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Mathematical Operations Type 2

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  1. Question 1 of 27
    1. Question

    Directions (Qs. 1-4) : ‘∆’ means ‘is equal to’, ‘□’ means ‘is not equal to’, ‘+’ means ‘is greater than’, ‘–’ means ‘is less than’, ‘×’ means ‘is not greater than’, ‘÷’ means ‘is not less than’; a – b – c implies:

    Hint

    a – b – c means a < b < c and this relation implies that b > a < c, i.e., b + a – c.

  2. Question 2 of 27
    2. Question

    Directions (Qs. 1-4) : ‘∆’ means ‘is equal to’, ‘□’ means ‘is not equal to’, ‘+’ means ‘is greater than’, ‘–’ means ‘is less than’, ‘×’ means ‘is not greater than’, ‘÷’ means ‘is not less than’; a + b ÷ c implies:

    Hint

    a + b ÷ c means that a > b ≥ c and this relation implies that c < b < a, i.e., c – b – a.

  3. Question 3 of 27
    3. Question

    Directions (Qs. 1-4) : ‘∆’ means ‘is equal to’, ‘□’ means ‘is not equal to’, ‘+’ means ‘is greater than’, ‘–’ means ‘is less than’, ‘×’ means ‘is not greater than’, ‘÷’ means ‘is not less than’; a × b ÷ c implies that:

    Hint

    a × b ÷ c means a ≤ b ≥ c and this relation implies that c ≤ b < a, i.e., c × b ÷ a.

  4. Question 4 of 27
    4. Question

    Directions (Qs. 1-4) : ‘∆’ means ‘is equal to’, ‘□’ means ‘is not equal to’, ‘+’ means ‘is greater than’, ‘–’ means ‘is less than’, ‘×’ means ‘is not greater than’, ‘÷’ means ‘is not less than’; a + b + c does not imply:

    Hint

    a + b + c means a > b > c and this relation does not imply that b < a < c, i.e., b – a – c.

  5. Question 5 of 27
    5. Question

    Directions (Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; a × b θ c implies that:

    Hint

    a × b θ c is equivalent to a < b = c. Hence between a and b , we have a < b or a ≠ b or a > b
    Further b = c implies that b and c are interchangeable.
    Hence (a), (b) and (c) are not possible.
    [Observe that (b) states b < a which means a > b which is not possible. Similarly in (c) b > a which means a < b which contradicts the hypothesis.] (d) Is the correct answer which states that a ≠ b and b > c. Both statements are possible.

  6. Question 6 of 27
    6. Question

    Directions (Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; a □ b ∆ c implies that:

    Hint

    Hypothesis (stem of the question) states a ≠ b & b > c. Only relation not possible between a and b is that of equality. Hence (a), (b), (c), (d) are all possible from the relation between a and b.
    Coming to the second relation only (a) is possible . Hence (a) is the answer.

  7. Question 7 of 27
    7. Question

    Directions (Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; a ∆ b ∆ c does not imply:

    Hint

    Note that in this question we have to determine which relation is not possible.
    It is given that a > b > c.
    Both relation in (a), (c) and (d) are possible. It is only (b) in which b = c is not true. Hence (b) is the answer.
    [It should be noted that in case of negation of implication it is enough to show that just one relation is not possible.]

  8. Question 8 of 27
    8. Question

    Directions (Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; a × b θ c does not mean:

    Hint

    With the situations given, a × b θ c mean a < b = c From option (a), a ∆ b φ c means a > b ≠ c, this is not true.
    From option (b), a + b θ c means a ≤ b = c, this is true.
    From option (c) ,a φ b θ c means a ≠ b = c, this is true From option (4), b θ c □ a means b = c ≥ a, this is true. So, the answer is (a).

  9. Question 9 of 27
    9. Question

    Directions (Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; c + b × a means:

    Hint

    With the notations given, c + b × a means c ≤ b < a From option (a), a × b θ c means a < b = c, this is not true. From option (b), c ∆ b ∆ a means a > b > c, this is true.
    From option (c), c × b × a means a < b < c, this is not true. From option (d), b θ c ∆ a means b = c > a, this is not true.

