Number System - Study Material

 Number System For Bank Exams – Notes, Tips – Tricks And Questions

A number system is defined as a systematic way of expressing numbers. The number system is a mathematical notation for representing numbers of a given set by using a set of digits or symbols in a logical manner. Number System helps to understand the basics of quantitative ability.

The value of any specific digit in a number can be determined by

• The actual digit
• Its position in the number
• The base of the number system

Classification of Numbers:

The number system is classified into following types:

Natural Numbers:

Numbers which are used for counting objects are known as Natural numbers. The natural numbers are denoted by N.

N = {1, 2, 3, 4…………}

Whole Numbers:

Whole numbers are the set of numbers in which zero is included in addition to natural numbers. The whole numbers are denoted by W.

W = {0, 1, 2, 3, 4…….}

Integers:

Integers include all natural numbers in addition to zero & negative numbers. Integers are denoted by I or Z.

I = {-3, -2, -1, 0, 1, 2, 3…..}

Rational Numbers:

Rational numbers are expressed in the form of p/q where ‘p’ & ‘q’ are integers and q≠0. They are denoted by Q.

Q = 5/6, 7/8 etc.

Irrational Numbers:

The numbers which cannot be expressed in the form of p/q where ‘p’ & ‘q’ are integers and q≠0. They are denoted by Q.

Example - π = 3.141592653589793238….

Prime Numbers:

A prime number is a natural number which is divisible only by 1 and itself. It is greater than 0.

Example - 2, 3, 5, 7, 11, 31, etc.

Composite Numbers:

All the numbers (except 1) which do not fall under the category of prime numbers are known as composite numbers.

Example - 4, 8, 10, 22, 100 etc.

Co-Prime Numbers:

Co-Prime Numbers are the set of integers which have only 1 as their common factor or the highest common factor (HCF) is 1.

Example – 13 & 14 are co-prime.

Even Numbers:

The numbers which are divisible by 2 are known as even numbers.

Example – 2, 4, 6, 8, 10….

Odd Numbers:

The numbers which are not divisible by 2 are known as odd numbers.

Example – 3, 5, 7, 9……

Tricks to remember while solving number system questions:

• 1 is neither divisible nor prime.
• Two consecutive odd prime numbers are known as prime pair.
• All natural numbers are whole, integer, rational and real.
• All whole numbers are rational, Integer and real.
• All rational numbers incorporates integers, since every integer can be written as a fraction with denominator 1. Example (9/1).
• The square of an even is even and the square of an odd number is odd.
• Any given Prime Number can never be a Composite Number.
• Fractions are rational.
• Zero is neither negative nor positive number.
• If x is any number then, if x divides zero, result will be zero. If 0 divides x, then result will be infinite or not defined or undetermined i.e. 0/x =0, but x/0 =∞ (infinite) where x is real number.
• The sum and the product of two rational number is always a rational numbers.
• The product or the sum of a rational number and irrational number is always an irrational number.

Number System Practice Set

Read More

Data Interpretation - Study Material

 What is Data Interpretation?

Data Interpretation refers to the extraction of data from the source. It can be obtained from multiple sources eg. data from running of industries, census population data, etc. Data Interpretation basically requires the data first and analyzing data later to infer information from it in order to answer questions. Data can be provided in any format like Bars, Table, Line graphs, Pie graphs.
    
Given below are the DI students are expected to comprehend data given and find out the answers:

• Tabular DI
• Bar Graph
• Line Graph
• Pie Chart
• Combination DI
• Miscellaneous DI

Tips for Date Interpretation:

Here are some hints to remember while solving problems based on data interpretation:

1. Take your time and read carefully. Understand what you are being asked to do before you begin figuring.

2. Check the dates and types of information required. Be sure that you are looking in the proper columns, and on the proper lines, for the information you need.

3. Check the units required. Be sure that your answer is in thousands, millions, or whatever the question calls for.

4. Check the units required. Be sure that your answer is in thousands, millions, or whatever the question calls for.

5. In computing averages, be sure that you add the figures you need and no others, and that you divide by the correct number of years or other units.

6. Be careful in computing problems asking for percentages.

• Remember that to convert a decimal into a percent you must multiply it by 100. For example, 0.04 is 4%.
• Be sure that you can distinguish between such quantities as 1% (1 percent) and 0.01% (one-hundredth of 1 percent), whether in numerals or in words.
• Remember that if quantity X is greater than quantity Y, and the question asks what percent quantity X is of quantity Y, the answer must be greater than 100 percent.

