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QUESTION: 1

In each of the following questions, two rows of numbers are given. The resultant number of each row is to be worked out separately based on the following rules and the question below the row of numbers is to be answered. The operations of numbers progress from left to right.

Rules:

(i) If an odd number is followed by a 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 a perfect square, the even number is to be subtracted from the perfect square.

(iv) If an odd number is followed by a prime 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.

**14 196 23
10 x 152**

Q. If x is the resultant of the first row, what is the resultant of the second row?

Solution:

In the first row

14 196 23

Here 196 is a perfect square and 14 is even.

∴ According to rule (iii)

it will be (196 − 14) = 182, which is an even number.

23 is an odd number.

According to rule (ii)

182 + 23 = 205 = x, is an odd number.

In the second row

10 205 152

10 is an even number.

∴ According to rule (ii), (10 + 205) = 215 which is odd.

152 is even.

Hence, the resultant of the second row is (215 − 152) = 63.

QUESTION: 2

In each of the following questions, two rows of numbers are given. The resultant number of each row is to be worked out separately based on the following rules and the question below the row of numbers is to be answered. The operations of numbers progress from left to right.

Rules:

(i) If an odd number is followed by a 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 a perfect square, the even number is to be subtracted from the perfect square.

(iv) If an odd number is followed by a prime 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.

**65 5 9
109 24 5**

Q. What is the difference between the resultants of the two rows?

Solution:

The first row is 65 5 9.

The resultant of first two numbers = 65 ÷ 5 = 13 (odd)

Resultant of the new number and the last number

= 13 × 9 = 117

The second row

109 24 5

Resultant of the first two number = (109 − 24) = 85 (odd)

∴ Resultant of the new number and the third number

= 85 ÷ 5 = 17.

∴ The difference between the resultants.

= 117 − 17 = 100.

QUESTION: 3

In each of the following questions, two rows of numbers are given. The resultant number of each row is to be worked out separately based on the following rules and the question below the row of numbers is to be answered. The operations of numbers progress from left to right.

Rules:

(i) If an odd number is followed by a 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 a perfect square, the even number is to be subtracted from the perfect square.

(iv) If an odd number is followed by a prime 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.

79 64 21

m 7 28

Q. If m is the resultant of the first row, what is the resultant of the second row?

Solution:

In the first row,

The resultant of the first two numbers = 79 − 64 = 15

The resultant of the resultant of the first two numbers and

the last number = 15 × 21 = 315 = m

In the second row,

Resultant of the first two numbers = 315 ÷ 7 = 45.

Now the resultant of the resultant of the first two numbers

and the last number = 45 − 28 = 17.

QUESTION: 4

In each of the following questions, two rows of numbers are given. The resultant number of each row is to be worked out separately based on the following rules and the question below the row of numbers is to be answered. The operations of numbers progress from left to right.

Rules:

(i) If an odd number is followed by a 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 a perfect square, the even number is to be subtracted from the perfect square.

(iv) If an odd number is followed by a prime 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.

**143 11 8 12 36 3**

Q. What is the sum of the resultants of the two rows?

Solution:

1st row 143 11 8

The resultant of the first two numbers = 143 ÷ 11 = 13

The resultant of the resultant of first two numbers and the

last number = 13 − 8 = 5

The resultant of the first two numbers of the second row

= 36 − 12 = 24

The resultant of the resultant of first two numbers and the

last number = 24 + 3 = 27.

∴ The sum of the resultants of the two rows = 27 + 5 = 32.

QUESTION: 5

Each question contains a number series, one of the numbers is a wrong number. Find out the wrong number and form a new series starting with the wrong number and using the pattern in the given series. Answer the questions based on the new series.

7, 10, 15, 22, 33, 48

Q. What is the fifth term in the new series?

Solution:

The given series can be represented as follows.

7 + 3,10 + 5, 15 + 7, 22 + 11, 33 + 13, 46

(consecutive prime numbers are added)

∴ 48 is the wrong term in the series.

∴ The new series will be

48 + 3, 51 + 5, 56 + 7, 63 + 11, 74

∴ 74 is the fifth term in the new series.

QUESTION: 6

Each question contains a number series, one of the numbers is a wrong number. Find out the wrong number and form a new series starting with the wrong number and using the pattern in the given series. Answer the questions based on the new series.

7, 21, 66, 138, 420, 846

Q. What is the fifth term of the new series?

Solution:

The series can be represented as follows.

7 + 3 × 2, 20 + 2 × 3, 66 + 3 × 2, 138 + 2 x 3, 420 + 3 × 2,846

∴ The wrong term is 21.

∴ The new series will be

21 + 3 × 2, 48 + 2 × 3, 150 + 3 × 2, 306 + 2 × 3, 924

∴ 924 will be the fifth term in the new series.

QUESTION: 7

Each question contains a number series, one of the numbers is a wrong number. Find out the wrong number and form a new series starting with the wrong number and using the pattern in the given series. Answer the questions based on the new series.

5, 7, 12, 15, 60, 65

Q. What is the fourth term in the new series?

Solution:

The series can be represented as follows.

5 + 1, 6 × 2, 12 + 3, 15 × 4, 60 + 5, 65

∴ The wrong term is 7.

New series will be 7 + 1, 8 × 2, 16 + 3, 19

∴ 19 is the fourth term in the new series. Choice (d)

QUESTION: 8

In each of these questions a number series is given. After the series, a number is given along with (a), (b), (c), (d) and (e). You have to complete the series starting with the number given to find the values of (a), (b), (c), (d) and (e) applying the same pattern followed in the given series. Then answer the question given below each.

2, 3, 5, 7, 11, 13

13, (a), (b), (c), (d), (e)

Q. What is the value of (d) in the series?

Solution:

The given numbers are consecutive prime numbers in

increasing order starting with 2. Hence, the new series is:

13, 17, 19, 23, 29, 31

(a) (b) (c) (d) (e)

The value of (d) is 29. Choice (b)

QUESTION: 9

In each of these questions a number series is given. After the series, a number is given along with (a), (b), (c), (d) and (e). You have to complete the series starting with the number given to find the values of (a), (b), (c), (d) and (e) applying the same pattern followed in the given series. Then answer the question given below each.

7, 9, 18, 21, 63, 67, 268

(a), (b), (c), (d), 39, (e)

Q. What is the value of (b) in the series?

Solution:

The given series can be represented as

7 + 2, 9 × 2, 18 + 3, 21 × 3, 63 + 4, 67 × 4, 268,

The fifth term of the next series given, i.e., 39

∴ The series is

(a) (b) (c) (d) 39 (e)

3 + 2, 5 × 2,10 + 3, 13 × 3, 39 + 4, 43

∴ The value of (b) is 5. Choice (d)

QUESTION: 10

In each of these questions a number series is given. After the series, a number is given along with (a), (b), (c), (d) and (e). You have to complete the series starting with the number given to find the values of (a), (b), (c), (d) and (e) applying the same pattern followed in the given series. Then answer the question given below each.

1, 3, 11, 47, 239, 1439

(a), (b), (c), (d), (e), 2159

Q. What is the value of (a) in the series?

Solution:

The given series can be written as

1 × 2 + 1, 3 × 3 + 2, 11 × 4 + 3, 47 × 5 + 4, 239 × 6 + 5, 1439,

In the same way

(a) (b) (c) (d) (e)

2 x 2 + 1, 5 x 3 + 2 ,17 x 4 + 3, 71 x 5 + 4, 359 x 6 + 5, 2159

∴ The value of (a) is 2. Choice (d)

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