10 Most Common Sentence Correction Cases.

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First of all it is important to understand a few basics about sentence correction.

Whenever there are questions related to sentence correction, it could mean there is an error in any part of the sentence. It could be related to any part of speech. It is essential to clear class 7 Grammar basics before you sit for any exam that focuses on verbal ability especially the sentence correction part.  The best would be to have a thorough reading of ‘High School English Grammar’ -by Wren and Martin.

 

TIP 1 – Identify what sentence correction concept is being tested.

 

Every sentence correction question will test at least one concept: and you must be able to identify what that is. If you have no clue what concept is being tested, it means that you need to revisit your Grammar fundamentals!

 

TIP 2- Look for subject verb mismatches. 

Subject Verb Agreement is one of the easiest errors to identify and in many sentence correction questions; at least 1 option can be eliminated in this way. So look for these first.

 

TIP 3- Treat options A, B, C, D equally. 

Even if you feel sure that a particular answer choice is right, don’t make up your mind till you have really looked at the other options.
TIP 4- Pick up clues from the non-underlined part of the sentence.

Often, the non-underlined part of the sentence can give you vital clues about tenses, lists, modifiers and meaning that will help you eliminate 1-2 answer choices. So never ignore this part.

 

TIP 5- Answer choice A may not always get the meaning right.

Never ever assume that the sentence given in answer choice A has the intended meaning of the sentence. Read all the answer choices and make up your own mind about what the intended meaning is.

 

TIP 6- Always substitute the choice in the original sentence.

Substitute the answer choice you picked back into the original sentence and see whether it makes sense.
TIP 7- Go to the basics.

If you are not able to make out what is best option, then going back to fundamentals is important.

 

And of course, if you are stuck between the last 2 answer options and have already spent 90 seconds on the question, use one of these thumb rules to take your pick and move on!

Now let’s begin with the questions. Here the errors could be related to any part of speech namely- Noun, Verb, Pronoun, Adverb, Adjective, Conjunction, Preposition etc. Check out for the words the Bold that need correction!

 

  1. She married with an Italian.
    1. To
    2. By
    3. Along
    4. An

Reason- In this sentence the preposition ‘with’ seems redundant. ‘Married’ itself implies union of two people. So the correct answer is ‘She married an Italian’. Option D is the correct one.

 

  1. What is the time in your watch?
  2. At
  3. For
  4. By
  5. Inside

 

Reason- We use ‘in or inside’ for the objects or places that have hollow or empty space in them. ‘For’ anyway doesn’t seem to be a suitable option. So eliminating the other three options, the correct option is C.

 

  1. One of the most significant phenomenons of our time has been the development of cinema.
    1. Phenomenon
    2. Phenomena
    3. Phenomenas
    4. No correction required

 

Reason- This is the case when an incorrect Noun has been used. Phenomenon means ‘event’ and the plural form of ‘Phenomenon’ is ‘Phenomena’. So the correct option is B.

 

  1. This is one of the most important inventions of this century.
    1. invention of this century
    2. invention of these century
    3. invention of the centuries
    4. No correction required

 

Reason- Here the phrase ‘one of the most important inventions’ implies that there have been many inventions but out of them one has been the most important. ‘Most’ defines the Superlative degree of adjective ‘Important’. The correct option is D.

 

  1. Don’t worry. It’s almost safe.You won’t fall.
    1. completely
    2. No correction required
    3. finely
    4. fully

 

Reason- All the words that have been mentioned here are adverbs. These modify the meaning of the word ‘Safe’. If we have to choose the best option it would be option A. One must be completely safe. ‘Almost’ means there is some possibility of being unsafe.

 

  1. It was a long time ago, but I do nearly remember when we first arrived in our new home.
    1. vaguely
    2. softly
    3. no correction needed
    4. hardly

 

Reason- In this sentence the person is talking about long time back and what to say that he has some faint memories of that time. The best option to go is A. ‘Vaguely’ means ‘slightly or roughly’.

 

  1. People in northern parts of Scotland can occasionally see a Northern Lights at night, when weather conditions are right.
    1. the
    2. None of these
    3. an
    4. some

 

Reason- In this sentence the article ‘a’ is mentioned before the ‘Northern Lights’ which is a specific phenomenon. Before Unique things we use the article ‘the’. E.g. the Sun, the Eiffel Tower and the Ganges.

 

  1. Sunil watched the Cricket match so his country’s team was playing.
    1. but
    2. whereas
    3. because
    4. so

 

Reason- All the options are words used as ‘conjunctions’.  If you look at the sentence you will realize that a person X was watching the match as his country’s team was playing. The correct option will be C. The word ‘because’ justifies the reason why the action was being done.

 

  1. Which is your favorite color?
    1. what
    2. that
    3. none of these
    4. who

 

Reason- The correct option is A. ‘Which’ can be used when options or alternatives are given. E.g. which is your favourite colour- Blue or Green? When no options are mentioned we should use the word ‘what’. Here the words ‘which, what, that, who’- are Pronouns.

 

  1. All the women of our badminton league that don’t smoke have caught colds. That just shows that smoking is good for you.
    1. Which
    2. when
    3. whose
    4. who

 

Reason- Since we are talking about group of people here. The Pronoun that fits well in the sentence will be ‘who’. Correct option is D

 

(Written by- Pallavi Chauhan)

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All the subject-verb agreement are belong to us.

subjectverb

How the “All Your Base Are Belong To Us Meme” came to be.

kristi

You might have heard of this meme before or variations of it.  But do you know where this meme comes from and why this grammatical error became so popular?

It started in 1989 when a video game called Zero Wing came out on the SEGA Mega Drive gaming system. The phrase comes from a poor translation of the phrase “all of your bases are now under our control.”

Let’s break this phrase down to see what is happening here grammatically.

The subject in this phrase should be “bases”, a plural subject, but the video game translation used the singular “base”.  This grammar error and a few other mistakes like leaving out “of your” and using the helping verb “are” with “belong” led to this phrase taking over the internet.

In this post, we are going to focus on how subject-verb agreement works so that you can avoid becoming an internet meme (unless you want to, of course.)

Here’s how it works.

First, you need to understand the difference between a subject and a verb and what the term subject-verb agreement is all about.

The most basic sentence has two main parts, a subject and a verb.

See below:

 

She grew.

He flew.

Elves exist.

Words hurt.

 

In these sentences the subject comes first and then the verb follows.  This is true for most sentences, but not all.  The English language is tricky in that for every rule, there are many exceptions.

Identifying the subject in a sentence is not always so easy.

Take the following examples:

  1. He who must not be named is a great, but terrible wizard.
  2. Both Cinderella and the werewolf need to be home by midnight.
  3. There is a boy with a scar on his forehead who lived.
  4. How will the young wizards and witches defeat the dragons and steal their eggs?

The correct subject for each of these sentences is:

  1. He who must not be named is a great, but terrible wizard.
  2. Both cinderella and the werewolf need to be home by midnight.
  3. There is a boy with a scar on his forehead who lived.
  4. How will the young wizards and witches defeat the dragons and steal their eggs?

