## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

1. 7   21   3
d   7   33
If 'd' is the resultant of the first row, what will be the resultant of the second row ?
1. 40
2. 138
3. 231
4. 80
5. None of the above

1. Rules
(i) (Odd number) x (Composite odd number)
(ii) (Even number) + (Odd number)
(iii) (Even number) → (Perfect square number), then (Perfect square number) - (Even number)
(iv) (Odd number) ÷ (Prime odd number)
(v) (Odd number) - (Even number)
Hint
1st Row 7   21   3 ⇒ 7 x 21 = 147       [rule (i)]

##### Correct Option: C

Rules
(i) (Odd number) x (Composite odd number)
(ii) (Even number) + (Odd number)
(iii) (Even number) → (Perfect square number), then (Perfect square number) - (Even number)
(iv) (Odd number) ÷ (Prime odd number)
(v) (Odd number) - (Even number)
Solution
1st Row 7   21   3 ⇒ 7 x 21 = 147       [rule (i)]
⇒     147 ÷ 3 = 49 = d     [rule (iv)]
2nd Row d   7   33 ⇒ 49   7   33
⇒         49 ÷ 7 = 7   [rule (iv)]
⇒       7 x 33 = 231     [rule (i)]
∴ Resultant of second row = 231

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 an odd number is followed by another composite odd number, they are to be multiplied.
(ii) If an even number is followed by an odd number, they are to be added.
(iii) If an even number is followed by a number which is the perfect square, the even number is to be subtracted from the perfect square.
(iv) if an odd number is followed by a prime odd number, the first number is to be divided by the second number.
(v) If an odd number is followed by an even number, the second one is to be subtracted from the first one.

1. 73   34   13
32    p    15
If 'p' is the resultant of the first row, what will be the resultant of the second row ?
1. 713
2. 50
3. 20
4. 525
5. None of these

1. Rules
(i) (Odd number) x (Composite odd number)
(ii) (Even number) + (Odd number)
(iii) (Even number) → (Perfect square number), then (Perfect square number) - (Even number)
(iv) (Odd number) ÷ (Prime odd number)
(v) (Odd number) - (Even number)
Hint
1st Row 73   34   13 ⇒ 73 - 34 = 39       [rule (v)]

##### Correct Option: D

Rules
(i) (Odd number) x (Composite odd number)
(ii) (Even number) + (Odd number)
(iii) (Even number) → (Perfect square number), then (Perfect square number) - (Even number)
(iv) (Odd number) ÷ (Prime odd number)
(v) (Odd number) - (Even number)
Solution
1st Row 73   34   13 ⇒ 73 - 34 = 39       [rule (v)]
⇒     39 ÷ 13 = 3 = p     [rule (iv)]
2nd Row 32   p   15 ⇒ 32   3   15
⇒         32 + 3 = 35   [rule (ii)]
⇒       35 x 15 = 255     [rule (i)]
∴ Resultant of second row = 525

1. 14   5   9
24   w   88
If 'w' is the resultant of the first row, what will be the resultant of the second row ?
1. 171
2. 283
3. 195
4. 107
5. None of these

1. Rules
(i) (Odd number) x (Composite odd number)
(ii) (Even number) + (Odd number)
(iii) (Even number) → (Perfect square number), then (Perfect square number) - (Even number)
(iv) (Odd number) ÷ (Prime odd number)
(v) (Odd number) - (Even number)
Hint
1st Row 14   5   9 ⇒ 14 + 5 = 19       [rule (ii)]

##### Correct Option: D

Rules
(i) (Odd number) x (Composite odd number)
(ii) (Even number) + (Odd number)
(iii) (Even number) → (Perfect square number), then (Perfect square number) - (Even number)
(iv) (Odd number) ÷ (Prime odd number)
(v) (Odd number) - (Even number)
Solution
1st Row 14   5   9 ⇒ 14 + 5 = 19       [rule (ii)]
⇒     19 x 9 = 171     [rule (i)]
= w
2nd Row 24   w   88 ⇒ 24   171   88
⇒         24 + 171 = 195   [rule (ii)]
⇒       195 - 88 = 107     [rule (v)]
∴ Resultant of second row = 107

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. 84     14   13
360   24   17
What is the difference between the resultant of the first row and the second row ?
1. 100
2. 46
3. 56
4. 90
5. None of these

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 84   14   13 ⇒ 84 ÷ 14 = 6       [rule (i)]

##### 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 84   14   13 ⇒ 84 ÷ 14 = 6       [rule (i)]
⇒     6 x 13 = 78     [rule (ii)]
2nd Row 360   24   17 ⇒ 360 ÷ 24 = 15     [rule (v)]
⇒         15 + 17 = 32     [rule (iii)]
∴ Resultant difference = 78 - 32 = 46

1. If '+' mean '-', '-' means 'x', 'x' means '÷' and '÷' means '+', then value of 16 x 2 ÷ 25 + 7 - 4 is
1. 104
2. 5
3. 22
4. 4

1. 16 x 2 ÷ 25 + 7 - 4
= 16 ÷ 2 + 25 - 7 x 4

##### Correct Option: B

16 x 2 ÷ 25 + 7 - 4
= 16 ÷ 2 + 25 - 7 x 4
= 8 + 25 - 28
= 25 - 20 = 5