## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

Direction: In each of the following questions two rows of number are given. The resultant number in each row is to be worked out separately based on the following rules and the questions below of number are to be answered. The operations of number progress from left to right.

Rules
(i) if a two-digit odd number is followed by a two-digit odd number, they are to be added
(ii) if a two-digit even number is followed by a two digit odd number which is a perfect square, the even number is to be subtracted from the odd number.
(iii) If a three-digit number is followed by a two-digit number, the first number is to be divided by the second number .
(iv) if a prime number is followed by an even number, the two are to be added .
(v) If an event number is followed by another even number, the two are to be multiplied.

1. 345   23   X
45    17    81
It 'X' is the resultant of the second row, what is the resultant of the first row ?

1. Rules
(i) (2-digit odd number) + (2-digit odd number)
(ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number)
(iii) (3-digit number) ÷ (2-digit number)
(iv) (Prime number) + (Even number)
(v) (Even number) x (Even number)

##### Correct Option: D

Rules
(i) (2-digit odd number) + (2-digit odd number)
(ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number)
(iii) (3-digit number) ÷ (2-digit number)
(iv) (Prime number) + (Even number)
(v) (Even number) x (Even number)
Solution:
2nd Row 45   17   81 ⇒ 45 + 17 = 62     [rule (i)]
⇒         81 - 62 = 19 [rule (ii)]
1st Row 345   23   X ⇒ 345   23   19
⇒ 345 ÷ 23 = 15 [rule (iii)]
⇒ 345 ÷ 15 + 19 [rule (i)]
∴ Resultant of first row = 34

1. 12   28   84
37   22   18
What is the sum of the resultant of the two rows ?

1. Rules
(i) (2-digit odd number) + (2-digit odd number)
(ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number)
(iii) (3-digit number) ÷ (2-digit number)
(iv) (Prime number) + (Even number)
(v) (Even number) x (Even number)

##### Correct Option: E

Rules
(i) (2-digit odd number) + (2-digit odd number)
(ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number)
(iii) (3-digit number) ÷ (2-digit number)
(iv) (Prime number) + (Even number)
(v) (Even number) x (Even number)
Solution:
1st Row 12   28   84 ⇒ 12 x 28 = 336     [rule (v)]
⇒         336 ÷ 84 = 4 [rule (iii)]
2nd Row 37   22   18 ⇒ 37 + 22 = 59     [rule (iv)]
⇒         59 + 18 = 77 [rule (iv)]
∴ Required sum = 4 + 77 = 81

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. 16   7   25
m   23   22
If 'm' is the resultant of the first row, what will be the resultant of the second row ?

1. 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 16   7   25 ⇒ 16 x 7 = 112       [rule (ii)]

##### Correct Option: E

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 16   7   25 ⇒ 16 x 7 = 112       [rule (ii)]
⇒     112 - 25 = 87 = m     [rule (iv)]
2nd Row m   23   22 ⇒ 87   23   22
⇒         87 + 23 = 110   [rule (iii)]
⇒       110 ÷ 22 = 5     [rule (v)]
∴ Resultant of second row = 5

1. 97   45   71
48    8    11
What is the sum of the resultants of the two rows ?

1. 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 97   45   71 ⇒ 97 + 45 = 142       [rule (iii)]

##### Correct Option: A

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 97   45   71 ⇒ 97 + 45 = 142       [rule (iii)]
⇒     142 ÷ 71 = 2     [rule (v)]
2nd Row 48   8   11 ⇒ 48 ÷ 8 = 6     [rule (i)]
⇒         6 x 11 = 66   [rule (ii)]
∴ Required sum = 2 + 66 = 68

1. 125   64   33
282    x     39
If 'x' is the resultant of the first row, what will be the resultant of the second row ?

1. 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 125   64   33 ⇒ 125 - 64 = 61       [rule (iv)]

##### Correct Option: B

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 125   64   33 ⇒ 125 - 64 = 61       [rule (iv)]
⇒     61 + 33 = 94     [rule (iii)]
= x
2nd Row 282   x   39 ⇒ 282   94   39
⇒         282 ÷ 94 = 3     [rule (v)]
⇒         3 + 39 = 42     [rule (iii)]
∴ Resultant of second row = 42