many such Symbols are there in the arrangement each of which is immediately preceded by a Number but NOT immediately followed by a Vowel?
• Sol: Check for the sequence of  Number - Symbol - Not Vowel (Shortcut: Write NSV (Just strike the letter V (or u can put the TICK marks above the letters N and S)
• How many such Numbers are there in the arrangement each of which is not immediately followed by a Letter and not Immediately preceded by a Symbol?
• Sol: Check for the sequence of no Symbol - Number - no Letter (SNL)
• How many such Symbols are there in the arrangement each of which is Either Immediately preceded by a Number or immediately followed by a Consonant but not both?
• Sol: Check for the sequence of Number - Symbol / Symbol - Consonant (NS or SC)
• How many such Consonants are there in the arrangement each of which is either immediately preceded by a Number or immediately followed by a Symbol or Both?
• Sol: Check for the sequence of Number - Consonant / Consonant - Symbol / Number - Consonant - Symbol (NC or CS or NCS)

## BODMAS

• In The simplifications of numerical questions, the order of mathematical operations to be followed is given in the abbreviated form : "BODMAS", where
• B stands for 'Bracket'
• O stands for 'Of'
• D stands for 'Division'
• M stands for 'Multiplication'
• A stands for 'Addition' and
• S stands for 'Subtraction'.
• Order to be followed by in case of brackets is as follows :
• (   )  : Small Brackets,
• {  } : Curly Brackets   and
• [  ]  : Square Brackets