Number Series Interview questions and answer

Number Series Interview questions and answer 

Number Series

Generally, two kinds of series are asked in the examination.  One is based on numbers and the other based on alphabets.
In questions based on series, some numbers or alphabets are arranged in a particular sequence. You have to decipher that particular sequence of numbers or alphabets and on the basis of that deciphered sequence, find out the next number or alphabet of the series. Although there is no limit of logics which can be used to build a series, here are some important examples given which highlight the type of series asked in the examination.

How to solve number series problems:

Step 1: Observer are there any familier numbers in the given series.  Familier numbers are primes numbers, perfect squares, cubes ... which are easy to identify.
Step 2: Calculate the differences between the numbers.  Observe the pattern in the differences.  If the differences are growing rapidly it might be a square series, cube series, or multiplicative series.  If the numbers are growing slowly it is an addition or substration series.

If the differences are not having any pattern then
1.  It might be a double or triple series.  Here every alternate number or every 3rd number form a series
2.  It might be a sum or average series.  Here sum of two consecutive numbers gives 3rd number.  or average of first two numbers give next number
          
Step 3: Sometimes number will be multiplied and will be added another number So we need to check those patterns

TYPES :

I. Prime number Series :
  Example (1) : 2,3,5,7,11,13, ...........
 Answer : The given series is prime number series . The next prime number is 17.

 Example (2) :2,5,11,17,23,...........41.
 Answer: The prime numbers are written alternately.

II. Difference Series : Example (1): 2,5,8,11,14,17,...........,23.
 Answer: The difference between the numbers is 3. (17+3 = 20)
Example (2): 45,38,31,24,17,...........,3.
Answer: The difference between the numbers is 7. (17-7=10).

III. Multiplication Series: Example (1) : 2,6,18,54,162,.........,1458.
Answer: The numbers are multiplied by 3 to get next number. (162x3 = 486).

 Example: (2) : 3,12,48,192,............,3072.
Answer : The numbers are multiplied by 4 to get the next number. (192x4 =768).

IV.  Division Series:
Example (1): 720, 120, 24, .........,2,1
Answer: 720/6=120, 120/5=24, 24/4=6, 6/3=2, 2/2=1.

Example (2) : 32, 48, 72, 108, .........., 243.
Answer: 2. Number x 3/2= next number. 32x3/2=48, 48x3/2=72, 72x3/2=108,
 108x3/2=162.

V. n2$n^2$ Series:
Example(1) : 1, 4, 9, 16, 25, ......., 49
Answer:  The series is 12, 22, 32, 42, 52, .... The next number is 62=36;

 Example (2) : 0, 4, 16, 36, 64, ........ 144.
Answer :The series is 02, 22, 42, 62, etc. The next number is 102=100.

VI.  n2−1$n^2-1$ Series :
Example : 0, 3, 8, 15, 24,35, 48, ..........,
 Answer : The series is 12-1, 22-1, 32-1 etc. The next number is 82-1=63.
 Another logic : Difference between numbers is 3, 5, 7, 9, 11, 13 etc. The next number is (48+15=63).

VII.n2+1$n^2+1$ Series : 
Example : 2, 5, 10, 17, 26, 37, .........., 65.
Answer : The series is 12+1, 22+1, 32+1 etc. The next number is 72+1=50.

VIII. n2+n$n^2+n$ Series (or)n2−n$n^2-n$ Series :
 Example : 2, 6, 12, 20, ............, 42.
 Answer : The series is 12+1, 22+2, 32+3, 42+4 etc. The next number = 52+5=30.
 Another Logic : The series is 1x2, 2x3, 3x4, 4x5, The next number is 5x6=30.
 Another Logic : The series is 22-2, 32-3, 42-4, 52-5, The next number is 62-6=30.

IX. n3$n^3$ Series :
 Example : 1, 8, 27, 64, 125, 216, ......... .
 Answer : The series is 13, 23, 33, etc. The missing number is 73=343.

X. n3+n$n^3+n$ Series : 
Example : 2, 9, 28, 65, 126, 217, 344, ...........
 Answer : The series is 13+1, 23+1, 33+1, etc. The missing number is 83+1=513.

XI. n3−1$n^3-1$ Series :
Example : 0, 7, 26, 63, 124, ............, 342.
Answer:The series is 13-1, 23-1, 33-1 etc The missing number is 63-1=215.

XII. n3+n$n^3+n$ Series :
 Example : 2, 10, 30, 68, 130, .............., 350.
 Answer : The series is 13+1, 23+2, 33+3 etc The missing number is 63+6=222.

