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Clock based problems are one of the frequently asked questions in most of the competitive
exam. To solve these problems, it is always better to understand some of the basic principles and the types of problems that get asked. In this post I hereby explained simple tricks and some simple formulas for solving clock based problems.

In every competitive exams clock questions are categorized in to two ways.
  • Problems in angles
  • Problems on incorrect clocks
Problems in angles  

Method :1

Before we actually start solving problems on angles, we need to know couple of basic facts clear:
  • Speed of the hour hand     = 0.5 degrees per minute (dpm)
  • Speed of the minute hand  = 6 dpm
  • At ‘n’ o’ clock, the angle of the hour hand from the vertical is 30n
The questions based upon these could be of the following types

Example : 1  
   What is the angle between the hands of the clock at 7:20
At 7 o’ clock, the hour hand is at 210 degrees from the vertical.
In 20 minutes,
Hour hand = 210 + 20*(0.5) = 210 + 10 = 220 {The hour hand moves at 0.5 dpm}
Minute hand = 20*(6) = 120 {The minute hand moves at 6 dpm}
Difference or angle between the hands = 220 – 120 = 100 degrees

Method : 2

Example :2  
   
 At what time 3&4’o clock in the hands of clock together.
Approximately we know at 03:15 hands of the clock together
So 15*60/55=16.36 min


Example : 3 
  
Find the reflex angle between the hands of a clock at 05.30?
The above problem are solved by the bellow formula
Angle between X and Y =|(X*30)-((Y*11)/2)|
Angle between hands at 5:30
Step 1:  X=5 , Y=30
Step 2:  5*30=150
Step 3:  (30*11)/2 = 165
Step 4:  165-150=15
Thus, angle between hands at 5:30 is 15 degrees.

Method : 3

Problems on incorrect clocks

Such sort of problems arise when a clock runs faster or slower than expected pace. When solving these problems it is best to keep track of the correct clock.

Example : 4 
    A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?
The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.
From 8 AM to 10 PM on the same day, time passed is 14 hours.
In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.
So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

Important Notes
  • Two right angles per hour(Right angle = 90, Straight angle=180)
  • Forty four right angles per day
  • Between every two hours the hands of the clock coincide with each other for one time except between 11, 12 and 12, 1.In a day they coincide for 22 times.
  • Between every two hours they are perpendicular to each other two times except between 2, 3 and 3, 4 and 8, 9 and 9, 10.In a day they will be perpendicular for 44 times.
  • Between every two hours they will be opposite to each other one time except between 5, 6 and 6, 7.In a day they will be opposite for 22 times.

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    It's important to be prepared to respond effectively to the interview questions that employers typically ask at job interviews. Since these questions are so common, hiring managers will expect you to be able to answer them smoothly and without hesitation.
    You don't need to memorize an answer, but do think about what you're going to say so you're not put on the spot during the job interview. Your responses will be stronger if you prepare in advance and have a sense of what you want to play up during your interview.

    1. What is your greatest strength?
    This is one of the questions that employers almost always ask. When you are asked about your greatest strengths, it's important to discuss the attributes that will qualify you for the specific job and set you apart from the other candidates.
    2. What is your greatest weakness?
    Another typical question interviewers will ask is about about your weaknesses. Do your best to frame your answers around positive aspects of your skills and abilities as an employee.
    3. Tell me about yourself.
    Here’s how to answer questions about you without giving out too much – or too little – personal information. Start by sharing some of your personal interests which don't relate directly to work.
    4. Why should we hire you?
    Are you the best candidate for the job? Be prepared to say why.  Make your response a concise sales pitch that explains what you have to offer the employer, and why you should get the job.
    5. Why Did You Leave (Or Why Are You Leaving) Your Job?
    If you're unemployed, state your reason for leaving in a positive context: "I managed to survive two rounds of corporate downsizing, but the third round was a 20 percent reduction in the workforce, which included me."
    If you are employed, focus on what you want in your next job: "After two years, I made the decision to look for a company that is team-focused, where I can add my experience."
    6. When Were You Most Satisfied in Your Job?
    The interviewer wants to know what motivates you. If you can relate an example of a job or project when you were excited, the interviewer will get an idea of your preferences. "I was very satisfied in my last job, because I worked directly with the customers and their problems; that is an important part of the job for me."
    7. What Can You Do for Us That Other Candidates Can't?
    What makes you unique? This will take an assessment of your experiences, skills and traits. Summarize concisely: "I have a unique combination of strong technical skills, and the ability to build strong customer relationships. This allows me to use my knowledge and break down information to be more user-friendly."
    8. What Are Three Positive Things Your Last Boss Would Say About You?
    It's time to pull out your old performance appraisals and boss's quotes. This is a great way to brag about yourself through someone else's words: "My boss has told me that I am the best designer he has ever had. He knows he can rely on me, and he likes my sense of humor."
    9. What Salary Are You Seeking?
    It is to your advantage if the employer tells you the range first. Prepare by knowing the going rate in your area, and your bottom line or walk-away point. One possible answer would be: "I am sure when the time comes, we can agree on a reasonable amount. In what range do you typically pay someone with my background?"
    10. If You Were an Animal, Which One Would You Want to Be?
    Interviewers use this type of psychological question to see if you can think quickly. If you answer "a bunny," you will make a soft, passive impression. If you answer "a lion," you will be seen as aggressive. What type of personality would it take to get the job done? What impression do you want to make?

