# NUMBER SYSTEM

A golden opportunity for Bank exams aspirants. Thousands of posts in SBI and other Banks. Out of five papers in the SBI clerk exam, Quantitative Aptitude plays major role. Arithmetic and Data Interpretation questions will be there in this paper. Arithmetic is the maths, which we use in our day-to-day life. As arithmetic chapters are there upto 10th class only all the aspirants inclusive of non-maths might have studied this. By understanding all the chapters thoroughly and with a lot of practice it is not difficult to solve all the questions of the paper. Also important is simplifications. Out of 40 questions in Q.A., 20 are simplification questions. Students need to mug up tables upto 20, squares of numbers upto 25 and cubes of numbers upto 15 to make simplifications easy. They also learn Speed Maths for solving simplification questions in seconds without pen. All the chapters in arithmetic have to be practiced thoroughly. Let us see all the chapters of arithmetic in detail.

Digit: 0 to 9 are the digits.

Number: By using digits we write numbers.

Face Value: The real value of the digit.

Place Value: The value of the digit according to the place.

e.g.: In 2794, the face value of 7 is '7'and the place value is '700'.

Classification of Numbers:
Odd Numbers
Numbers which are not divisible by 2
e.g.: 1, 3, 5, 7, .......

Even Numbers
Numbers which are divisible by 2
e.g.: 2, 4, 6, 8, .......

Natural Numbers
All counting numbers             e.g.: N = {1, 2, 3, ........}
Sum of first 'n' natural numbers is

Sum of squares of first 'n' natural numbers is
Sum of cubes of first 'n' natural numbers is

Whole Numbers
0 and all natural numbers
e.g.: W = { 0, 1, 2, 3, ...}
Integers
Natural numbers, zero and negative of natural numbers
e.g.: I = { ........, -3, -2, -1, 0, +1, +2, +3, .......}

Rational Numbers
These are of the form of p/q, where q π 0
e.g.:  etc

Irrational Numbers
Can't be written in p/q form, where q ≠ 0
e.g.:  π  etc

Composite Numbers
Numbers having more than two factors

Prime Numbers
Numbers divisible by one and the number itself or numbers having only two factors.
e.g.: 2, 3, 5, 7, 11, 13, ...... etc
*  All prime numbers end with 1, 3, 7 or 9 except 2 and 5.
*  2 is the only even prime number.
*  '1' is neither a prime nor composite number. It is a unitary.
*  There are 25 prime numbers upto 100.

Twin prime numbers
The difference between two prime numbers is '2'.
e.g.: 3 - 5, 5 - 7, 11 - 13 etc

Co prime numbers
Numbers not having any common factors.
e.g.: 3, 5 and 8 are co primes to each other.

Some important Identities:
1. (a + b)2 = a2 + b2 + 2ab
2. (a - b)2 = a2 + b2 - 2ab
3. (a + b)(a - b) = a2 - b2
4. (a + b)2 = a2 + b2 + 3a2b + 3ab2
5. (a - b)3 = a3 - b3 - 3a2b + 3ab2
6. a3 + b3 = (a + b)(a− ab + b2)
7. a3 - b3 = (a − b) (a2 + ab + b2)
8. (a + b + c)2 = a+ b+ c2 + 2ab + 2bc + 2ac
9. a3+b3+c3− 3abc = (a+b+c) (a2 + b2 + c2 - ab - bc - ac)

e.g.:
1) 2.01            2) 2             3) 1                 4) 1.93                5) None of these
Sol: It is based on the formula a3 + b3 = (a + b)(a− ab + b2)
∴ 1.07 + 0.93 = 2, hence answer (2).

To solve the equations based on numbers, the number is written in algebraic form.
For example let the number be x.

The numerator of a fraction is written in the following form
Three-fourth of a number =
Two-third of a number =
Double of a number = 2x, Thrice of a number = 3x
20% of a number =
30% of 3/4 of one-third of a number =

e.g.: 1.  4/5  of  4/7  of  5/6  of  1218 = ?     (SBI 2008)
(A) 415               (B) 384                (C) 492               (D) 346               (E) None of these
sol:

2. One-seventh of a number is 51. What will be 64% of that number?       (SBI 2008)
(A) 248.12          (B) 228.48           (C) 238.24          (D) 198.36             (E) None of these
Sol:

3. If (16)3 is subtracted from the square of a number, the answer so obtained is 3825. What is the number ?      (SBI 2008)
(A) 69              (B) 59                     (C) 89                    (D) 79                   (E) None of these
Sol: Let the number be x
x2 − 163= 3825 --- x = 89

4. If (92)2 is added to the square of a number, the answer so obtained is 10768. What is the number?          (SBI 2008)
(A) 46            (B) 2304                (C) 48                    (D) 2116              (E) None of these
Sol: Let the number be x
x2 + 922 = 3825    x = 48

5. If an amount of Rs. 97,836 is distributed equally amongst 31 children. How much amount would each child get?    (SBI 2008)
(A) Rs.3,756        (B) Rs.3,556       (C) Rs. 3,356       (D) Rs. 3,156       (E) None of these
Three consecutive odd numbers are x, (x+2) and (x+4), or (x-2), x and (x+2), where x is an odd number.
Similarly, three consecutive even numbers are x, (x+2) and (x+4) or (x-2), x and (x+2) where x is an even number
If a number 'a' is multiplied by itself for n times, the product is called n th power of
'a'. This is written as an.
In an, a is called base and n is called index or exponent or power.