One trick to identifying the subject is to see if you can replace it with “it” or “they”.  If you can do that and the sentence still makes sense, then you’ve probably found the right subject.

Now that you know how to identify the subject, let’s move on to making verbs and subjects agree.

Subjects and verbs need to agree in number.  This means that if the subject is singular, then it should correspond with a singular verb.  If the subject is plural, then you should have a plural verb.

It sounds pretty basic in those terms, but there are some tricky situations to keep an eye out for.  We’ll go over the basics first and then we’ll move on to the tricky situations that will help you crack the verbal ability section on aptitude exams.

In present tense, a sentence with a singular subject has a verb ending in “s” or “es”.  For plural subjects, you remove the “s”.

E.g. The boy wishes.

The boys wish.

In the simple past tense, there is no change to the verb for a plural subject.

E.g. The boy wished.

The boys wished.

 

When the helping verbs has/have, is/are, was/were, and does/do are used with another verb, then there are subject-verb agreement rules.

E.g. They have shown us the magic trick.

He has shown us the magic trick.

kriti2

 

Tricky situation #1: Personal Pronouns Exception

When using “I” or “you”, we use the plural form of a verb.

E.g. You are at the hockey game.

He is at the hockey game.

 

I choose to be a part of this.

She chose to be a part of this.

 

Compound Subjects:

As we mentioned above, sometimes subjects are joined by clauses or include more than one person and this can make the subject verb agreement rules difficult to determine.

 

Tricky situation #2: When subjects are joined by and

 

Think of “and” as the glue that binds subjects together.  Once “and” is part of the subject, it makes them a whole subject which is always plural.

 

E.g. Sam and Frodo need to return the ring to Mordor.

 

Tricky situation #3: When subjects are joined by or

Think of “or” as a magnet that repels the two phrases on either side of it.  They cannot join, so the verb only agrees with the subject closest to it.

 

E.g. Either Sam or Frodo needs to return the ring to Mordor.

Frodo is singular, so the verb gets an “s” added to it.

If one of the subjects is singular and the other plural, the verb agrees with the subject that is closest to it.

E.g. Either Sam or the elves are in grave danger.

Either the orcs or Smeagle is going to steal the ring.

 

Tricky situation #4: When a collective noun is used

Some subjects sound plural, but are actually something called a collective noun and they take a singular form.  For example, some collective nouns are “family”, “group”, “organization”, and “team”.  Others might be nouns like “news”, “politics”, or “economics”.

These nouns are treated as singular subjects.

E.g.

The team performs completely in sync.

Similarly, indefinite pronouns like “each”, “everyone”, “nobody”, “anyone”, and “someone” are all treated as singular subjects.

E.g.

Everyone is at the mall today.

The exceptions to this rule are: both, many, few, several, and others.

These indefinite pronouns take the plural form.

E.g. Both of us are feeling hungry right now.

A few of us are going to head out for chai.

 

Tricky situation #5: When prepositional phrases or phrases that start with who/that/which are a part of the subject

We saw some of these phrases in the examples I gave earlier.

E.g. He who must not be named is an evil but great wizard.

The trick to figuring out the subject verb agreement in these sentences is to completely ignore the prepositional or adjective phrase.  You can block that part out with your thumb and you will get the phrase “He is an evil but great wizard.”  This is way less complicated!

 

Tricky situation #6: Random exceptions

Leave it to the English language to give you random exceptions every time you figure out the rules.

The following words are treated as plural subjects: scissors, tweezers, trousers, pants, and shears.  You can remember this because all of these nouns have two parts to them.

E.g. The left-handed scissors are of no use to me because I am right-handed!

Can you fix the following sentences?  Comment below with your answers.

 

  1. Hermione along with the Quidditch player, Victor Krum, are going to the Yule Ball together.
  2. Neither Hagrid nor Dumbledore are going to die in this book.
  3. A few of the members of the Order of the Phoenix is going to join us in the fight against Voldemort.
  4. Either Kristi or the people at Leap is a nerd that likes to write about Harry Potter and the Lord of the Rings.
  5. The statistics shows that people with better soft skills end up advancing more in their careers.

Now all of the answers about subject-verb agreement are belongs to us, or should we say, all of the answers about subject-verb agreement belong to us?

 

(Written by Kristi Littleton)

 

Parajumbles.

parattt

Hi!!  This blog will explain how one should approach Para Jumbles. One can reasonably expect four to five questions in a competitive exam. With practice one can solve para jumbles quickly with high accuracy. This topic can make a huge difference to your score , so make sure that in every mock you take , you attempt the para jumbles question and solve them accurately. So let’s get started!!

LET’S FIRST TRY TO UNDERSTAND WHY PARA JUMBLES ARE ASKED IN EXAMS

why-1

 

  • Being able to unscramble paragraph seems like an odd skill requirement for the managers. But the ability really being tested in para jumbles is your comprehension skills.
  • Thus reading comprehension, para completion and critical reasoning and para jumbles essentially test the same thing-your ability to read and understand a paragraph.
  • This is a crucial skill for a manager who should be able to not only read reports but also understand the significance of them.

“Hence the only way to really get better at para jumbles is to read extensively”.

Read good quality publications, this includes books, editorials, essays essentially anything  where the author is not only describing something but is driving at a point.
Now let’s take a close look at how one should approach para jumbles. We will now focus on identifying the chain of thought within the para jumbles.

penalty_vs_premiumSTART WITH THE PARA, NOT OPTIONS-Always start by reading the paragraph, do not go to the option until you have a fair idea about what the author is about to say. After you have had your first read through, you would have only a small idea of what the author is trying to say.

 

IDENTIFY-However you should try to identify the following elements within the paragraph.

Context: Firstly the context of the paragraph, the context of the paragraph may be the idea being discussed or the scene being described or the events being narrated. It essentially answers the question, what is being talked about. Find the one line or two lines that gives the most information about the context of the paragraph and mark them as context.

Main Point: This will generally be the most important line of the paragraph. At times the main point is implied without being stated. If an idea were being discussed or narrated, the main point would be the line describing the author’s view of the idea.

For e.g. : If the paragraph talks about the needs of family planning, the main point would be the line where the author expresses why he think family planning is necessary.

If a scene is being described, the main event or occurrence in the scene would be the main point of the paragraph.

If events were being narrated in the paragraph, then the main point of the paragraph would be the one line answer to the question, What Happened? Essentially the main point of the paragraph is the point that the author hopes to get across to his readers.

Details: Now that you have identified the main points of the paragraph, mark the details of the paragraph. For e.g. – if the para were arguing the case for something, the details would be the supporting arguments, mark these as arguments. If the scene were being described, the details would be the visual description of the scene, mark these as description. If the events are being narrated the details would be the time order of what took place and when, mark these as events.

