6. Symbols & Notations

Introduction:-
In Symbols & Notations one has to study the symbols & their meanings carefully which are given against them. Then, the meanings given are to be used in place of those symbols in answering the questions.

The word “notation” basically stands for the meaning which each symbol will be assigned. The questions can be based on comparisons (in equalities), mathematical operations, sequencing order, word/ number/formations.

Mathematical operations:-
Symbols for these type of questions stands for mathematical operations like +, -, ×, ÷, >, <, .

In the mathematical operations we have to follow BODMAS rule to find the value of the given expression.

Symbols like etc. are used by giving a proper definition of the symbol used.

1. If ‘+” means ‘×’, ‘-‘ means ‘÷’, ‘×’ means ‘+’, ‘÷’ means ‘-‘, then what is the value of ‘16× 8 ÷ 4 + 6 – 3”?
   (1) 24
   (2) 26
   (3) 16
   (4) 18
   (5) 20
   Sol: Given expression 16× 8 ÷ 4 + 6 -3
   Convert the symbols according to given definition = 16+8-4×6÷3
   Solve this expression by BODMAS rule, we get the value as 16
   Ans: 3
   
2. If 6@ 8 = 70, 9@6=45, then 8@7=_____
   (1) 57
   (2) 71
   (3) 50
   (4) 80
   (5) 15
   Sol: 6@8=70 6+8² 6 + 64 = 70
   9@6 = 45 9+6² 9+36 = 45
   Similarly 8@7 8+7² 8+49 = 57
   Ans: 1
   
3. If a.b = a2 + 2ab +b2, then 5.3 = ______
   (a) 50
   (b) 60
   (c) 52
   (d) 64
   (e) None of these
   Sol: Given a.b = a2 + 2ab + b2
   We have to solve 5.3 = _______ here a= 5, b =3 substitute a=5, b=3 in the expression
   5.3 = 5² + 2×5×3 + 3² = 25+30+9 =64
   Ans: d
   
4. If “#” means “is less than”, “ ” means “is greater than”, “$” means “is equal to”, given that a#b, a c, b$d then which of the following is true?
   (a) a d
   (2) c d
   (3) c#d
   (4) a$c
   (5) b$c
   Sol: given #- means “<”
   - means “>”
   $ - means “=”
   a#b = a < b
   a c= a>c
   b$d = b = d
   (a) a d = a>d = false
   (b) c d = c>d = false
   (c) c#d = c
   (d) a$ c = a = c = false
   (e) b$c = b=c = false
   Ans: c
   
   EXERCISE
   Directions for 1 to 5: In a certain code language ‘+’ means ‘×’, ‘-‘ means '÷’, ‘×’ means ‘+’, ‘÷’ means ‘-‘. Simplify the following expressions using the above directions, in which the mathematical operators are written according to the code language.

1. 25-5÷4+16-8
   (1) -3
   (2) 3
   (3) 12
   (4) 16
   (5) -12
   
2. 24-8+(3×2)+5
   (1) 25
   (2) 20
   (3) 75
   (4) 40
   (5) 30
   
3. 16×8÷4+6-3
   (a) 30
   (b) 20
   (c) 26
   (d) 16
   (e) 18
   
4. 44÷ 8 × 16 × 2 × 6 – 6
   (a) 65
   (b) 55
   (c) 50
   (d) 125
   (e) 120
   
5. (4×8)-2÷64-8-4
   (a) 4
   (b) 8
   (c) 10
   (d) 6
   (e) 15
   
   Directions for 6 to 10:
   In a certain code language “+” means ‘-‘, ‘-‘ means ‘×’, ‘×’ means ‘÷’, ÷ means ‘+’. Using the above directions, simplify the following expressions, in which the mathematical operators are written in the code languages
   
6. 14× 7 – 6 +15 ÷ 27 × 9
   (a) 97
   (b) 90
   (c) 0
   (d) 105
   (e) 30
   
7. (19+3)× 4 ÷ 26 × 2 + 48 × 2÷ 108
   (a) 152
   (b) 101
   (c) 93
   (d) -101
   (e) -93
   
8. 256× 16 ÷ 49 × 7 + 125 × 5 -2 ÷ 289 × 17
   (a) -10
   (b) 22
   (c) 10
   (d) -15
   (e) -17
   
9. 278+8× 2 – 7 ÷ 316 + 7 × 28 – 364
   (a) 250
   (b)-220
   (c) 395
   (d) 305
   (e) 475
   
10. 25 × 5 -50 – 3× 10 + 15 =
    (a) 60
    (b) 50
    (c) 5
    (d) 15
    (e) 20
    