XIII. n3−n$n^3-n$ Series :
 Example :0, 6, 24, 60, 120, 210, ..............,
 Answer : The series is 13-1, 23-2, 33-3, etc. The missing number is 73-7=336.
 Another Logic : The series is 0x1x2, 1x2x3, 2x3x4, etc. The missing number is 6x7x8=336.

XIV. n3+n2$n^3+n^2$ Series :
 Example : 2, 12, 36, 80, 150, ............,
 Answer: The series is 13+12,23+22,33+32etc. The missing number is 63+62=252

XV. n3−n2$n^3-n^2$ Series:
 Example: 0,4,18,48,100,.................,
 Answer :  The series is 13-12,23-22,33-32 etc. The missing number is 63-62=180

XVI. xy, x+y Series:
Example: 48,12,76,13,54,9,32,...............,
 Answer :2.  4+8=12, 7+6=13, 5+4=9   .: 3+2=5.

XVII. Image Series or (Interchange Series):
Example : 34, 81, 72, 47, 74, 27, 18, ................
 Answer :  (47,74,), (72,27), (81,18), are images.   :. Image of 34 is 43.

Assumptions Interview questions and answer

Assumptions Interview questions and answer

Assumptions

Every argument contains a few propositions which act as a base.  But there are some propositions, an author deliberately leaves as they are obvious to the reader.

For example, If A suggests B to go to ENT specialist as B is suffering from Throat infection, A assumes that a specialist doctor may diagnose better than normal physician.

So an Assumption is an unstated premise. 

In finding assumption to any question, we need to search for the reason which gives strength to the argument and without which the entire argument may not hold good.

Note:  Always remember, Assumption is an unstated premised from the author point of view which may not be true for the reader.

For example, A suggests B, Let us go to XYZ movie, as Mahesh acts in that.
Here A assumes if Mahesh acts in a movie, they are worth watching.  But from B point of view, It may not be true.

Solved Examples

Directions : In each question below is given a statement followed by two assumptions numbered I and II. An assumption is something supposed or taken for granted. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement.

Give answer (a) if only assumption I is implicit; (b) if only assumption II is implicit; (c) if either I or II is implicit; (d) if neither I nor II is implicit; and (e) if both I and II are implicit.



Statement :
 “ A taxi is required on rent.” - an advertisement.
Assumptions :
I. All types of vehicles are available on rent.
II. People will respond to the advertisement.
 b. The statement says that a taxi is required on rent. It does not say that any vehicle is required. So the statement cannot be said to have assumed that any vehicle is available for rent. But II is obviously implicit; whenever an advertisement is made it is assumed that people will respond to it.

Statement :
“Buy pure ghee of company ABC.” - an advertisement in a news paper
Assumptions :
I. No other company supplies pure ghee.
II. People read advertisements.
b. I is definitely not mentioned in the advertisement. II is implicit, otherwise Company ABC wouldn’t have given the advertisements.

Statement : 
Of all the TV sets manufactured in India, ‘XYZ’ brand has the largest sale.
Assumptions : 
I. The sale of all the TV sets manufactured in India is known.
II. The manufacturing of no other TV set in India is an large as ‘XYZ’ brand TV.
 a. Unless the sale of all TV sets manufactured in India was known, the statement could not have been made. Hence I is implicit. II is not implicit because we do not know about manufacturing; we know only about sales. XYZ brand has the largest sale but it may not be the largest manufacturer of TV sets. May be Y company manufactured more sets than XYZ does but it exports all its sets. In that case Y is a bigger manufacturer but its sale in India would be lesser than that of XYZ.

Statement :
Ram’s advice to Gopal - “Go to Tirupathi via Gudur - the shortest route.”
Assumptions :
I. Gopal wishes to go to Tirupathi.
II. Ram gives advice to everybody.

a. Unless Gopal would be going to Tirupathi, Ram would not have advised him this. Hence I is implicit. But it is not certain that Ram gives advice to everybody. Maybe Ram is giving advice to Gopal because Gopal is Ram’s friend.

Statement :
Cricket matches have become indispensable for the entertainment of people.
Assumptions : 
I. Cricket matches are the only medium of entertainment.
II. People enjoy Cricket matches.
 b.  Cricket matches have become indispensable but it does not imply that they are the only medium of entertainment. But it is certain that people enjoy Cricket matches. Hence II is implicit.