Now that you have carved out the paragraph into three different parts, it’s time to IDENTIFY THE CHAIN OF THOUGHT. Imagine yourself in the place of author, how would you make your point.

Context->Details->Main Point

Context->Main Point->Details

Main Point->Context->Details

Essentially the context should be either the first line or the second line of the paragraph.

 

WHAT YOU WOULD NOT DO IS:

Details->Main Point->Context

Main Point-> Details->Context

LET’S TRY TO UNDERSTAND THIS WITH THE HELP OF EXAMPLE-

Read the following paragraph:

  1. The food and clothing of one man is not the food and clothing of another; if the supply is insufficient, what one man has is obtained at the expense of some other man
  2. There are goods in regard to which individual possession is possible, and there are goods in which all can share alike
  3. On the other hand, mental and spiritual goods do not belong to one man to the exclusion of another
  4. We may distinguish two sorts of goods, and two corresponding sorts of impulses
  5. This applies to material goods generally, and therefore to the greater part of the present economic life of the world
  6. If one man knows a science, that does not prevent others from knowing it; on the contrary, it helps them to acquire the knowledge

Now let’s try to identify the context of the paragraph, the author is talking about two different kind of goods-possessive and non possessive. The context is establish by the combination of two lines d and b, hence d-b together form the context of the paragraph. Let’s mark them as C1 and C2.

  1. The food and clothing of one man is not the food and clothing of another; if the supply is insufficient, what one man has is obtained at the expense of some other man
  2. There are goods in regard to which individual possession is possible, and there are goods in which all can share alike <——- C2
  3. On the other hand, mental and spiritual goods do not belong to one man to the exclusion of another
  4. We may distinguish two sorts of goods, and two corresponding sorts of impulses <———- C1
  5. This applies to material goods generally, and therefore to the greater part of the present economic life of the world
  6. If one man knows a science, that does not prevent others from knowing it; on the contrary, it helps them to acquire the knowledge

Now that we know the context of the paragraph, now let’s identify the main point of the paragraph, we see that there’s no single line where the author states a conclusion or view of the general idea being discussed. Instead all the remaining four lines are details that explain the implied main point. As the paragraph is discussing an idea, the details are arguments. The basic conclusion one can derive from the arguments is that possessive goods are obtained by one person at the expense of other while this is not the case with the non possessive goods. This is the main point of the paragraph. Hence we group the arguments as possessive goods arguments , a-e and non possessive goods arguments, c-f. Since c starts with on the other hand, we have kept c before f.

We now have the order as=> d-b-a-e-c-f.

THIS IS ONE WAY TO APPROACH PARA JUMBLES, STAY TUNED FOR MORE EXAMPLES / TRICKS AND LET US KNOW IF YOU WANT MORE ARTICLES ON ANY TOPIC.

HAPPY READING!!!

Written By:

Sheenam Gambhir

 

Tips to approach a direction sense test

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Hey guys,
Thanks for your views and comments. Today we will pick one more interesting as well as important topic of reasoning i.e directions.

Many students feel that this is very complex as they find that this topic includes lots of diagrams but let me know one thing , do all of you know that sun rises from the east and sets in west?

large

Kashmir is in north and kanyakumari in south? West bengal is in east and Gujarat in west ? Do you agree with me on these points, look at the map of India and check it once and if you already know these things 50% of the job is done and for the rest 50% scroll down.

Directions questions asked in the exam are based on two principles

  1. Distance
  2. Direction

You might be asked to calculate either of this. The first thing you need to do is either visualize or draw a basic map.

map

 

 

 

 

 

 

Let’s take a case :

A. If I move 4 km towards east and then I travel 3 km towards north. What is my distance from the starting point?

Soln– First thing that you should keep in your mind is that your starting point is always the center of the direction map.

Now draw the map according to the directions.

b

Ohhh !! This is a right angled triangle and here I am supposed to calculate nothing bur hypotenuse and for that Mr. Pythagoras has already given a theorem, let us use it to find the answer.

Pythagoras says:  Hypotenuse2  =  Perpendicular2 +Base2
H2 = 32 + 42
= 9+16 

=25
Hence , H = 5 km.

So, I am 5 Km away from my starting point. Simple ??

B. What if you are asked to find the direction, Let suppose If I move 4 km towards east and then I travel 3 Km towards north. In which direction I am from the starting point ?

Soln Draw the map and try to superpose the direction map like this

 

c

Now, can you tell me where am I ? I am in North east direction from my starting point.

C.What if I walked 3 km towards south and then 4 km towards west?  In which direction I am from starting point now ?

d

Ohhh!! I reached south west. Now are you getting idea how to calculate distance and analyze directions ??

Let’s solve some miscellaneous cases.
D.  A person starts from position A. He goes towards the east and then takes a right turn .Again the person takes a left turn and moves and then again he move 45 degree right. In which direction he is from the starting position?

Soln Whenever such question comes consider yourself in place of the person mentioned and enjoy walking.

e

So, the person is in south east direction of the starting point. Look at the way I am drawing the maps , follow the same and you will never make a mistake in solving these questions. Always draw a reference map of NSEW  as drawn above so that you are clear with the direction.

E.  A person P is standing at a point , another person Q is standing in the north of P. Q’s friend R is in right of Q and P’s friend S is standing left of P.In which direction S is standing with respect to R.

f

Can you figure out the answer now ? S is in south west direction w.r.t R.

And in which direction is R with respect to S ?

g

R is in North east direction w.r.t S .

F. I start from my house and go straight and come at a cross road. The road which is coming from opposite direction ends at a hospital. When I walk from my house and turn right , there is a park on that road and opposite to park there is a school.What would be the direction of my house from the school.

Soln–  When such case come where you are allowed to walk straight and no particular direction is given, you can assume any direction. Let’s suppose I am walking towards EAST.

h

So, My house is in south west direction from the school.Many students face difficulties to determine the direction even after successfully drawing the diagram.

Remember this point.
Can you see I have drawn a reference map above. Whenever you are asked questions  like -in which direction is my house from school, consider school at the middle point of you reference map and then look at the superpose figure, you will find that your house is in south west direction. This is very simple.

What would be direction of school from my house ?

Now in this case just consider your house at the middle point of the reference map, now can you determine direction of the school ?

i

School is in North east direction from my house.

SUNRISE AND SUNSET

Always remember these two points:
1. Sun rises in the EAST then it shadow will be in the WEST.
2. Sun sets in the WEST then it shadow will be in the EAST.

You can be asked questions related to these such as:

G. Ranbir kapoor went for a shooting and is facing towards the NORTH. At sunrise where will his shadow be? And if he is facing SOUTH. Then where will his shadow be?

j

If Ranbir is facing north, his shadow will be in west or to his left.

k

And If he is facing south his shadow will be in west or towards his right.

I hope you guys enjoyed reading this post, There are few points you need to remember before approaching to directions problem.

  1. Direction : N S E W.
  2. Left –Right.
  3. Straight / opposite.
  4. Sunrise and sunset.

Stay tuned, leave back your comments and till then Eat Pray Calculate Analyze Repeat.

