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 twodigit 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 threedigit number is followed by a twodigit number which is a perfect square, the second number is to be subtracted from the first number.
(v) If a threedigit number is followed by a twodigit number which is not a perfect square, the first number is to be divided by the second one.
 97 45 71
48 8 11
What is the sum of the resultants of the two rows ?

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Rules
(i) (2digit even number) ÷ ( Even number)
(ii) (Even number) x (Prime number)
(iii) (Odd number) + (Odd number)
(iv) (3digit number)  (2digit perfect square number)
(v) (3digit number) ÷ (2digit nonperfect square number)
Hint
1st Row 97 45 71 ⇒ 97 + 45 = 142 [rule (iii)]Correct Option: A
Rules
(i) (2digit even number) ÷ ( Even number)
(ii) (Even number) x (Prime number)
(iii) (Odd number) + (Odd number)
(iv) (3digit number)  (2digit perfect square number)
(v) (3digit number) ÷ (2digit nonperfect 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
 125 64 33
282 x 39
If 'x' is the resultant of the first row, what will be the resultant of the second row ?

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Rules
(i) (2digit even number) ÷ ( Even number)
(ii) (Even number) x (Prime number)
(iii) (Odd number) + (Odd number)
(iv) (3digit number)  (2digit perfect square number)
(v) (3digit number) ÷ (2digit nonperfect square number)
Hint
1st Row 125 64 33 ⇒ 125  64 = 61 [rule (iv)]Correct Option: B
Rules
(i) (2digit even number) ÷ ( Even number)
(ii) (Even number) x (Prime number)
(iii) (Odd number) + (Odd number)
(iv) (3digit number)  (2digit perfect square number)
(v) (3digit number) ÷ (2digit nonperfect 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
 24 7 81
x 27 19
If 'x' is the resultant of the first row, what will be the resultant of the second row ?

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Rules
(i) (2digit even number) ÷ ( Even number)
(ii) (Even number) x (Prime number)
(iii) (Odd number) + (Odd number)
(iv) (3digit number)  (2digit perfect square number)
(v) (3digit number) ÷ (2digit nonperfect square number)
Hint
1st Row 24 7 81 ⇒ 24 x 7 = 168 [rule (ii)]Correct Option: D
Rules
(i) (2digit even number) ÷ ( Even number)
(ii) (Even number) x (Prime number)
(iii) (Odd number) + (Odd number)
(iv) (3digit number)  (2digit perfect square number)
(v) (3digit number) ÷ (2digit nonperfect 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
 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

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√100 + √16
= √225 √1Correct Option: B
√100 + √16
= √225 √1
10 + 4 = 15  1
⇒ 14 = 14
 Which of the following interchange of signs would make the given equation correct ?
5 + 3 x 8  12 ÷ 4 = 3

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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 = 3Correct 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