Laws of Indices

All simplification questions have to be solved based on BODMAS rule only.
B - Bracket
O - Of
D - Division
M - Multiplication
S - Subtraction

e.g. 1: What is 394 times 113? (SBI 2008)
(A) 44402             (B) 44632              (C) 44802           (D) 44522         (E) None of these
Sol:   394 × 113 = 44522,     hence answer (D)

2. What approximate value should come in place of the question mark (?) in the following question?  4780 ÷ 296 × (23)2 = ?
(A) 9870                (B) 6760                  (C)7590              (D) 3430           (E) 8540
Sol: 4780/296 × 529 = 8542.63

3. When 40% of first number is added to the second number the second number becomes 1.2 times of itself. What is the ratio between the first and second numbers?
(A) 2:3                  (B) 4:3                     (C) 1:2                  (D) 5:7                 (E) None of these
Sol: Let the first and second number be x and y

Model Questions

1. A number when divided by 5 leaves a remainder of 4, when the double (i.e., twice) of that number is divided by 5 the remainder will be:

A) 4          B) 5            C) 3       D) 2

2. If the sum of the three consecutive integers is 21, then the sum of the two smaller integers is:

A) 20         B) 2        C) 10       D) 13

3. Find the unit digits of the expression: 785562 × 56256 × 971250

A) 0       B) 8           C) 6            D) 9

4. What is the unit digit of 1! + 2! + 3! +.......+ 99! + 100!?

A) 3            B) 2           C) 6          D) 7

5. A number 2A4B is divisible by 8, find the minimum value of A + B?

A) 0          B) 5           C) 2          D) 1

6. If one-third of one-fourth of a number is 15, then three-tenth of the number is?

A) 38 B) 33 C) 25 D) 54

7. No square of a number ends with....

A) 2, 3, 7 and 8           B) 3, 6, 7 and 8

C) 1, 2, 3 and 9          D) 2, 3, 6 and 5

8. 20% of the 4/5 of a number is 60. Then the number is....

A) 420        B) 375         C) 476          D) 285

9. The ratio between two numbers is 3 : 4 and their sum is 420. The greater of the two numbers is...

A) 175         B) 222            C) 240           D) 315

10. The ratio between two numbers is 5 : 2 and their sum is 560. What is the greater of the two numbers?

A) 1000               B) 1500            C) 1300            D) 400

11. A number divided by 56 gives 29 as remainder. If the same number is divided by 8, the remainder will be....

A) 4           B) 5           C) 6            D) 7

12. What is the least value assigned to so that the number 98576a2 is divisible by 8?

A) 2           B) 3            C) 4         D) 5

13. Find the unit digit in the product of (468 × 259 × 686 × 212).

A) 5         B) 3            C) 4           D) 2

14. Find the total number of factors for 720?

A) 72           B) 45           C) 20            D) 30

15. In an examination, 35% of the candidates failed in Mathematics and 25% in English. If 10% failed in both Mathematics and English, then what is the percentage of students who passed in both the subjects?

A) 50          B) 40           C) 45          D) 60

Key
1-C   2-D   3-C   4-A   5-A   6-D   7-A    8-B   9-C   10-D   11-B   12-B   13-C   14-D    15-A

Explanations

1. Take any such number when you divide
the number with 5 leaves
remainder 4 . Example Remainder = 4
Remainder  = 3

2. 6, 7, 8 are consecutive numbers and
6 + 7 + 8 = 21
So sum of smaller two numbers = 6 + 7 = 13

3. Unit digit of 785562 = 82 = 4
Unit digit of 56256 = 6 (Since 6n = 6)
Unit digit of 971250 = 72 = 9
So, 4 × 6 × 9 = 6 (unit digit)

4. Unit digit of a sum will always depend
upon unit digits of individual numbers. So,
1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 3 (unit digit)
5! + 6! + 7! + …….. (All of their unit digits are 0)
(Example 5! = 120)

5. By assuming A = 0 and B = 0
We get number as 2040 and Remainder

So minimum value should be 0 + 0 = 0

6. Let the number be x

7. Considering unit digits :
12 = 1; 22 = 4; 32 = 9; 42 = 6; 52 = 5; 62 = 6;
72 = 9; 82 = 4; 92 = 1
So square numbers do not end with 2, 3, 7, 8.

8. Let the number be x

x = 375

9. Let the numbers be 3x and 4x respectively Going through the options there is only one such multiple where the number is divisible by 4 . So, 240 (4x) is correct. (Divisibility of 4: Two two digits of a number should be divisible by 4).

10. Let the numbers be 5x , 2x respectively
5x + 2x = 560, x = 80
Greater number 5x = 5 × 80 = 400

11. Shortcut method : Remainder = 5

12. For divisibility by 8, the last 3 numbers should be divisible by 8. Going by options, only option B fits the rule.
(Since Remainder (¾¾) = 0)

13. Unit digit of a product will always depend

upon unit digits of individual numbers.
So, 8 × 9 × 6 × 2 = 4

14. Prime factorization of the number
720 = 24 × 32 × 51
So number of factors = (4 + 1) (2 +1) (1 + 1)
= 30

15. n(A È B ) = n(A) + n(B) − n(A Ç B)
Total number of people failed in any one of
the subjects
= 35% + 25% − 10% = 50%
Number of students passed in

Posted Date : 06-05-2022

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.