Mathematical operation and symbol notation
Direction: What should be the correct signs to balance the following equations ?
 7 4 8 2 = 24

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Let us check all the options onebyone.
From option (a),
7  4 x 8 x 2 = 24 (using VBODMAS rule)Correct Option: C
Let us check all the options onebyone.
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).
 If 264 * 2 = 6, 870 * 3 = 11, then what should 735 *5 be ?

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Divide and add all numbers.
Correct Option: B
Divide and add all numbers.
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 twodigit odd number is followed by a twodigit odd number, they are to be added
(ii) if a twodigit 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 threedigit number is followed by a twodigit 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.
 23 15 12
X 24 49
If 'X' is the resultant of the first row, what is the resultant of the second row ?

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Rules
(i) (2digit odd number) + (2digit odd number)
(ii) 2digit even number → 2digit perfect square odd number then, (odd number)  (Even number)
(iii) (3digit number) ÷ (2digit 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 = 68Correct Option: E
Rules
(i) (2digit odd number) + (2digit odd number)
(ii) 2digit even number → 2digit perfect square odd number then, (odd number)  (Even number)
(iii) (3digit number) ÷ (2digit 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
 37 12 21
38 81 14
What is the difference between the resultants of the two rows ?

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Rules
(i) (2digit odd number) + (2digit odd number)
(ii) 2digit even number → 2digit perfect square odd number then, (odd number)  (Even number)
(iii) (3digit number) ÷ (2digit number)
(iv) (Prime number) + (Even number)
(v) (Even number) x (Even number)Correct Option: C
Rules
(i) (2digit odd number) + (2digit odd number)
(ii) 2digit even number → 2digit perfect square odd number then, (odd number)  (Even number)
(iii) (3digit number) ÷ (2digit 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
 16 8 32
132 11 X^{2}
If X is the resultant of the first row, what is the resultant of the second row ?

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Rules
(i) (2digit odd number) + (2digit odd number)
(ii) 2digit even number → 2digit perfect square odd number then, (odd number)  (Even number)
(iii) (3digit number) ÷ (2digit number)
(iv) (Prime number) + (Even number)
(v) (Even number) x (Even number)Correct Option: A
Rules
(i) (2digit odd number) + (2digit odd number)
(ii) 2digit even number → 2digit perfect square odd number then, (odd number)  (Even number)
(iii) (3digit number) ÷ (2digit 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 X^{2} ⇒ 132 11 16
⇒ 132 ÷ 11 = 12 [rule (iii)]
⇒ 12 x 16 = 192 [rule (v)]
∴ Resultant of second row = 192