  10. Question 10 of 27
    10. Question

    Directions (Qs. 10-11) : Different alphabets stand for various symbols as indicated below:

    Addition : O, Subtraction : M, Multiplication : A, Division : Q, Equal to : X, Greater than : Y, Less than : Z. Which one of the following alternatives is correct ?

    Hint

    Using the proper notations in (b), we get the statement as 2÷1 + 20 × 1 < 6 × 4 or 22 < 24, which is true.

  11. Question 11 of 27
    11. Question

    Directions (Qs. 10-11) : Different alphabets stand for various symbols as indicated below:

    Addition : O, Subtraction : M, Multiplication : A, Division : Q, Equal to : X, Greater than : Y, Less than : Z. Which one of the following alternatives is correct ?

    Hint

    Using the proper notations in (b), we get the statement as 10 = 2 × 3 × 2 – 2 ÷ 1 or 10 = 10, which is true.

  12. Question 12 of 27
    12. Question

    Directions (Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.

    Total age of 12 boys is ‘X’ and the total age of 13 girls is ‘Y’. What is the average age (A) of all the boys and girls together?

    Hint

    Average age of all boys and girls mathematical-operations-21884.png
    ⇒ A1 = (x @ y) # 25

  13. Question 13 of 27
    13. Question

    Directions (Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.

    Population of state M (P1) is less than half of population of state N (P2) by 1,50,000.

    Hint

    mathematical-operations-21878.png–1,50,000
    ⇒ P1 = (P2 # 2) $ 150000

  14. Question 14 of 27
    14. Question

    Directions (Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.

    Number of boys (B) in a class is equal to one-fourth of three times the number of girls (G) in the class.

    Hint

    mathematical-operations-21871.png
    ⇒ B = (3 * G) # 4

  15. Question 15 of 27
    15. Question

    Directions (Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.

    Salary of Mr. X (S1) is more than 40% of Mr. Y’s salary (S1) by Rs 8,000

    Hint

    mathematical-operations-21865.png
    ⇒ S1 = [S2 *(40 # 100)] @ 8,000

  16. Question 16 of 27
    16. Question

    Directions (Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.

    Marks obtained by Sujit in History (H) are 85% of his marks obtained in Science (M).

    Hint

    mathematical-operations-21859.pngs
    ⇒ H = (85 # 100) * M

  17. Question 17 of 27
    17. Question

    If ‘L’ denotes ‘÷’, ‘M’ denotes ‘×’, ‘P’ denotes ‘+’ and ‘Q’ denotes ‘–’, then which of the following statements is true?

    Hint

    Using the proper notations in (d), we get
    9 + 9 ÷ 9 – 9 × 9
    = 9 + 1 – 9 × 9 = 9 + 1 – 81 = –71.
    ∴ option (d) is true.

  18. Question 18 of 27
    18. Question

    If ‘P’ denotes ‘+’, ‘Q’ denotes ‘–’, ‘R’ denotes ‘×’ and ‘S’ denotes ‘÷’, which of the following statements is correct?

    Hint

    Using the proper notations in (d), we get
    8 × 8 + 8 ÷ 8 – 8
    = 8 × 8 + 1 – 8 = 64 + 1 – 8 = 57

  19. Question 19 of 27
    19. Question

    Which one of the four interchanges in signs and numbers would make the given equation correct ?3 + 5 – 2= 0

    Hint

    By making the interchanges given in (a), we get the equation as
    2 – 5 + 3 = 0 or 0 = 0 which is true.
    By making the interchanges given in (b), we get the equation as
    3 – 2 + 5 = 0 or 6 = 0, which is false.
    By making the interchanges given in (c), we get the equation as
    5 – 2 + 2 = 4 or 4 = 0 which is not true.
    So, the answer is (a).

  20. Question 20 of 27
    20. Question

    If the given interchanges namely : signs ‘+’ and ‘÷’ and numbers ‘2’ and ‘4’ are made in signs and numbers, which one of the following four equations would be correct ?

    Hint

    Interchanging (+ and ÷) and (2 and 4), we get :
    (a) 4 ÷ 2 + 3 = 3 or 5 = 3, which is false
    (b) 2 ÷ 4 + 6 = 1.5 or 6.5 = 1.5, which is false.
    (c) 2 + 4 ÷ 3 = 4 or ¹⁰⁄₃ = 4, which is false.
    (d) 4 ÷ 2 + 6 = 8 or 8 = 8, which is true.