    II. Comparisons:-
    Directions for 11 to 15:-
    These questions are based on the following information’s:-
    If P#Q means P is less than Q
    P £Q means P is greater than Q
    P $ Q means P is either greater than (or) equal to Q
    P @ Q means P is either less than (or) equal to Q
    P % Q means P is equal to Q
    Mark answer as.
    1. If only conclusion (I) follows
    2. If only conclusion (II) follows
    3. If either (I) or (II) follows
    4. If neither (I) nor (II) follows
    5. LIf both conclusions (I) and (II) follows
    
    
11. A $ B, C % D, B£C
    I) D # B
    (II) A£D
    
12. X @ Y, Z£W, W % x
    I) Y@Z
    (II) Y$W
    
13. G$H, H#I, J£I
    I) G@I
    II) G@J
    
14. P £ Q, R@S, Q$R
    I) R#P
    II) P%S
    
15. A#B, B £ D, C@D
    I) A@D
    II) C#B
    Directions for 16-20:-
    In the following questions, the symbols $, @, ã, % and * are used with the following meaning as illustrated below:
    ‘P$Q’ means ‘P is not smaller than Q’
    ‘P@Q’ means ‘P is not greater than Q’
    ‘PãQ’ means that ‘P is neither greater than nor smaller than Q’
    ‘P%Q’ means ‘P is neither smaller than nor equal to Q’
    ‘P*Q’ means “P is neither greater than nor equal to Q’
    Now in each of the following questions assuming the given statements to be true /find which of the two conclusions I and II given below them is/are definitely true?
    Give answer (a) if only conclusions I is true.
    Give answer (b) if only conclusion II is true.
    Give answer (c) if either conclusion I or II is true.
    Give answer (d) if neither conclusion I nor, II is true.
    Give answer (e) if both the conclusion I and II are true.
    
16. Statements: K@B, B*J, J©T
    Conclusions:
    I. K*T
    II. B@T
    
17. Statements: F$M, M@L, L*W
    Conclusions:
    I. W$M
    II. F@L
    
18. Statements: R*Q, Q@F, F%A
    Conclusions:
    I. R©A
    II. R*F
    
19. Statements: V$X, X©Y, Y%H
    Conclusions:
    I. Y@V
    II. H*V
    
20. Statements: M@B, B*A, A@F
    Conclusions:
    I. M*A
    II. B*F
    
    III. Sequence:-
    Directions for Questions 21-25: Study the following sequence carefully and answer the questions below it.
    
    
21. How many such elements are there in the above sequence, which are either immediately preceded by a letter (or) immediately followed by a digit?
    (a) 10
    (b) 12
    (c) 13
    (d) 15
    (e) 16
    
22. Fill in the blank based on the above sequence. FHG, S @, A2&, ________, 7F8
    (a) Q 8
    (b) E1L
    (c) 3A
    (d) *P?
    (e) None of these
    
23. How many such digits are there which are neither preceded nor followed by a symbol?
    (a) 5
    (b) 6
    (c) 2
    (d) 4
    (e) 0
    
24. Which of the following is the 12th element to the left of the 3rd element to the right of the 6th element from the right end?
    (a)
    (b) H
    (c) @
    (d) S
    (e) 9
    
25. If the 1st half of the given sequence is reversed, then which element is the 10th to the right of the 2nd to the left of the 7th from left end?
    (a) Q
    (b) 7
    (c)
    (d) 4
    (e) $
    
    Directions for the questions 26-30:-
    Study the following sequence carefully and answer the following questions:
    
    
26. Which element is 6th to the left of the 7th element from the right end?
    (a) G
    (b) Q
    (c) K
    (d) 7
    (e) M
    
27. If the 2nd half of the sequence is reversed, then which element is 4th to the right of the 9th element from the right end?
    (a) K
    (b) $
    (c) 7
    (d)
    (e) %
    
28. How many symbols are immediately preceded by a digit but not immediately followed by a letters?
    (a) 3
    (b) 1
    (c) 2
    (d) 0
    (e) 4
    
29. Find the next series 4@B, 3 C 4 , * 3 , 12*, ______
    (a) LX1
    (b) $1f
    (c) 9$£
    (d) L1F
    (e) None of these
    
30. How many letters are either immediately followed by a letter (or) immediately preceded by a digit but not both?
    (a) 2
    (b) 4
    (c) 5
    (d) 3
    (e) 1
    
    IV. Word/Number formations: 
    Directions (31-35): The following questions are based on the five three digit numbers given below:
    574 658 821 945 247
    
31. If one is added to the last digit of each of the numbers, in how many numbers thus formed will the last digit be a perfect square (1 is also be a perfect square)?
    (a) One
    (b) two
    (c) three
    (d) Four
    (e) None of these
    
32. If 1 is subtracted from the 1st digit of each number then how many numbers thus formed will be divisible by three?
    (a) None
    (b) one
    (c) two
    (d) Three
    (e) four
    
