## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

Direction: What should be the correct signs to balance the following equations ?

1. 7   4   8   2 = 24

1. Let us check all the options one-by-one.
From option (a),
7 - 4 x 8 x 2 = 24 (using VBODMAS rule)

##### Correct Option: C

Let us check all the options one-by-one.
From option (a),
7 - 4 x 8 x 2 = 24 (using VBODMAS rule)
⇒ 7 - 64 = 24 ⇒ -57 = 24
∴ LHS ≠ RHS ≠ RHS
So, option (a) is incorrect.

From option (b),
7 - 4 x 8 ÷ 2 = 24 (using VBODMAS rule)
⇒ 7 - 4 x 8 ÷ 2 = 24 (using VBODMAS rule)
⇒ 7 - 4 x 4 = 24 ⇒ 7 - 16 = 24
⇒ -9 = 24 ⇒ LHS ≠ RHS
So, option (b) is incorrect .
From option (c),
7 x 4 - 8 ÷ 2 = 24 (using VBODMAS rule)
⇒ 7 x 4 - 4 = 24 ⇒ 28 - 4 = 24
⇒ 24 = 24 ⇒ LHS = RHS
So, option (c) is correct and hence, there is no need to check option (d).

1. If 264 * 2 = 6, 870 * 3 = 11, then what should 735 *5 be ?

1. Divide and add all numbers.

##### Correct Option: B

As, 264/2 = 132 ⇒ 1 + 3 + 2 = 6
⇒ 870/3 = 290 ⇒ 2 + 9 + 0 = 11
Similarly, 735/5 = 147 ⇒ 1 + 4 + 7 = 12

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. 23   15   12
X     24    49
If 'X' is the resultant of the first row, what is the resultant of the second 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)
Solution:
1st Row   23     15     12 ⇒ 23 + 15 = 38
[rule (i)]     ⇒ 38 x 12 = 456     [rule (v)]
2nd Row   X   24   49 ⇒ 456   24   49
⇒ 456 ÷ 24 = 19 [rule (iii)] ⇒ 19 + 49 = 68     [rule (i)]
∴ Resultant of second row = 68

##### 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   23     15     12 ⇒ 23 + 15 = 38
[rule (i)]     ⇒ 38 x 12 = 456     [rule (v)]
2nd Row   X   24   49 ⇒ 456   24   49
⇒ 456 ÷ 24 = 19 [rule (iii)] ⇒ 19 + 49 = 68     [rule (i)]
∴ Resultant of second row = 68

1. 37   12   21
38   81   14
What is the difference between the resultants 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: C

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 37   12   21 ⇒ 37 + 12 = 49     [rule (iv)]
⇒         49 + 21 = 70 [rule (i)]
2nd Row 38   81   14 ⇒ 81 - 38 = 43     [rule (ii)]
⇒         43 + 14 = 57 [rule (iv)]
∴ Required difference = 70 - 57 = 13

1. 16      8     32
132   11   X2
If X is the resultant of the first row, what is the resultant of the second 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: A

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 16   8   32 ⇒ 16 x B = 128     [rule (v)]
⇒         128 ÷ 32 = 4 [rule (iii)]
X
2nd Row 132   11   X2 ⇒ 132   11   16
⇒         132 ÷ 11 = 12 [rule (iii)]
⇒         12 x 16 = 192 [rule (v)]
∴ Resultant of second row = 192