## Mathematical operation and symbol notation

#### 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. 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

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. 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. Which of the following sets of operation with the usual notations replacing the starts in the order given makes the statements valid ?
100 * √16 * √225 * √1

1. 100 + √16
= √225 -√1

##### Correct Option: B

100 + √16
= √225 -√1
10 + 4 = 15 - 1
⇒ 14 = 14

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

1. 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