7. Don’t be afraid of the unfamiliar: Maybe you have never seen such charts before; do not panic and approach with an open mind.

8. Practice from a lot of sources: Look at different graphs and charts and see how data is represented.

9. Note that there are no purely DI or purely Reasoning Questions. All the questions require some amount of Reasoning.

10. Look at different newspapers and also the sites on the Internet where you find graphs and charts. An exposure to different types of charts is essential.

11. In Reasoning, do some puzzles from varied sources. Doing these from a variety of sources will help.

12. Do a number of section tests before you start doing full-length tests. Time yourself and stick to the time limits strictly.

13. Rather than doing conventional sums, rely on logic and develop a reasoning mind. In the exam, there is no particular type of question that will be repeated, but most questions can be done by using logic.

14. Do the questions with low weight at the outset. This will give you the confidence to attempt the more difficult questions.

15. Develop your strategy by appearing in a number of mock tests. Do not change it at the last moment by listening to friends or others.

16. Finally, Do Not Panic. Even if you are scoring well in the mock tests, be prepared for something that you may not have seen before. Learn to keep control even if the paper is formidable; usually it is not.

 

Data Interpretation Practice Sets

Read More

English Practice Set for IBPS- RRB / SO Exams 2021

English Practice Set for IBPS- RRB /  SO Exams 2021

Directions (1-10): Which of the following phrases (a), (b), (c) and (d) given below each sentence should replace the phrase printed in bold letters to make the sentence grammatically correct? If the sentence is correct as it is, mark (e) i.e., “No correction required” as the answer.

Q1. The significance of Modi’s visit to Israel, as the first Indian Prime Minister there, can of great historical importance.

(a) is a great historical importance
(b)was of great historical importance
(c)historically had great importance
(d)has a great important historically
(e)No correction required

Q2. Seven decades ago, Nehru first articulated his vision of China and India holding to assure the togetherness of the future of Asia.

(a)holding togetherness and assuring
(b)to hold together assuring
(c)holding together to assure
(d)in order to hold together and assurance
(e)No correction required

Q3. Scientists have developed a hypoallergenic, breathable sensor that can be worn on the skin continuously for a week without discomfort, and may pave the way for wearable devices that can monitor health continuously over a long period.

(a)which could be worn under the skin continuously
(b)that will wear on the skin continuously
(c)which can wear continuous on the skin
(d)that is wear over the skin continuously
(e)No correction required

Q4. Addressing the session, Mr. Puri said China has already lifted hundreds of millions of people out of poverty and India too have done quite well in recent.

(a)has too done well quite recently
(b)too has done quite well recently
(c)had recently done quite well
(d)has been doing quite well recent
(e)No correction required

Q5. Expressing concern at the growing gap over the overarching goals of the bilateral Indo-US defence relationship, a powerful Senate Committee has asked Pentagon to work with New Delhi in cyber and space operating domain.

(a)at the growing gap among
(b)on the gap growing with
(c)over the growing gap between
(d)on the grown up gap between
(e)No correction required

Q6. The Institute for Energy Economics and Financial Analysis (IEEFA) has long predicted India’s growing global leadership role in the transformation in low carbon economies.

(a)transforming in a low carbon economy
(b)transforming a low carbon economy
(c)transformation of a low level carbon economy
(d)the transformation to a low carbon economy
(e)No correction required

Q7. The latest National Electricity Plan has made it clear that no new coal-fired generation has been a need beyond what is already planned.

(a)will have needed beyond
(b)would beyond be needed
(c)will be needed beyond
(d)are a need beyond
(e)No correction required

Q8. The steel ministry might have expressed concern that cost of steel manufacturing will increase as electricity, being one of the major inputs, has been kept out of the Goods and Service Tax.

(a)had express concerns
(b)has expressed concerns
(c)will be expressing concerns
(d)may expressed concerns
(e)No correction required

Q9. RBI cancelled two tenders issued earlier for supply of security features and fibre for currency notes in order to incorporate ‘Make in India’ as an essential requirement.

(a)supplying security
(b)for supplying  of security
(c)in a supply to secure
(d)to supply for security
(e)No correction required

Q10. Deposits in Jan Dhan accounts have touched a new high of Rs.64,564 crore, in which over Rs.300 crore came in the first seven months of demonetisation, according to government data.

(a)of which over
(b)to around
(c)estimating to
(d)all of which
(e)No correction required

Directions (11-15): There are two different sentences with a blank space in each question. Choose the word from the given options which fits into both the blanks appropriately without altering their meanings.