Statement :
“Do not lean out of the door of the bus.” - a warning in a school bus.
Assumptions :
I. Leaning out of a running bus is dangerous.
II. Children do not pay any heed to such warnings.
a. Leaning out of a running bus must be dangerous, otherwise the warning would not have been there. Hence I is implicit. But II is not implicit. If the authorities would have assumed that children do not pay any need to such warning, they would not have put it up there.

Statement :
 “If you are a software engineer, we want you as our programmer.” - an advertisement by company XYZ.
Assumptions : 
I. Software engineers are expected to be better performers by company XYZ.
II. The company XYZ needs programmers.
b.  I is not implicit. The company wants software engineers. One reason could be that the company expects software engineers to be good performers, as I suggests. But there could be another reason: for example, the company’s programmer job could be such that only a software engineer could perform it. But one thing is certain. The advertisement was for programmers; this means programmers are needed. Hence II is implicit.

Statement : 
Be humble ever after being victorious.
Assumptions : 
I. Many people the after being victorious.
II. Generally, people are not humble.

d. The statement asks a man to be humble ever after being victorious. This implies that people are usually not humble after victory. I is just the opposite of it. II is not implicit because it generalises the statement. Generally, people may be humble; the point is if they are humble or not after victory.


Statement :
A sentence in the letter to the candidates called for written examinations ---- ‘You have to bear your expenses on travel etc.’
Assumptions :
I. If not clarified, all the candidates may claim reimbursement of expenses.
II. Many organisations reimburse expense on travel to candidates called for written examinations.

e. If the letter mentions expenses to be borne by candidates, those who sent the letter must have assumed that the candidates may demand for reim-bursement if the point is not clarified to them. Also, the candidates would not demand reimbursement if it was not a prevalent practice. So I and II both are implicit.


Statement :
One of the opposition leaders said that the time had come for like-minded opposition parties to unite and dislodge the corrupt government.
Assumptions : 
I. Like minded opposition parties should unite only when they have to dislodge a corrupt government.
II. Opposition parties are not corrupt.
d. To dislodge a corrupt government has been mentioned as the present purpose for the call of unity. But this does not mean that this is the only purpose. So I is not implicit. Further, the leader asks like-minded parties to unite against the government and not the entire opposition. So we cannot generalise that (all) opposition parties are non-corrupt. Hence II is not implicit.

Statement :
Bus charges have been increased to meet the deficit.
Assumptions :
I. The present charges are very low.
II. If the charges are not increased, the deficit cannot be met.
b. Bus charges have been increased. The cause: to meet the deficit. This never means that the present are low. If the price of goods increase, it is not necessary that the earlier price was low. But the tone of the statement clearly implies that Bus charges have been increased out of compulsion: so II is implicit.

Statement : 
If degrees are de-linked from jobs, students will think twice before joining college.
Assumptions : 
I. Students  join college education to get jobs.
II. A degree is of no use in getting a job.
a. The statement says that if degrees are delinked from jobs, students  will not join colleges. This implies that jobs are a major reason for them to join college. So, I is implicit. Now, if I is implicit, II is not because II is just the opposite of I.

Statement : 
“ Present-day education is in a shambles and the country is going to the dogs.”
Assumptions : 
I. A good educations system is essential for the well-being of a nation.
II. A good education alone is sufficient for the well-being of a nation.
a. The statement uses a tone that implies that if education is in a shambles, then the country deteriorates. This means that a good education is needed for the well-being of a nation. But this does not mean that a good education alone is sufficient for it. So, I is implicit but II is not.

Statement : 
The next Annual general meeting of the Company will be held after one year.
Assumptions : 
I. The Company will remain in function after one year.
II. The Governing Board will be dissolved after one year.
a. Obviously, the author assumes that the Company will be functioning after one year, otherwise he would not have fixed the date of the meeting one year later. But there is no hint that the Board will be dissolved after that. So I is implicit, II is not.

Statement :
 “Computer education should start at schools itself.”
Assumptions :
I. Learning computers is easy.
II. Computer educations fetches jobs easily.
 a. If one says that computers should be taught at schools he must have assumed that it is an easy subject, because schools are a place of elementary education; tougher things are taught at colleges. But the statement does not say anything about jobs. So I is implied, II is not.

Statement : 
The new education policy envisages major modifications in the education system.
Assumptions : 
I. Present education system is inconsistent with national needs.
II. Present education system needs change.
e. If major modifications are being envisaged, it must have been assumed that the present educational system is inconsistent with what the nation needs. So I is implicit. Again, if I is implicit, II also is, because II says the same thing as I.