(Written by Yeshu)

 

Family Tree: Part II

dddddrree

So continuing from our last post (Family tree and Photographs ) where we discussed how to create family tree and how to make conclusions from the tree to decide relationships, now we will discuss the bigger problem mentioned in that post.

So here’s the problem that we will now try to solve through family tree –

  1. A is the father of two children. B and D, Who are of different sexes.
    2.  C is B’s spouse.
    3.  E is the same sex as D.
    4.  B and C have two children : F, who is the same sex as B, and G, who is the same sex as C.
    5.  E’s mother, H, who is married to L, is the sister of D’s mother, M.
    6.  E and E’s spouse. I, have two children, J and K, who are the same sex as I.
    7.  No persons have married more than once and no children have been born out of wedlock. The only restrictions on marriage are that marriage to a sibling, to a direct descendant, or to more than one person at the same time is forbidden.

According to the rules, D can marry
a. F only    b. G only    c. J only    d.  J or K only    e.  F, J or K

So lets create a family tree for this problem. Rules of creating the family tree are same as mentioned in the last post. So lets pick conditions one by one and start drawing the tree-

1.A is the father of two children. B and D, Who are of different sexes.–> okay ! Here we don’t know the sexes of B and D, they haven’t mentioned if anyone of them is male or female. So we will skip that information and create the rest of the tree as –

d1

2. C is B’s spouse.–> Okay so we will draw this as –

d2

Here we used ~ symbol for showing that two person are spouse.

 

3.E is the same sex as D.– > Okay! Since we are not recording gender information in tree right now, we will keep this information as text and will not draw this into tree.

 

4.B and C have two children : F, who is the same sex as B, and G, who is the same sex as C. —> Ignoring gender information, we will just draw that B and C have two children F and G.

d3

 

5.E’s mother, H, who is married to L, is the sister of D’s mother, M. —> Here we have some critical information. We can draw this as –

d4

Here we used ~ for spouse and <–> for siblings. So H and M are siblings and H and L are spouse.

 

6. E and E’s spouse. I, have two children, J and K, who are the same sex as I. –>  again very simple to draw . E and I are spouse and J and K are their children.

d5

7. No persons have married more than once and no children have been born out of wedlock. The only restrictions on marriage are that marriage to a sibling, to a direct descendant, or to more than one person at the same time is forbidden.  —>  This is a very generic information. only only means that you can’t marry you mother/father/son/daughter and that’s all !!!! You can’t marry same sexes person. Also all children are from people who are already married.

 

Now next step !!!!

Next step is to combine step 1,2,3,4,5,6,7 and come up with a combined family tree – just combine all the trees we formed and make a big one like –

drawing3

 

Now what ?!!!! Now we have a combined family tree.

Remember we have not taken into consideration the gender of any of the members of the family. But now we should. Because people with same gender are not supposed to get married. So how do we figure out gender?

We start randomly by assigning a gender symbol to any one of the member of tree. Ok! So lets start with condition 1- B and D, Who are of different sexes. So, lets assign B and D two different symbols, B –> Pentagon, D—> Rectangle.

Now lets scroll through all the conditions and assign gender symbols –

2. C is B’s spouse.=> Means C and B are of different gender. If B is Pentagon, then C is rectangle.

3.E is the same sex as D => Means if D is rectangle, E is also rectangle.

4.B and C have two children : F, who is the same sex as B, and G, who is the same sex as C. => So B is pentagon, means F is also pentagon. C is rectangle(from pt 2 above), so G is also rectangle.

5.E’s mother, H, who is married to L, is the sister of D’s mother, M. => So we don’t know who’s male and who’s female. We are just going keep this info as it is and not draw because we are only assigning symbols to different genders but we don’t know who’s male and who’s female.

6.E and E’s spouse. I, have two children, J and K, who are the same sex as I. => Since E is spouse of I, so if E is rectangle( from pt 3 above) means I is pentagon. J and K as same gender as I means J and K are pentagon.

So if we look at pt 1,2,3,4,5,6 above, we have the following family tree –

drawing4

Now the above tree is actually enough you to make a conclusion for question given –

According to the rules, D can marry
a. F only    b. G only    c. J only    d.  J or K only    e.  F, J or K

So you can see that D is rectangle, so it can’t marry another rectangle, it will only marry a pentagon that too who’s not direct descendant or sibling. Check the family tree. F, J K are only people who are pentagon (diff sex to D) and are also direct descendant or sibling. So D can marry F,J or K. (Option e)

 

So here’s how you can actually break a really big problem into small branches and then make a tree joining all those branches. Once the tree is created, you can solve any problem by just looking at the tree.

Family Tree and Photographs.

73626181

Ever heard of problems like this-

Pointing to a photograph, a man said, “I have no brother or sister but that man’s father is my father’s son.” Whose photograph was it ?

Try it once! I am pretty sure you can solve this problem orally even without anyone telling you anything. Right?

Okay, so you solved this problem. Now try this one –

  1. A is the father of two children. B and D, Who are of different sexes.
    2.  C is B’s spouse.
    3.  E is the same sex as D.
    4.  B and C have two children : F, who is the same sex as B, and G, who is the same sex as C.
    5.  E’s mother, H, who is married to L, is the sister of D’s mother, M.
    6.  E and E’s spouse. I, have two children, J and K, who are the same sex as I.
    7.  No persons have married more than once and no children have been born out of wedlock. The only restrictions on marriage are that marriage to a sibling, to a direct descendant, or to more than one person at the same time is forbidden.

According to the rules, D can marry
a. F only    b. G only    c. J only    d.  J or K only    e.  F, J or K

Can you solve this problem orally like you solved the first one??

No you can’t. Simply because your brain can only process certain amount of information. The first problem didn’t have much information but the second one is mammoth.  So how do we logically solve these type of problems??

FAMILY TREE

The answer is drawing family tree. A family tree is a logical construct or drawing of information of a group. So lets go back to problem no.1 –

Pointing to a photograph, a man said, “I have no brother or sister but that man’s father is my father’s son.” Whose photograph was it ?

Lets create a family tree for information given in this problem. Here is step by step construction-

  1. Identify each human being: This problem is primarily talking about two men – first one who is pointing to the photograph and the second one whose photograph it is. So lets draw them like –

(M1), man pointing to pic and (M2), man in the pic.

  1. Draw relationships as given: Now start drawing relationships as mentioned in problems. So here it says that M1 has no brother or sister, so draw it like

(M1) —-X — Brother , (M1) —-X—-Sister

Also problem talks about M1’s father, and also father of M2.

Now Fathers,Mothers, uncles, aunties etc (i.e. people of previous generation ) will be drawn like –

ft

Where F1 is father of M1 and F2 is father of M2. If it was mother, we would have used a different symbol other than ( ) that we used for males.