Q11. (I) Many formations are divided into separate strata, as though the process of ________________ had been periodically interrupted.
(II) A coral reef is built by the ___________________of tiny, identical organisms

(a)accretion
(b)stock
(c)expansd
(d)achievement
(e)profit

Q12. (I) It has too great a tendency to harden the muscles; a swimmer’s should be soft and _______________.
(II) The repetition of these flexions will soon render the legs supple, ________________ and independent of the thighs.

(a)floatable
(b)whimsical
(c)steady
(d)pliable
(e)playful

Q13. (I) The _____________ system lasted for two thousand years in China.
(II) The way some landowners treat their tenants today seems almost ______________.

(a)gross
(b)insensible
(c)oblivious
(d)private
(e)feudal

Q14. (I) They are mostly in the form of ________________ and command, as was only likely, since they were intended for the guidance of conduct.
(II) He was determined that the son should do better than himself, being willing to furnish the ______________, if not the example.

(a)true
(b)precept
(c)moral
(d)request
(e)ideology

Q15. (I) He is simple-minded, learned, tolerant, and the quintessence of __________.
(II) There was a good deal of ___________ and pleasantry in his conversation.

(a)bonhomie
(b)sensitivity
(c)responsibility
(d)smart
(e)technique

Solutions

S1. Ans. (b)
Sol. “was of great historical importance” is the correct phrase to make the sentence grammatically correct. It is to be noted that the sentence is in Past Tense. If we go by options, all phrases except option (b) are not in correct grammar structure. Hence (b) is the correct choice.

S2. Ans. (c)
Sol. “holding together to assure” is the correct phrase to make the sentence grammatically correct as the “holding together” is the correct phrasal verb which means remain or cause to remain united. Other options are in accordance to correct grammar structure.

S3. Ans. (e)
Sol. The given sentence is grammatically correct. “that can be worn” is the correct phrase as the sentence is in Present Tense and it is talking about some new invention in the field of science and technology. Hence (e) is the correct choice.

S4. Ans. (b)
Sol. “too has done quite well recently” is the correct phrase to make the sentence grammatically correct. It is to be noted that both “China” and “India” are used in Singular number; so “has” will be used in place of “have”.

S5. Ans. (c)
Sol. “over the growing gap between” is the correct phrase to make the sentence grammatically correct as “expressing concern over something” is the correct phrasal usage. Hence (c) is the correct option.

S6. Ans. (d)
Sol. “the transformation to a low carbon economy” is the correct phrase to make the sentence grammatically correct. “transformation into/to” is the correct phrase in context of the sentence. Hence (d) is the correct choice.

S7. Ans. (c)
Sol. “will be needed beyond” is the correct phrase to make the sentence grammatically correct. All other options except (c) are not in accordance with correct grammar structure. Hence (c) is the correct option.

S8. Ans. (b)
Sol. “has expressed concerns” is the correct phrase to make the sentence grammatically correct. It is to be noted that the sentence is in Present Tense. Hence (b) is the correct option.

S9. Ans. (e)
Sol. The given sentence is grammatically correct. “for supply of something” forms the correct grammar structure. Hence (e) is the correct choice.

S10. Ans. (a)
Sol. “of which over” is the correct phrase to make the sentence grammatically correct. “Of which” is part of a relative clause. “Which” is the relative pronoun and “of” is a preposition placed at the beginning of the relative clause, instead of at the end. Hence (a) is the correct option.

S11. Ans. (a)
Sol. Accretion means growth or increase by the gradual accumulation of additional layers or matter.

S12. Ans. (d)
Sol. Pliable means easily bent; flexible.

S13. Ans. (e)
Sol. Feudal means absurdly outdated or old-fashioned.

S14. Ans. (b)
Sol. Precept means a general rule intended to regulate behaviour or thought.

S15. Ans. (a)
Sol. Bonhomie means cheerful friendliness; geniality.

Read More

Reasoning Practice Set for IBPS- RRB / SO Exams 2021

 Reasoning Practice Set for IBPS- RRB /  SO Exams 2021

Direction (1-5): Study the following information and answer the given questions:
Nine persons are sitting in a row either facing north or south direction. They like different colors green, blue and red. They are sitting adjacent to each other in a group of three each likes different color from each other. No two persons who like same color sit together. Not more than two persons facing same direction sit together. D is one of the persons and does not like same color as H. More than three persons sit between H and I. F sits exactly in middle of the row. H is 3rd to the left of F and likes green. One of the neighbor of H is A, who likes red. G is 3rd to the left of C and likes blue. B likes red. The number of person sitting between E and B is same as between B and I. All the persons who like blue face north except the one sitting 2nd to the right of F. H and I face opposite direction. One person sits between H and C, who faces south. All the persons who like red face north. I does not like blue or red. E likes Blue.