    Proposition is one of the important part in Elitmus pH test, in verbal section contains more than three questions are asked from proposition part. Proposition is easiest one in verbal section. In this post you find more details about Proposition and logical deduction questions and important rules for handling those questions.

    Proposition

    In Logic, any categorical statement is termed as the Proposition.

    A Proposition is a statement that asserts that either a part of, or the whole of, one set of objects - the set identified by the subject term in the sentence expressing that statement - either is included in, or is excluded from, another set - the set identified by the predicate term in that sentence.

    The standard form of a proposition is:

    Quantifier + Subject + Copula + Predicate

    Thus, the proposition consists of four parts:

    1)  Quantifier: The words 'all', 'no' and 'some' are called quantifiers because they specify a quantity 'All' and 'no' are universal quantifiers because they refer to every object in a certain set, while the quantifier 'some' is a particular quantifier because it refers to at least one existing object in a certain set.

    2)  Subject (denoted by 'S'): The subject is that about which something is said.

    3)  Predicate (denoted by 'P'): The predicate is the part of the proposition denoting that which is affirmed or denied about the subject.

    4)  Copula: The copula is that part of the proposition which denotes the relation between the subject and the predicate.


    Four-Fold Classification of Propositions:

    A proposition is said to have a universal quantity if it begins with a universal quantifier and a particular quantity if it begins with a particular quantifier. Besides, propositions which assert something about the inclusion of the whole or a part of one set in the other are said to have affirmative quality, while those which deny the inclusion of the whole or a part of one set in the other are said to have a negative quality. Also, a term is distributed in a proposition if it refers to all members of the set of objects denoted by that term. Otherwise, it is said to be undistributed. Based on the above facts, propositions can be classified into four types:

    1) Universal Affirmative Proposition (denoted by A): It distributes only the subject i.e. the predicate is not interchangeable with the subject while maintaining the validity of the proposition.
     
    2) Universal Negative Proposition (denoted by E): It distributes both the subject and the predicate i.e. an entire class of predicate term is denied to the entire class of the subject term, as in the proposition.


    3) Particular Affirmative Proposition (denoted by I): It distributes neither the subject nor the predicate.


    4) Particular Negative Proposition (denoted by O): It distributes only the predicate. e.g., Some animals are not wild. Here, the subject term 'animals' is used only for a part of its class and hence is undistributed while the predicate term 'wild' is denied in entirety to the subject term and hence is distributed. These facts can be summarized as follows:

    Statement Form
    Quantity
    Quality
    Distributed
    (A): All S is P.
    Universal
    Affirmative
    S only
    (E): No S is P.
    Universal
    Negative
    Both S and P
    (I): Some S is P.
    Particular
    Affirmative
    Neither S nor P
    (O): Some S is not P
    Particular
    Negative
    P only

    Logical Deduction:

    The phenomenon of deriving a conclusion from a single proposition or a set of given propositions, is known as logical deduction. The given propositions are also referred to as the premises.


    Two Inferential Processes of Deduction:

    I.Immediate Deductive Inference:

    Here, conclusion is deduced from one of the given propositions, by any of the three ways -conversion, obversion and contraposition.

    1) Conversion: The Conversion proceeds with interchanging the subject term and the predicate term i.e. the subject term of the premise becomes the predicate term of the conclusion and the predicate term of the premise becomes the subject of the conclusion.
    The given proposition is called converted, whereas the conclusion drawn from it is called its converse.

    Table of Valid Conversions

    Converted
    Converse
    A: All S is P
    Ex. All pins are tops.
    I: Some P is S
    Some tops are pins.
    E: No S is P.
    Ex. No fish is whale.
    E: No P is S.
    No whale is fish.
    I: Some S is P.
    Ex. Some boys are poets.
    I: Some P is S.
    Some poets are boys.
    O: Some S is not P.
    No valid conversion

    Note that in a conversion, the quality remains the same and the quantity may change.

    2) Obversion: In obversion, we change the quality of the proposition and replace the predicate term by its complement.

    Table of Valid Obversions
    Obverted
    Obverse
    A: All birds are mammals.
    E: No birds are non-mammals.
    E: No poets are singers.
    A: All poets are non-singers.
    I: Some nurses are doctors.
    O: Some nurses are not non-doctors.
    O: some politicians are not statesmen.
    I: Some politicians are non-statesmen


    Contraposition: To obtain the contra positive of a statement, we first replace the subject and predicate terms in the proposition and then exchange both these terms with their complements.

    Table of Valid Contrapositions

    Proposition
    Contra positive
    A: All birds are mammals.
    A: All non-mammals are non-birds.
    I: Some birds are mammals.
    I: Some non-mammals are non-birds.


    Note: The valid converse, obverse or contra positive of a given proposition always logically follows from the proposition.

    II. Mediate Deductive Inference (SYLLOGISM): First introduced by Aristotle, a Syllogism is a deductive argument in which conclusion has to be drawn from two propositions referred to as the premises.

    Example:
    1. All lotus are flowers.
    2. All flowers are beautiful.
    3. All lotus are beautiful.

    Clearly, the propositions 1 and 2 are the premises and the proposition 3, which follows from the first two propositions, is called the conclusion.

    Term: In Logic, a term is a word or a combination of words, which by itself can be used as a subject or predicate of a proposition.

    Syllogism is concerned with three terms:
    1. Major Term: It is the predicate of the conclusion and is denoted by P (first letter of 'Predicate').
    2. Minor Term: It is the subject of the conclusion and is denoted by S (first letter of 'Subject').
    3. Middle Term: It is the term common to both the premises and is denoted by M (first letter of 'Middle').