 

3.Join the information and conclude: Now we have individual information drawn and we just have to join. So read the problem again. It says F2 , father of man in pic ,is son of F1- father of man pointing to pic. This means-

ftree

But from step two, we know that M1 and M2 are son of F1 and F2 receptively. So we join the two tress drawn in step 2 with one drawn above as –

ftrredd

Now observe that F2 and M1 lie in same level. If two elements lie in same level in a family tree that means they are of same generation- brother, sister, cousins, spouse etc. But since F2 and M1 have same father, they can only be brothers or sisters.

But our problems also says that M1 doesn’t have any brother or sister.Remember point 2? So, if M1 doesn’t have any brother or sister, then how can F2 be in same level as M1? Think how?

Well , this is only possible if M1 himself is F2. Yup!! M1=F2. M1 is F2. And then M1 becomes father of M2. So whose picture it is? It is his son’s pic. M2’s pic.

 

So creating family tree and extracting information based on that is really simple. Can you now solve the second problem mentioned above? We will post that problem’s solution next. Till then, try solving it, drawing the family tree.

 

 

 

Probability (You will love this post probably)

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What is Probability?

the value or state of presence probable; the range to some degree is likely to happen or be the case. Probability is defined as a number between 0 and 1 (where 0 shows impossibility and 1 shows certainty).

Probability is day to day used term, for example we always say whenever we toss a coin is ‘head may come’. This statement has a certain uncertainty.

 

Relation between two sets A and B: 

∩ = intersection

U= Union

 

Lets get a clear view on three sets A,B,C

 

 

 

Probability:

Let E be an event and S be the sample space. Then probability of the event E can be defined as

P(E) = n(E)/n(S) 

where P = probability, n= number of cases

 

Let’s start with simpler example:

  1. What is the probability of getting head?

Solution: n(S)= 2 … (either Head may come or Tail at a time, which means 2 possibilities)

n(E)= 1… (no. of heads presents in sample)

P(Head)= ½ = 0.5

  1. Two dice are rolled. What is the probability that the sum on the top face of both the dice will be greater than equal to 10?

Solution:

Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)

Hence, total number of outcomes possible two dice are rolled, n(S) = 6 × 6 = 36

E = Getting a sum greater than 9 when the two dice are rolled = {(4, 6), {5, 5}, {5, 6}, {6, 4}, {6, 5}, (6, 6)}

Hence, n(E) = 6

P(getting sum >= 10) = 6/36 = 1/36

 

Q. Two dice are rolled, find the probability that the sum is

a) less than 2

b) equal to 5

c) less than 14

Solution

a) The sample space S of two dice is shown below.S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }

Let E be the event “sum equal to 1”. There are no outcomes which correspond to a sum equal to 1, hence

P(E) = n(E) / n(S) = 0 / 36 = 0

  1. b) Three possible outcomes give a sum equal to 4: E = {(1,3),(2,2),(3,1)}, hence.P(E) = n(E) / n(S) = 3 / 36 = 1 / 12
  2. c) All possible outcomes, E = S, give a sum less than 13, hence.P(E) = n(E) / n(S) = 36 / 36 = 1

 

Let’s touch higher level of Probability question with same logic we used earlier coin problem with some combination concept.

Q. If 100 coins are tossed, what is the probability that exactly 50 heads will be showing.?

Solution:

One coin is tossed , possible outcome = 2 = 21              (H,T)

Two coin are tossed, possible outcome =4= 22            ( HT,TH,TT,HH)

Three Coins are tossed, possible outcome =8= 23       (TTT,HHH,HHT,HTT,THT,TTH,THH,HTH)

Similarly for 100 coins ,possible outcome = 2100

No. of combination of getting 50 heads over 100 coins = 100C50

Probability (50 heads) =  100C50/2100

 

Alternative:

THE BINOMIAL EXPANSION

P(  r success in n trials) = nCr (p) r (q) n-r                          ( p= favorable outcome ; q= 1-p 😉

P(getting 50 head out of 100 coin) = 100C50 (1/2) 50 (1/2) 50

 

Basic concept on drawing a card:

 

In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣.

Cards of Spades and clubs are black cards.

Cards of hearts and diamonds are red cards.

The card in each suit, are ace, king, queen, jack or knaves, 10, 9, 8, 7, 6, 5, 4, 3 and 2.

King, Queen and Jack (or Knaves) are face cards. So, there are 12 face cards in the deck of 52 playing cards.

Let’s do a single problem to clear out all concept of cards

 

Q. A card is drawn from a well shuffled pack of 52 cards. Find the probability of:

(i) ‘2’ of spades

(ii) a jack

(iii) a king of red colour

(iv) a card of diamond

(v) a king or a queen

(vi) a non-face card

(vii) a black face card

(viii) a black card

(ix) a non-ace

(x) non-face card of black colour

(xi) neither a spade nor a jack

(xii) neither a heart nor a red king

Solution:

In a playing card there are 52 cards.

Therefore the total number of possible outcomes = 52

(i) ‘2’ of spades:

Number of favourable outcomes i.e. ‘2’ of spades is 1 out of 52 cards.

Therefore, probability of getting ‘2’ of spade

               Number of favorable outcomes
P(A)     Total number of possible outcome 

= 1/52

(ii) a jack

Number of favourable outcomes i.e. ‘a jack’ is 4 out of 52 cards.

Therefore, probability of getting ‘a jack’

               Number of favorable outcomes
P(B) =     Total number of possible outcome 

= 4/52
= 1/13

(iii) a king of red colour

Number of favourable outcomes i.e. ‘a king of red colour’ is 2 out of 52 cards.

Therefore, probability of getting ‘a king of red colour’

               Number of favorable outcomes
P(C) =     Total number of possible outcome 

= 2/52
= 1/26

(iv) a card of diamond

Number of favourable outcomes i.e. ‘a card of diamond’ is 13 out of 52 cards.

Therefore, probability of getting ‘a card of diamond’

               Number of favorable outcomes
P(D) =     Total number of possible outcome 

= 13/52
= 1/4

(v) a king or a queen

Total number of king is 4 out of 52 cards.

Total number of queen is 4 out of 52 cards

Number of favorable outcomes i.e. ‘a king or a queen’ is 4 + 4 = 8 out of 52 cards.

Therefore, probability of getting ‘a king or a queen’

               Number of favorable outcomes
P(E) =     Total number of possible outcome 

= 8/52
= 2/13

(vi) a non-face card

Total number of face card out of 52 cards = 3 times 4 = 12

Total number of non-face card out of 52 cards = 52 – 12 = 40

Therefore, probability of getting ‘a non-face card’

               Number of favorable outcomes
P(F) =     Total number of possible outcome 

= 40/52
= 10/13

(vii) a black face card:

Cards of Spades and Clubs are black cards.

Number of face card in spades (king, queen and jack or knaves) = 3

Number of face card in clubs (king, queen and jack or knaves) = 3

Therefore, total number of black face card out of 52 cards = 3 + 3 = 6

Therefore, probability of getting ‘a black face card’

               Number of favorable outcomes
P(G) =     Total number of possible outcome 

= 6/52
= 3/26

(viii) a black card:

Cards of spades and clubs are black cards.