33. If in each number, all the three digit are arranged in ascending order within the number which of the following will be the highest number?
    (a) 574
    (b) 658
    (c) 821
    (d) 945
    (e) 247
    
34. If each numbers the first two digits are replaced by their sum then which number will be the largest?
    (a) 574
    (b) 658
    (c) 821
    (d) 945
    (e) 247
    
35. If in each number the position of 1st and the 2nd digit are interchanged which number will be the smallest?
    (a) 574
    (b) 658
    (c) 821
    (d) 945
    (e) 247
    
    Directions for the questions 36-40
36. If the digits of the number “82759146” are arranged in increasing order, then how many digits remain in the same position?
    (a) Three
    (b) Two
    (c) One
    (d) None
    (e) Four
    
37. If the digits of the number “72516898” are arranged in the descending order, then from left to right, then what will be the sum of the digits which are 6th from the left and 5th from the right in the new arrangement?
    (a) 14
    (b) 10
    (c) 12
    (d) 11
    (e) 13
    
38. If one is added to each odd digit & one is subtracted from each even digit in the number “5643782” & then the digits so formed are arranged in the descending order, which of the following will be the 3rd digit from the left end?
    (a) 4
    (b) 5
    (c) 8
    (d) 6
    (e) 3
    
39. How many such pairs of letters are there in the words “CREATIVE” which have as many letters between them in the word as they have between them in English alphabet?
    (a) Two
    (b) Three
    (c) Four
    (d) One
    (e) None
    
40. How many such pairs of letters are there in the words “PRODUCTION” which have as many letters between them in the word as they have between them in English alphabet?
    (a) One
    (b) four
    (c) three
    (d) Two
    (e) None
    
41. If it is possible to make a meaning full word with the 1st, 3rd, 5th and the 6th letters of the word “TRADEMARK”, which of the following will be the last letter of that word? If NO such word can be formed, give ‘X’ as the answer. If more than one such word can be formed, given ‘M’ as the answer?
    (a) M
    (b) E
    (c) X
    (d) M
    (e) T
    
42. If each of the vowels in the word “DIGITAL” is changed to the next letter in the English alphabet & each consonant is changed to the previous letter in the English alphabet, and then the letters in the word so formed are arranged in the alphabetical order from left to right, then which letter is 2nd from the right end?
    (a) J
    (b) B
    (c) S
    (d) K
    (e) None of these
    
43. In the following sequence of digits, how many pairs of digits are there which have as many digits between them as they have between them as in natural number series? “138969273”
    (a) 4
    (b) 2
    (c) 8
    (d) 6
    (e) 3
    
44. If the letters of the word “INSTITUTE” are arranged in alphabetical order, then how many letters remain in same position?
    (a) 3
    (b) 2
    (c) 4
    (d) 1
    (e) None
    
45. If the digits of the number “83604159” are arranged in the descending order, then how many digits occupy the same position as in the number?
    (a) One
    (b) Two
    (c) Three
    (d) Four
    (e) None
    
    Directions for questions 46 -50:-
    
46. Shyam ranked 9th from the left & 38th from the right in a class. How many students are there in the class? (a) 46
    (b) 48
    (c) 45
    (d) 4
    (e) None
    
47. A class of boys stands in a single line, one boy is 19th in order from both the ends. How many boys are there in the class?
    (a) 38
    (b) 37
    (c) 39
    (d) 40
    (e) None
    
48. In a queue, Mahesh is the 5th person from the front. Suresh is the 6th person from the back end. How many persons are standing on the queue if two persons are in between Mahesh & Suresh?
    (a) 13
    (b) 6
    (c) 7
    (d) 10
    (e) Can’t be determined
    
    Directions for the questions 49-50
    Six students P,Q, R, S, T & U are the top six rankers of the class. No two persons got the same rank. The student who got the highest marks is given rank 1 and the student who got the least mark is given rank 6. Q got less marks than both R & U. ‘P’ got more marks than T but less than S. Q got the second least rank & ‘U’ got the second highest rank, R got less marks than ‘P’.
    
49. Who got the third rank?
    (a) T
    (b) R
    (c) P
    (d) S
    (e) Can’t be determined
    
50. Who got the sixth rank?
    (a) T
    (b) R
    (c) P
    (d) S
    (e) Can’t be determined
    

ANSWERS
1	1	11	5	21	d	31	a	41	d
2	3	12	2	22	b	32	d	42	d
3	d	13	4	23	a	33	b	43	a
4	b	14	1	24	c	34	d	44	b
5	a	15	2	25	a	35	c	45	b
6	c	16	a	26	a	36	b	46	a
7	b	17	d	27	c	37	c	47	b
8	a	18	b	28	c	38	d	48	e
9	e	19	e	29	a	39	b	49	c
10	a	20	e	30	d	40	c	50	a