Statement :
Sriram’s advice to Krishna - “If you want to study Management, join Institute Y.”
Assumptions : 
I. Institute Y provides good Management education.
II. Krishna listens to Sriram’s advice.
e. If Sriram advises Krishna to join a particular institute, Sriram must have assumed that the particular institute was a good institute. So I is implicit. While advising Krishna, Sriram must also have thought that Krishna would listen to Sriram’s advice; so II is implicit.

Statement :
 “Drop this letter in the letter in the letter-box on your way to school.” - A mother to her daughter.
Assumptions :
I. The child knows the address of the person to whom the letter is being sent.
II. The child will comply with the orders of his mother.
b. The mother only asks her son to drop the letter. I would have been implicit if she had asked her son to drop the letter and write the address also. But II is implicit. Had the mother not assumed that her son would comply, she wouldn’t have asked him to do the job.

Statement : 
Everybody loves reading romantic stories.
Assumptions : 
I. Romantic stories are the only reading material.
II. Nobody loves reading any other material.
d. People love reading romantic stories but this does not means that they have nothing else to read. Nor does it mean that they do not like to read anything else So, both I and II are not implicit.

Statement :
Read this notice before entering the office.
Assumptions :
I. People coming to the office are literate.
II. No blind person comes to the office.
e. When some says “read this notice” he must have assumed that the other person can read. This would be possible only if the person is literate and not blind. So both I and II are implicit.

Interview Forcefulness of Arguments questions

Interview Forcefulness of Arguments questions and answer 

Forcefulness of Arguments

We know that an argument consists of a few premises, unstated premises (Assumptions) and a conclusion.  But not all the the arguments are strong enough to convince others to agree with the author.  So students will be tested on his capability of judging whether a given argument is strong enough or not.

Model question:
Should women be provided more job opportunities.
Argument 1: No.  They will be given household jobs to manage
Argument 2: Yes. They should also go into the outside world. 

Solving Argument questions:

Step 1:

Remove the options based on the preliminary screening as some arguments are just too simple, or ambiguous and may not contain any substance to convince others clearly why this has to be followed.

Example:
One should enjoy one's life to the fullest extent as tomorrow one has to die.  
Argument  1: No because, one should strive to achieve a goal 
Argument  2: No. This philosophy hardly enables us to do anything. 

Analysis: Argument 1 seems to be good but it is not suggesting how achieving a goal is a priority than enjoying one's life and one can achieve a goal in his life and simultaneously enjoy his life also. So argument 1 is weak.
Argument 2 is just try to oppose the statement and not suggesting any course of action.  This is a simple opinion rather than an argument.

Example: 
Love marriages should be encouraged compared to arranged marriages
Argument 1: No. Both are having their good points as well as bad points
Argument 2:  Yes. Arranged marriages are of no use in these days. 

Analysis:  Argument 1 is just an elusive answer rather than taking a stance. It is not addressing the core issue.
Argument 2 is also a mere statement and not saying why arranged marriages are of no use in these days.
So both are weak arguments.

Step 2: 

Check whether the result follows or not if the said argument holds good.  A result follows in the following cases

1. Established fact / Prevailing notions of truth
2. Experiences predict that the result will follow
3. Logically, the result will follow

Similarly we can reject an argument based on the following

1.  Established fact suggests that the result may not follow
2.  Experience predict that the result may not follow
3.  Logically it is impossible
4.  If it is an individual perception
5.  If based on analogy or an example

Example: 
Government must give more funds to midday meal system to reduce the dropouts from schools
Argument 1: Yes.  It act as an incentive to poor families to send their children to schools
Argument 2: No.  It increases additional burden on the government

Analysis: Experience shows that midday meal system improves the attendance rate if properly executed.  We are not arguing here that whether it is really successful or not, but we know that it is surely act as an incentive to many poor families to send their children to school.  But second one is not so strong.  Though it increases burden on the government exchequer, this action is desirable as education is a fundamental right and government must take necessary actions to make people enjoy this right.

Step 3: 
Check whether the result is desirable to follow? Some arguments which pass the first two steps appear to be good arguments but they may not bring the desired benefits.  Even though it gives the desired benefit, the course of doing it may bring more trouble or expenditure. The best way to check the validity of argument is to ask yourself "if it is true, why many people or institutions or government is not following it?" .  

Example: 
Military training must be made compulsory in schools
Argument : Yes. It brings discipline to students
Analysis: Military discipline may improve discipline as it is an established fact that as in the areas of army, navy etc. it is highly desirable and results are proven.  But the suggested argument is like killing a mosquito with an ax.  There are other proven methods are in place to bring discipline to students.