  21. Question 21 of 27
    21. Question

    It being given that : ‘>’ denotes ‘+’, ‘<’ denotes ‘–’, ‘+’ denotes ‘÷’, ‘–’ denotes ‘=’, ‘=’ denotes ‘less than’ and ‘×’ denotes ‘greater than’; find which of the following is a correct statement:

    Hint

    Using proper notations, we have:
    (a) given statement is 3 ÷ 2 + 4 < 9 ÷3 – 1 or ¹¹⁄₂ < 2, which is not true. (b) given statement is 3 + 2 + 4 < 18 ÷ 3 – 2 or 9 < 4, which is not true. (c) given statement is 3 + 2 – 4 > 8 ÷ 4 – 2 or 1 > 0, which is true.
    (d) given statement is 3 ÷ 2 – 4 > 9 ÷ 3 – 3 or – ⁵⁄₂ > 0, which is not true . So, the statement (c) is true.

  22. Question 22 of 27
    22. Question

    If ‘×’ stands for ‘addition’, ‘<’ for ‘subtraction’, ‘+’ stands for ‘division’, ‘>’ for ‘multiplication’, ‘–’ stands for ‘equal to’, ‘÷’ for ‘greater than’ and ‘=’ stands for ‘less than’; state which of the following is true ?

    Hint

    Using the proper notations in (2), we get the statement as 5 × 2 ÷ 2 < 10 – 4 + 2 or 5 < 8 , which is true.

  23. Question 23 of 27
    23. Question

    If ‘→’ stands for ‘addition’, ‘←’ stands for ‘subtraction’, ‘↑’ stands for ‘division’, ‘↓’ stands for ‘multiplication’, ‘↗’ stands for ‘equal to’; then which of the following alternatives is correct?

    Hint

    Using the proper notations in (d) we get the statement as
    2 × 5 – 6 + 2 = 6
    or 10 – 6 + 2 = 6 or 6 = 6, which is true.

  24. Question 24 of 27
    24. Question

    Of ‘x’ Stands for ‘addition’, ‘z’ for ‘subtraction’, ‘+’ for ‘division’, ‘>’ for ‘multiplication’, ‘–’ for ‘equal to’, ‘+’ for ‘greater than’ and ‘=’ for ‘less than’; state which of the following is true. ?

    Hint

    Using the proper notations in (c), we get the statement as
    5 × 2 ÷ 2 < 10 – 4 + 8 or 5 × 1 < 18 – 4 or 5 < 14, which is true.

  25. Question 25 of 27
    25. Question

    It being given that ‘x’ denotes ‘greater than’, ‘φ’ denote ‘equal to’, ‘<’ denotes ‘not less than’, ‘⊥’ denotes ‘not equal to’, ‘∆’ denotes ‘less than’ and ‘+’ denotes ‘not greater than’; then choose the correct statement from the following if a x b ∆ c, it follows that:

    Hint

    Using the usual notations, we have
    (a) The statement is a > b < c ⇒ a = c < b , which is false [since c > b]
    (b) The statement is a > b < c ⇒ b < a > c, which is false. [since b < a] (c) The statement is a > b < c ⇒ a < b > c , which is true
    (d) The statement is a > b < c ⇒ c < b < a , which is false. [since b < a]

  26. Question 26 of 27
    26. Question

    If A + D > C + E, C + D = 2B and B + E > C + D, it necessarily follows that

    Hint

    A + D > C + E
    ⇒ A + D > (2B – D) + E (since C + D = 2B)
    ⇒ A + D > (B + E) + (B – D)
    ⇒ A + D > (C + D) + (B – D)
    ⇒ A + D > B + C.

  27. Question 27 of 27
    27. Question

    If A + D = B + C, A + E = C + D, 2C < A + E and 2A > B + D, then

    Hint

    2 C < A + E, A + E = C + D ⇒ 2C < C + D ⇒ C < D ...(1) A + D = B + C, C < D ⇒ A < B ...(2) 2A > B + D, A < B ⇒ A > D …(3)
    A + E = C + D , A > D ⇒ E < C ...(4)

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