Mathematical operation and symbol notation

Mathematical operation and symbol notation

1. Which of the following interchange of sing or numbers would make the given equation correct ?
(18 ÷ 9) + 3 x 5 = 45
1. x ÷
2. + ÷
3. 18 and 5
4. 3 and 9

1. Apply all option one by one.

Correct Option: B

∵ (18 ÷ 9) + 3 x 5 = 45
⇒ (18 + 9) ÷ 3 x 5 = 45 ⇒ 27 ÷ 3 x 5 = 45

1. Which of the following interchange of sing or numbers would make the given equation correct ?
5 + 6 ÷ 3 - 12 x 2 = 17
1. ÷ and x
2. + and x
3. + and ÷
4. + and -

1. Apply all option one by one.

Correct Option: A

Apply all option one by one.
∵ 5 + 6 x 3 - 12 ÷ 2 = 17
⇒ 5 + 18 - 6 = 17 ⇒ 23 - 6 = 17

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 added.
(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 add number is followed by an even number, the second one is to be subtracted from the first number.

1. 15   8   21
p     3    27
If 'p' is the resultant of the first row, what will be the resultant of the second row ?
1. 58
2. 76
3. 27
4. 82
5. None of these

1. Rules
(i) (odd number) + (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)
1st Row   15   8   21 ⇒ 15 - 8 = 7     [rule (v)]
⇒       7 + 21 = 28     [rule (i)]

Correct Option: A

Rules
(i) (odd number) + (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)
1st Row   15   8   21 ⇒ 15 - 8 = 7     [rule (v)]
⇒       7 + 21 = 28     [rule (i)]
2nd Row   p   3   27 ⇒ 28   3   27
⇒ 28 + 3 = 31     [rule (ii)]
⇒ 31 + 27 = 58     [rule (i)]
∴ Resultant of second row = 58

1. 12   64   17
20   m    16
If 'm' is the resultant of the first row, what will be the resultant of the second row ?
1. 69
2. 85
3. 101
4. 121
5. None of these

1. Rules
(i) (odd number) + (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)
1st Row 12   64   17 ⇒ 64 - 12 = 52

Correct Option: E

Rules
(i) (odd number) + (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)
1st Row 12   64   17 ⇒ 64 - 12 = 52       [rule (iii)]
⇒     52 + 17 = 69     [rule (ii)]
= m
2nd Row 20   m   16 ⇒ 20   69   16
⇒         20 + 69 = 89   [rule (ii)]
⇒       89 - 16 = 73     [rule (v)]
∴ Resultant of second row = 73

1. 85   17   35
16   19     r
If 'r' is the resultant of the first row, what will be the resultant of the second row ?
1. 175
2. -5
3. 75
4. 210
5. None of these

1. Rules
(i) (odd number) + (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 85   17   35 ⇒ 85 ÷ 17 = 5

Correct Option: B

Rules
(i) (odd number) + (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 85   17   35 ⇒ 85 ÷ 17 = 5       [rule (iv)]
⇒     5 + 35 = 40     [rule (i)]
= r
2nd Row 16   19   r ⇒ 16   19   40
⇒         16 + 19 = 35   [rule (ii)]
⇒       35 - 40 = -5     [rule (v)]
∴ Resultant of second row = -5