Number of spades = 13

Number of clubs = 13

Therefore, total number of black card out of 52 cards = 13 + 13 = 26

Therefore, probability of getting ‘a black card’

               Number of favorable outcomes
P(H) =     Total number of possible outcome 

= 26/52
= 1/2

(ix) a non-ace:

Number of ace cards in each of four suits namely spades, hearts, diamonds and clubs = 1

Therefore, total number of ace cards out of 52 cards = 4

Thus, total number of non-ace cards out of 52 cards = 52 – 4

= 48

Therefore, probability of getting ‘a non-ace’

               Number of favorable outcomes
P(l) =     Total number of possible outcome 

= 48/52
= 12/13

(x) non-face card of black colour:

Cards of spades and clubs are black cards.

Number of spades = 13

Number of clubs = 13

Therefore, total number of black card out of 52 cards = 13 + 13 = 26

Number of face cards in each suits namely spades and clubs = 3 + 3 = 6

Therefore, total number of non-face card of black colour out of 52 cards = 26 – 6 = 20

Therefore, probability of getting ‘non-face card of black colour’

               Number of favorable outcomes
P(J) =     Total number of possible outcome 

= 20/52
= 5/13

(xi) neither a spade nor a jack

Number of spades = 13

Total number of non-spades out of 52 cards = 52 – 13 = 39

Number of jack out of 52 cards = 4

Number of jack in each of three suits namely hearts, diamonds and clubs = 3

[Since, 1 jack is already included in the 13 spades so, here we will take number of jacks is 3]

Neither a spade nor a jack = 39 – 3 = 36

Therefore, probability of getting ‘neither a spade nor a jack’

               Number of favorable outcomes
P(K) =     Total number of possible outcome 

= 36/52
= 9/13

(xii) neither a heart nor a red king

Number of hearts = 13

Total number of non-hearts out of 52 cards = 52 – 13 = 39

Therefore, spades, clubs and diamonds are the 39 cards.

Cards of hearts and diamonds are red cards.

Number of red kings in red cards = 2

Therefore, neither a heart nor a red king = 39 – 1 = 38

[Since, 1 red king is already included in the 13 hearts so, here we will take number of red kings is 1]

Therefore, probability of getting ‘neither a heart nor a red king’

               Number of favorable outcomes
P(L) =     Total number of possible outcome 

= 38/52
= 19/26

(Written by Atul)

 

Missing Series

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Hi Guys,

Hope you liked our last post on different approaches to calculate averages, today we will be discussing about missing series. A very clear instruction- To be proficient in solving series you have to practice a lot because series can be made by using any of the mathematical operation known so you need to practice as much type of questions as you can. But today we will discuss certain questions that are frequently asked in exams also I will provide you with some tips which will help you determine the missing number in series.

Let us take a question:

A.   9   11   16   26   ?   69.    

How do i solve this ? Look at the series above. Numbers are increasing from left to right so suddenly only two things comes in mind either they are getting added by certain number or multiplied. Now, which one of the two should I choose ‘multiplication or addition’. Just look at the series again, all the numbers are very close to each other there is no such two numbers which has a big difference so this strictly tells us that addition must be going on between them. Let us see.

9+2=11
11+5=16
16+10=26
26+17=43
43+26=69

So. basically an addition of 2 , 5 , 10, 17 , 26 took place where each of these numbers had a difference of 3 , 5 , 7 , 9 . (Common difference of 2).

So, the missing number was 43

Look at this series:

B.  3   4   10   33   136   ?

In this case you can see that 33 is preceded by 10 and immediately followed by 136 which simply says that this must be a case of multiplication, you cannot obtain 136 by adding certain number to 33 if you have obtained 33 by adding certain number to 10. so this is only possible in case you are multiplying. Let us see:

3*1 + 1 = 4
4*2 + 2 = 10
10*3 + 3= 33
33*4 + 4 = 136

You have the series now, thus the missing number would be 136*5 + 5 = 685

C.  6   3    3    6    24    ?

What could be the answer in this case ? here we have a decreasing – increasing series of numbers. But can you notice one thing- 6 is followed by 3 and how can you get that ?

Either you do 6-3=3 but no, I can see that series increases further so subtraction will not work or you divide 6/2=3 but again you can see that 24 is preceded by 6 which means there must be multiplication going on.

But did you notice one thing in above line I wrote 6/2=3 , which also means 6*0.5=3 . Let us see if this works.

6*0.5=3
3*1=3
3*2=6
6*4=24
24*8=192

So the numbers were getting multiplied by 0.5, 1, 2,  4,  8 and each of them are getting multiplied by (*2).

Let us take another case :

D.  3   4   12   16    48    ?

Can you identify which type of series is this ? look at the numbers.

3*4=12
4*4=16
12*4=48
16*4=64

Did you notice there was a relation between alternate numbers and the mathematical operation used was multiplication (*4). Such series are known as Alternate series. 

Try this out :

E.  2   3    4    9    8    27   ?

2*2=4
3*3=9
4*2=8
9*3=27
8*2=16

Did you notice? Here the consecutive elements of series don’t have relations, but the alternate elements have a relation.

2-4-8- these elements have a relationship- they are elements of table of 2.

3-9-27- these elements have relationship- they are elements of table of 3.

This was also an alternate series but here the multiplying factor wasn’t common unlike the previous questions.You will have to keep a check as your multiplying factors may also appear in series.

So these were certain tips that you can keep in mind while solving missing series and I am sure this will save your time and help you obtain missing numbers.

It’s Practice time, Try yourself :

1) 5, 25, 7,______, 9, 19

a) 23
b) 22
c) 25
d) 32
e) None of The Above

 2) 62, 64,______, 32, 14,16

a) 26
b) 28
c) 30
d) 32
e) None of The Above

3) 100, 50, 52, 26, 28,______

a) 30
b) 32
c) 14
d) 16
e) None of The Above

4) 980, 392, 156.8,______, 25.088, 10.0352

a) 62.72
b) 63.85
c) 65.04
d) 60.28
e) None of The Above

5)113, 225, 449,_____, 1793

a) 789
b) 786
c) 897
d) 987
e) None of The Above

Answers:

  1. Solution (Option B)
  2. Solution (Option C)
  3. Solution (Option C)
  4. Solution (Option A)
  5. Solution (Option C)

Were you able to get all your answers correct ? Here are few points that will help you approach to an unknown question.

  1. When ever you find a series, look for relations between two numbers, you can find relations between consecutive numbers, alternate numbers, or numbers at a gap of two, three etc.
  2. Once you identify these two numbers, try to recognize which mathematical operation has been done between the two, above mentioned examples will help you find the trick to do so.
  3. Just follow the series to reach out to your answer.

 

(Written by Yeshu)

Averages- Different approaches to calculate averages.

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Hi,
Hope you guys liked our last post about relative speed. Let’s discuss some unique approaches to calculate averages, trust me you will fall in love with calculating averages.

