Mathematical operation and symbol notation


Direction: In each of the following questions, two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the questions below the rows of number are to be answered. The operations of numbers progress from left to the right.
Rules
(i) If a two-digit number is followed by another even number, the first one is to be divided by the second one.
(ii) If an even number is followed by a prime number, the two are to be multiplied.
(iii) If an odd number is followed by another odd number, the two are to be added.
(iv) if a three-digit number is followed by a two-digit number which is a perfect square, the second number is to be subtracted from the first number.
(v) If a three-digit number is followed by a two-digit number which is not a perfect square, the first number is to be divided by the second one.

  1. 24   7     81
    x     27    19
    If 'x' is the resultant of the first row, what will be the resultant of the second row ?
    1. 87
    2. 114
    3. 4
    4. 6
    5. None of these

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    Rules
    (i) (2-digit even number) ÷ ( Even number)
    (ii) (Even number) x (Prime number)
    (iii) (Odd number) + (Odd number)
    (iv) (3-digit number) - (2-digit perfect square number)
    (v) (3-digit number) ÷ (2-digit non-perfect square number)
    Hint
    1st Row 24   7   81 ⇒ 24 x 7 = 168       [rule (ii)]

    Correct Option: D

    Rules
    (i) (2-digit even number) ÷ ( Even number)
    (ii) (Even number) x (Prime number)
    (iii) (Odd number) + (Odd number)
    (iv) (3-digit number) - (2-digit perfect square number)
    (v) (3-digit number) ÷ (2-digit non-perfect square number)
    Solution
    1st Row 24   7   81 ⇒ 24 x 7 = 168       [rule (ii)]
    ⇒     168 - 81 = 87     [rule (iv)]
            = x
    2nd Row x   27   19 ⇒ 87   27   19
    ⇒         87 + 27 = 114     [rule (iii)]
    ⇒         114 ÷ 19 = 6     [rule (v)]
    ∴ Resultant of second row = 6


  1. If 'P' means '+', 'Q' means 'x', 'R' means '÷' and 'S' means '-', then
    44 Q 9 R 12 S 6 Q 4 P 16 = ?
    1. 36
    2. 124
    3. 25
    4. 112

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    After replacing all the symbol from question.
    44 x 9 ÷ 12 - 6 x 4 + 16 = ?
    Apply BODMAS rule,
    ⇒ 44 x 9 x 1/12 - 24 + 16 = ?

    Correct Option: C

    After replacing all the symbol from question.
    44 x 9 ÷ 12 - 6 x 4 + 16 = ?
    Apply BODMAS rule,
    ⇒ 44 x 9 x 1/12 - 24 + 16 = ?
    ⇒ 33 - 24 + 16 = ?
    ⇒ 49 - 24 = ?
    ∴ ? = 25



  1. Which of the following interchange of signs would make the given equation correct ?
    5 + 3 x 8 - 12 ÷ 4 = 3
    1. + and ÷
    2. + and -
    3. - and ÷
    4. + and x

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    Apply All option one by one
    5 + 3 x 8 - 12 ÷ 4 = 3
    Now, after changing the sign for option C
    5 + 3 x 8 ÷ 12 - 4 = 3
    Apply the BODMAS Rule
    5 + 3 x 8/12 - 4 = 3

    Correct Option: C

    Apply All option one by one
    5 + 3 x 8 - 12 ÷ 4 = 3
    Now, after changing the sign for option C
    5 + 3 x 8 ÷ 12 - 4 = 3
    Apply the BODMAS Rule
    5 + 3 x 8/12 - 4 = 3
    5 + 2 - 4 = 3
    3 = 3


  1. If P denotes '÷', Q denotes 'x', R denotes '+' and S denotes '-' then
    18 Q 12 P 4 R 5 S 6 = ?
    1. 95
    2. 53
    3. 51
    4. 57

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    Given Question is 18 Q 12 P 4 R 5 S 6
    After changing the letters in to signs as per given in the question, we have
    18 x 12 ÷ 4 + 5 - 6 ,
    Apply the BODMAS Rule,

    Correct Option: B

    Given Question is 18 Q 12 P 4 R 5 S 6
    After changing the letters in to signs as per given in the question, we have
    18 x 12 ÷ 4 + 5 - 6 ,
    Apply the BODMAS Rule,
    ⇒ 18 x 12/4 + 5 - 6
    ⇒ 18 x 3 + 5 - 6
    ⇒ 54 + 5 - 6
    ∴ 59 - 6 = 53



  1. If '-' stands for 'addition', '÷' for 'multiplication', 'x' for 'subtraction' and '+' for 'division', then which of the following is correct ?
    1. 25 x 12 -14 ÷ 4 + 6 = 16
    2. 25 - 12 + 14 ÷ 2 x 4 = 15
    3. 25 - 15 + 5 ÷ 4 x 16 = 21
    4. 25 + 11 - 4 ÷ 10 x 6 = 20

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    Solve All option one by one.
    After changing the Sign.
    25 + 15 ÷ 5 x 4 - 16 = 21
    Apply the BODMAS Rule,

    Correct Option: C

    Solve All option one by one.
    After changing the Sign.
    25 + 15 ÷ 5 x 4 - 16 = 21
    Apply the BODMAS Rule,
    ⇒ 25 + 3 x 4 - 16 = 21
    ⇒ 25 + 12 - 16 = 21
    ⇒ 37 - 16 = 21
    ∴ 21 = 21