Q1.Who among the following likes green?
(a) E
(b) F
(c) C
(d) B
(e) None of these

Q2. How many persons sit to the left of A?
(a) Two
(b) One
(c) Three
(d) Four
(e) None

Q3. How many persons sits between F and I?
(a) Two
(b) One
(c) Three
(d) Four
(e) None of these

Q4. Which of the following statement is not true regarding E?
(a) E likes Blue
(b) Both the neighbor of E like green
(c) Two persons sit between E and B
(d) D sits next to E
(e) None of these

Q5. Four of the following belongs to a group find the one that does not belong to that group?
(a) E
(b) F
(c) B
(d) C
(e) I

Direction (6-8): Study the following information and answer the given question.
T is the sister of D. D is married to P. P is the son of M.T is the mother of J. Y is the father of U.Y has only one son and only one daughter. U is the daughter of T. Q is the son of D.

Q6. How is P related to T?
(a) Brother
(b) Cannot be determined
(c) Brother-in-law
(d) Cousin Brother
(e) Uncle

Q7. How is J related to D?
(a) Son
(b) Niece
(c) Son-in-law
(d) Nephew
(e) Daughter

Q8. How is Q related to M?
(a) Son-in-law
(b) Grandson
(c) Nephew
(d) Son
(e) Cannot be determined

Directions (9-13): Study the following information carefully to answer the given questions.
Eight persons P, Q, R, S, T, U, V and W sitting around a circular table with equal distance between each other but not necessarily in the same order. Some of them are facing the centre while some are facing outside (i.e. away from the centre).
They all belong to four different places viz. East Coast, West Coast, North Wellington and South Africa, and two persons belong to each place.

Note: Same directions means that if one person facing the centre then the other person also faces the centre and vice versa. Opposite direction means if one person is facing the centre then the other person faces outside and vice versa.

R sits third to the left of W, who belongs to South Africa and both are facing the same direction. T sits fourth to the left of V and both are facing opposite directions but they are from same place. R and Q are not facing the same direction but R is an immediate neighbour of T. U sits second to the right of R.S is not facing the centre and belongs to North Wellington. The one who is on the immediate left of U is not facing the centre. The immediate neighbours of T are facing the centre. The persons who belong to East Coast sit adjacent to each other, but face opposite directions. The persons who belong to West Coast sit opposite to each other. S and U are immediate neighbours of W. One of the persons who belong to South Africa is an immediate neighbour of the persons who belongs to North Wellington. V sits on the immediate right of Q, who belongs to East Coast.

Q9. Who among the following belongs to South Africa?
(a) T, V
(b) R, W
(c) U, P
(d) S, W
(e) None of these

Q10. In the arrangement, how many persons are facing the centre?
(a) Five
(b) Two
(c)Three
(d) Four
(e) None of these

Q11. Which of the following statement is true about P?
(a) P is an immediate neighbour of R and the person who belongs to West Coast
(b) Both the immediate neighbours of P are facing the centre
(c) P is third to the right of the person who belongs to North Wellington
(d) None of the given statements is true
(e) P sits opposite W, who belongs to South Africa

Q12. Who among the following sits third to the right of W?
(a) V, who belongs to South Africa
(b) Q, who belongs to East Coast
(c) T, who belongs to West Coast
(d) Can’t be determined
(e) None of these

Q13. Four of the following five are alike in a certain way and hence form a group. Which is the one that does not belong to that group?
(a) U, W
(b) T, S
(c) R, P
(d) Q, S
(e) W, Q

Directions (14-15): In each of the questions given below three statements are followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically does not follows from the given statements disregarding commonly known facts.
Q14. Statements:
Only a few floor are circle
Only a few circle are row.
All row are mix.
Conclusions:
I. Some floor can be mix.
II. All mix can be circle.
III. Some mix is floor.
(a)Only I and II
(b)Only II and III
(c)Only III
(d)All follow
(e)None of these

Q15. Statements:
Only a few pens are papers.
No papers are paint.
Only a few papers are gold.
Conclusions:
I. All gold can be paper.
II. Some paint can be pen.
III. All gold can be paints.
(a)Only I and II
(b)Only II and III
(c)Only III
(d)All follow
(e)None follow

Solutions

Read More