Let us take a case:

If there are three rooms A, B and C, such that A has 20 students, B has 10 students and C has 15 students,

avg

 

Then average number of students in the three rooms is –

(20 + 10 + 15) /3 = 15.

So, Average refers to the sum of observation divided by number of observation.

Average = Sum of observation/ Number of observation

 

We got 15 as average number of students in three rooms, what does that mean? What is 15 trying to say?
Let us see- we had three numbers (20,10,15) whose average is 15.

Let say, below is a line representing “15”(Average value).

avg2

In this figure you can see that 20 is above the average, 10 is below the average and 15 is on the average line. Let us see how much deviation does 20 and 10 have from the average number.

20 – (+5) (Positive deviation)
10 – (-5) (Negative deviation)

Net deviation = Positive deviation + Negative deviation

i.e (+5) + (-5) = 0

Ohhh!! Did we get a “0” . Isn’t that interesting, yes it is ! Average is such a number which equals the net deviation of the whole observation to zero.

So If there is no deviation in any of the numbers of the observation, then what does it mean ? It means that every number has the same value. So when you get 15 as average you can say that each classrooms A, B & C have equal number of students i.e 15.

So the above arrangement of rooms can also be represented as –

avg3

Now if I tell you to calculate the sum of this new observation what will you do ?
Since you need to sum 15 three times therefore, You will directly write 15×3=45 or can you represent this equation as 15=45/3 . Can you now observe this equation ? This is the same thing that you write as formula:

Average = Sum of observation/ Number of observation

Now did you get an idea that if you know the concept there is no need of remembering formulas because ultimately the fact is, these formulas were derived from the same concepts.

More on Averages:

Q.The average of five numbers is 29. If one number is excluded the average becomes 27. What is the excluded number?

Ans.  As we know that the average of all 5 numbers is 29. Now as we have seen above in the room and students example, here all those 5 numbers can be assumed to be 29. So, Let’s suppose all those 5 numbers are 29.

avg4

Now in the second arrangement, the numbers become 27, originally they were 29, now how do we calculate the lost/excluded number ?

Here is our observation –looking at the figure I can clearly observe that initially I had 5 boxes where as now I am left with four boxes, so I have lost one box and since each box was numbered 29, thus I have lost “29” .

Wait !  I just had one more observation, apart from one box in which I lost 29. I can also see that each of my boxes are now numbered “27” , which means I lost two from each of my original boxes. Total number that I lost from each of my boxes is (4 × 2 = 8) – Since now I had total 4 boxes.

Now can you calculate what is the total number I lost/excluded?
It’s (29+8 = 37) , excluded number was 37.

Textual method to solve above problem:

Average of five numbers is 29, so let us consider (A+B+C+D+E)/5 = 29
If one number is excluded average becomes 27 or (B+C+D+E)/4 = 27

A+B+C+D+E = 145                     (1)
B+C+D+E = 108                        (2)

Putting value of (2) in (1) we get A = (145 – 108) = 37 .

Let me know is it required to perform these mathematical operations or forming equations if you can just visualize certain things to calculate the answer while solving Averages?  Leave back your traditional approaches and start visualizing things, this will increase your speed and save your time when you are sitting for limited hour examinations.

Let us take one question for which you think you will require to form equations to calculate answer:

  1. The average weight of the teacher and six students is 12 kg which is reduced by 5 kg if the weight of  the teacher is excluded. How much does the teacher weigh ?

Ans. Forget about methods that you have been using, Keep your pens down and just visualize with me. There are 7 people whose average weight is 12, so you can consider each one of them weigh 12 kg. If the weight of the teacher is excluded, average weight reduces by 5kg i.e now you are left with 6 people who weigh 7kgs each. Just like the previous question calculate the weight that you have lost [12kg (teacher’s weight) + 30kg (5kgs each of 6 students)] = 42 kg. So the excluded weight was 42kg and who’s weight was excluded? –  TEACHER’s.

Thus the teacher weighed- 42 kg.

Wasn’t that simple to calculate. Stay connected we’ll come up with unique approaches for more topics !!

So here’s joke, let’s see how many of you can figure this out-

Three statisticians went out hunting, and came across a large deer. The first statistician fired, but missed, by a meter to the left. The second statistician fired, but also missed, by a meter to the right. The third statistician didn’t fire, but shouted in triumph, “On the average we got it!   

(Written by Yeshu)

Relative Speed – Chases.

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Suppose you are travelling in a train. You are sitting inside the train and another train crosses you. Now there could be two scenarios here –

  1. The second train is moving in the same direction as your train.
  2. The second train is moving in opposite direction as your train.

 

How would you- a person sitting inside the train observe the second train? How would the second train look like when it is moving in same direction? How would it look like when moving in opposite direction?

 

  • Second train would appear to you moving faster than usual when moving in opposite direction.
  • Second train would appear to you moving slower than usual if it is moving in the same direction.

 

 

This phenomenon is used as a mathematical concept called relative speed. So relative speed is the speed at which you saw the other train crossing you in the two scenarios. You considered yourself stationary (as you were sitting inside the first train) and watched the other train crossing you.

 

Maths of relative speed?

 

  1. So when trains are moving in the same directions, sitting inside the train you would see other train crossing slowly – so relative speed here will be = Speed of second train – Speed of first train = V2 – V1

p1

2.  So when trains are moving in the opposite direction, sitting inside the train you would see the other crossing fast – So relative speed here will be = Speed of second train + speed of first year = V2 + V1

p2

 

WHERE TO USE RELATIVE SPEED AND HOW?

 

So here’s a story.  A bunch of robbers enter into a house at 9:00 pm, took hostage of servants and took away cash and important artifacts. When the owner returned to house with his dog, he found servants tied up and house robbed. But the robbers left one handkerchief. The dog was pretty good with sniffing things and catching it. So the owner gave handkerchief to dog and left dog to catch robbers. Dog left the house at 10:00 pm. Now if the robbers are running at a speed of 8kmph and dog is running at a speed of 10 kmph, when will the dog catch those robbers?

 

Solutions –

Okay! So when the dog started running after robbers, it was 10 pm. Means, the robbers would have run for an hour till then.  Speed of robber is 8kmph. So in one hour they would have covered 8 kms. So now dog and robbers are separated by 8kms at 10 pm.

Now imagine the time when the dog catches these robbers. The dog covered these 8kms as compared to robbers .Or since the dog and robbers both running in same direction, the dog has to cover this 8km to catch the robbers.

p3

Now the dog is running at a speed of 10kmph. Robbers are running at a speed of 8kmph. Means the relative speed of dog w.r.t robbers = 10-8 =2 kmph. Relative distance of dog and robbers = 8km. Time taken by dog to catch robbers = Time = Relative Distance / Relative Speed = 8/2 =4 Hours.

So the dog will catch robbers at 4 hours after 10pm, means at 2:00 AM.

And hopefully the police will get them at 3?? No we don’t know that !!!!