Solved Examples

Statement : Should there be no place for interview in selections?
Arguments 1: Yes. It is very subjective in assessment.
Arguments 2: No, It is only instrument to judge the candidate’s motives and personality.
I is strong as a subjective mode of selection is not desirable. II is of course, right.

Statement : Should higher education be completely stopped for some time?
Arguments 1: No. It will hamper the country’s progress.
Arguments 2:  Yes. It will reduce educated unemployment.
None is strong. Temporary stopping of higher education will not hamper the nation’s progress. It will reduce educated unemployment but so what? It will then increase uneducated unemployment.

Statement : Should all news be controlled by the government in a democracy?
Arguments 1:  Yes. Variety of new only confuses people.
Arguments 2:  No. Controlled news loses credibility.
Second is strong. First argument is debatable while the second is an established fact.

Statement : Should there be students union in college / university?
Arguments 1: No. This will create a political atmosphere in the campus.
Arguments 2: Yes. It is very necessary. Students are the future political leaders.
I is true as it is based on experiences. And political atmosphere in the campus is not really desirable as the campus is a place of learning not politics. II is also true because tomorrow’s leaders will come from today’s students and it is good that they get some political training early.

Statement : Should there be only one university throughout India?
Arguments 1: Yes. This is the only way to bring about uniformity in educational standards.
Arguments 2: No. This is administratively impossible.
Second is strong. First is weak because it is not correct. (Is it the only way?) Second is perhaps correct, on logical thinking.

Statement : Should all the remote parts of a country be connected by road?
Arguments 1: No. It will disturb peaceful simple life of the villages.
Arguments 2:. Yes. It must be done immediately.
None is strong. I is rejected because it may not happen (will not follow). II is rejected because it is too simple and does not have argumentative substance.

Statement : Should government jobs in rural areas have more incentives?
Arguments 1: Yes. Incentives are essential for attracting government servants there.
Arguments 2: No, Rural areas are already cheaper, healthier and less complex than big towns. So, why offer extra incentives!
Both are strong. Incentives do lure people. Second is also an established fact.

Statement : Should religion be taught in our schools?
Arguments 1: No. Ours is a secular state.
Arguments 2: Yes. Teaching religion helps inculcate moral values among children.
Second is strong. First is not very clear. If the state is secular, it means it is against religious bias but not against religion as such. Second is in consonance with the prevailing notions of truth.

Statement : Should mercy death be legalised?
Arguments 1: Yes. Patients undergoing terrible suffering and having absolutely no chance of recovery should be liberated from suffering through mercy death.
Arguments 2: No. Even mercy death is a sort of killing and killing can never be legalized.
Both are strong. They mention a positive and a negative feature of merry death; both these features are desirable/harmful respectively and both are related with important aspects of the topic of mercy death.

Statement : Should there be a world government?
Arguments 1: Yes. It will help in eliminating tensions among the nations.
Arguments 2: No. Then only the developed countries will dominate in the government.
Both are strong. On logical thinking both look probable, both are desirable (harmful in the case of second) and both touch significant aspects of the issue.

Statement : Should the institution of marriages be abolished?
Arguments 1: Yes. It is already showing cracks.
Arguments 2:  No. It is necessary for the survival of society.
Second is strong. First is weak as you cannot abolish a system simply because it is showing cracks. Second is an accepted truth.

Statement : Should telecasting feature films be stopped?
Arguments 1: Yes. Young children are misguided by feature films.
Arguments 2: No. This is the only way to educate the masses.
First is strong. First is an acceptable piece of truth backed by evidence. Second is weak as it is not true.

Statement : Should agriculture in rural India be mechanised?
Arguments 1: Yes. It would lead to higher production.
Arguments 2:  No. It would lead to rural unemployment.
Both are strong. Both are true (both will follow). The first is really desirable while the second it really harmful.

Statement : Should the illiterate be debarred from voting?
Arguments 1:  Yes. They are easily misguided.
Arguments 2:  No. It is their Constitutional right.
Second is strong. First talks of a negative feature which goes exist but is not sufficient enough to go for such a drastic action as disallowing for vote. Second is an established fact.

Statement : Can pollution be controlled?
Arguments 1: Yes. If every one realizes the hazard it may create and cooperates to be rid of it, pollution may be controlled.
Arguments 2: No. The crowded highways, factories and industries and an ever-growing population eager to acquire more land for constructing houses are beyond control.
Both are strong. Although both arguments contradict each other, yet both are based upon sound assumptions or facts and hence, independently, both are strong.