So this is how we use relative speed , to find out more gyan on races type situations, when will a person cross another one etc.  We can also use relative speed to find out time of one object crossing another object  when they are travelling in opposite directions.

p4

 

So in the above figure, the time taken by both the objects to cross each other will be

= D/(V1+V2)

IBPS CLERICAL – EXAM ANALYSIS (26/11/2016)

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Hey,

A good news for all of those who will be appearing for tomorrow’s exam (IBPS Clerical 2016). The pattern for slot 1, 2 & 3 of exam held on 26/11/2016 were all same, so you guys have sufficient time to revise the topics accordingly. It is expected that the pattern would be same for entire slots of this exam.

Let us do an over all analysis :

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Guys, the questions asked in these slots were moderate and we think those who have their exams tomorrow should just revise these topics once and chill !!

 

Below are the section wise topics and number of questions asked in 1st slot.

Quantitative Aptitude:
1. Simplification & Approximation- 15 questions
2. Missing series- 5 questions
3. Data Interpretation- 1 set (5 questions)
4. Miscellaneous- 10 questions

Note: There was no question from probability, maximum of the miscellaneous questions were from percentages, profit & loss, averages, problem on ages , SI & CI.

English:
1. Finding errors- 10 questions
2. Reading comprehension (A Jungle story)- 10 questions
3. Close test- 10 questions

Reasoning:
1. Inequality-5 questions
2. Seating arrangement- 3 sets (15 questions)- 2 Linear arrangement( Persons facing north & south| Persons facing north), 1 circular arrangement.
3. Alpha numeric series- 5 questions
4. Alphabet coding- 5 questions
5. Miscellaneous- 5 questions(Blood relations, directions)

Note: There were no syllogisms asked in reasoning.

Guys, the question paper was moderate and 60-65 questions is a good attempt. We will share the questions of missing series along with their answers that were asked today.

Missing series – IBPS clerk 2016|1st slot (26/11)

  1. 9 11 16 26 ?  69
    2. 3 4 10 33 136  ?
    3. 21 24 32 45 63 ?
    4. 6 3 3 6 24 ?
    5. 7 10 16 28 ? 100

Solutions:

number-series

 

Please send in your comments if you found this post helpful. Be in touch we ll keep you posted.

(Written by Yeshu)

How to solve quadratic equations just in few seconds.

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As all of you know that quadratic equations are one of the most important topics of banking exam and many students fail to attempt these questions because either they find it too lengthy or they are unable to derive a conclusion through equations. Today I will share some tips and tricks to solve quadratic equations I am sure this will make your life very easy and you will be able to solve equations just in few seconds.

 

Let us take a case:

For each of the given equation determine whether :

  1. X>Y 2. X<Y         3. X≥Y          4. X≤Y           5. X=Y or No relation can be established between ‘X’ and ‘Y’.
  2. 6×2 – 19x + 15 = 0
    II. 10y2 – 29y + 21 = 0

Solution: (Textual method)

6x²-19x+15=0
6x²-10x-9x+15=0
2x(3x-5)-3(3x-5)=0
2x-3=0, 3x-5=0
Hence, x₁=3/2 & x₂=5/3

10y²-29y+21=0
10y²-14y-15y+21=0
2y(5y-7)-3(5y-7)=0
2y-3=0, 5y-7=0
Hence, y₁=3/2 & y₂=7/5

We have studied this in class 8 or 9 thus finding roots of an equation is an easy task but we make mistakes when we have to compare two variables. Many students think that determining relationship between ‘x’ & ‘y’ means comparing x₁ and x₂ with y₁ and y₂ but this gives you a wrong result.

Rule 1 : To determine relationship between ‘X’ and ‘Y’ , you need to compare x₁ with y₁, y₂ and x₂ with y₁, y₂ or vice versa.

Look at the above roots:

X₁=3/2 or 1.5 , X₂=5/3 or 1.666
Y₁= 3/2 or 1.5, Y₂= 7/5 or 1.4

Here X₁=Y₁, X₁>Y₂ ; X₂>Y₁, X₂>Y₂ , Thus X≥Y (Option 3)

 

Trick to solve faster :

6x²-19x+15=0
10y²-29y+21=0

To find out roots of equation follow below mentioned steps:-

  1. Multiply coefficient of x² and last number (6*15=90)
    2. Factorize 90 in such a way that you get coefficient of x by adding the two factors
    i.e 90= (9*10) , 9+10 also gives you 19(coefficient of x)
    3. Divide the two factors of 90 by coefficient of X² i.e 9/6 and 10/6, This will give you x₁=3/2(1.5) &   x₂=5/3(1.666)
    4. If the coefficient of ‘X or Y’ are negative their roots would be positive and if their coefficient are positive, roots would be negative.
    4. Follow same steps for 2nd equation and compare the variables to obtain result.

Let us take another case:

This is an important question and every banking exam surely has one question of this type (Case-Relationship between X & Y cannot be established).

8x²+31x+21=0
5y²+11y-36=0

Solution :
Calculating roots 8*21= 168 , 168= 24*7 , x₁= -(24/8) ; x₂= -(7/8)
5*-(36) = -(180) , -(180)= -20*9, y₁= -(20/5) ; y₂= (9/5)

X₁= -3 ; X₂= -0.87
Y₁= -4 ; Y₂= 1.8

Here, ( X₁ > Y₁ , X₁<Y₂ ); ( X₂>Y₂, X₂<Y₂ ) Hence, relationship between X & Y cannot be established(Refer Rule 1)

I will provide you with some tips so that you never make mistake in this case.

 

Sandwich case:

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Look at the Number line (Figure) below, here roots of X  are coming between roots of Y. This is a case of sandwich, Thus, No relationship can be established between X & Y.

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Point to remember:- whenever any of the roots of either ‘X’ or ‘Y’ come between roots of ‘X’ or ‘Y’. Relationship between the variables cannot be determined.

Let us take one more question:

X²=144
Y=√169
Calculating the roots : X= ±12 , Y= 13
Comparing the variables: (X₁= 12, X₂= -12) ; Y= 13
X₁<Y , X₂<Y Thus, X<Y.

 

Point to remember in this case : X²= 144, Any such equation will always give you two roots (±12) as (12²=144)
& (-12²=144) square of both the roots give the same value.

Important points to keep in mind while marking your answer:

  1. X>Y : When each of the values of X are greater than each of the values of Y.
    2. X<Y : When each of the values of X are lesser than each of the values of Y.
    3. X≥Y : When one of the value of X is greater than each of the values of Y & one of the values of X is equal to either one or all of the values of Y.
    4. X≤Y : When one of the value of Y is lesser then each of the values of Y & one of the values of X is equal to either one or all of the values of Y.
    5. X=Y or relationship between X and Y cannot be established : Whenever there is a case of sandwich, this option follows.

I hope this post was helpful for you guys, practice more questions to gain perfection in solving quadratic equations. All the best for your exams !

 

(Written by Yeshu)