**Directions: (1-5) What will come in place of the question mark (?) In each of the following number series?**

1. 2 8 26 ? 242

(a) 78

(b) 72

(c) 80

(d) 84

### Show Answer

Answer : (c) 80

**Explanation :**

(c) The pattern is :

2 * 3 + 2 = 6 + 2 = 8

8 * 3 + 2 = 24 + 2 = 26

26 * 3 + 2 = 78 + 2 = 80

80 * 3 + 2 = 240 + 2 = 242

2. 3 4 12 ? 196

(a) 45

(b) 40

(c) 41

(d) 49

### Show Answer

Answer : (a) 45

**Explanation :**

(a) The pattern is :

3 * 1 + 1^2 = 3 + 1 = 4

4 * 2 + 2^2 = 8 + 4 = 12

12 * 3 + 3^2 = 36 + 9 = 45

3. 9 17 ? 65 129

(a) 32

(b) 24

(c) 35

(d) 33

### Show Answer

Answer : (d) 33

**Explanation :**

(d) The pattern is :

9 * 2 – 1 = 18 – 1 = 17

17 * 2 – 1 = 34 – 1 = 33

33 * 2 – 1 = 66 – 1 = 65

65 * 2 – 1 = 130 – 1 = 129

4. 7 13 ? 49 97

(a) 27

(b) 25

(c) 23

(d) 29

### Show Answer

Answer : (b) 25

**Explanation :**

(b) 7 * 2 – 1 = 14 – 1 = 13

13 * 2 – 1 = 26 – 1 = 25

25 * 2 – 1 = 50 – 1 = 49

49 * 2 – 1 = 98 – 1 = 97

5. 5 3 6 ? 64.75

(a) 15

(b) 15.5

(c) 17.5

(d) 17.25

### Show Answer

Answer : (c) 17.5

**Explanation :**

(c) The pattern is:

5 / 0.5 + 0.5 = 2.5 + 0.5 = 3

3 * 1.5 + 1.5 = 4.5 + 1.5 = 6

6 * 2.5 + 2.5 = 15 + 2.5 = 17.5

17.5 * 3.5 + 3.5 = 61.25 + 3.5 = 64.75

6.Out of 5 women and 4 men a committee of three members is to be formed in such a way that at least one member is a woman. In how many different ways can it be done?

(a) 80

(b) 84

(c) 48

(d) 72

### Show Answer

Answer : (a) 80

**Explanation :**

(1) The committee will be formed as follows:

(i) I woman and 2 men

(ii) 2 women and 1 man

(iii) 3 women

Therefore Required number of committees

= ^5^C1 * ^4^C2 + ^5^C2 * ^4^C1 + ^5C3

= 5 * 4 * 3 / 1 * 2 + 5 * 4 / 1 * 2 * 4 + 5 * 4 * 3 / 1 * 2 * 3

= 30 + 40 + 10 = 80

7. In how many different ways can the letters of the word TOTAL be arranged?

(a) 120

(b) 60

(c) 48

(d) 72

### Show Answer

Answer : (b) 60

**Explanation :**

(b) The word TOTAL has 5 letters in which T comes twice.

Therefore number of arrangements

= 51 / 21 = 5 * 4 * 3 * 2 * 1 / 2 * 1 = 60

8. B and C together can complete a work in 8 days. A and B together can complete the same work in 16 days. In how many days can A, B and C together complete the same work?

(a) 3 9 / 13

(b) 7 5 / 13

(c) 7 5 / 12

(d) 3 5 / 12

### Show Answer

Answer : (b) 7 5 / 13

**Explanation :**

(b) (B + C)’s 1 day’s work = 1 / 8 —————-(1)

(A + B)’s 1 day’s work

= 1 / 12 —————-(ii)

(A + C)’s 1 day’s work

= 1 / 16 —————(iii)

On adding all these three equations,

2(A + B + C)’s 1 day’s work

= 1 / 8 + 1 / 12 + 1 / 16 = 6 + 4 + 3 / 48 = 13 / 48

=> (A + B + C)’s 1 day’s work

= 13 / 96

Therefore A, B and C together can complete the work in 96 / 13 = 7 5 / 13 days

9. What will be the compound interest acccured on an amount of Rs. 10, 000 at the rate of 20 p.c.p.a in two years if the interest is compounded half yearly?

(a) Rs. 4, 400

(b) Rs. 4, 600

(c) Rs. 4, 641

(d) Rs. 4, 680

### Show Answer

Answer : (c) Rs. 4, 641

**Explanation :**

(c) Interest is compounded half yearly.

Therefore R = 20% p.a = 10% half year

T = 2years = 4 half years

Therefore C.I. = P[(1 + R / 100)^T-1]

= 10000[(1 + 10 / 100)^4 – 1]

= 10000[(11 / 10)^4 – 1]

= 10000[(121 / 100 + 1)(121 / 100 – 1)]

= = 10000[(121 / 100 + 1)(121 / 100 – 1)]

= = 10000 * 221 / 100 * 21 / 100

= Rs. 4641

10. Income of A is 150% of the income of B and income of C is 120% of the income of A. If the total income of A, B and C together is Rs. 86, 000, what is C’s in come?

(a) Rs. 30, 000

(b) Rs. 32, 000

(c) Rs. 20, 000

(d) Rs. 36, 000

### Show Answer

Answer : (d) Rs. 36, 000

**Explanation :**

(d) Let B’s income = Rs. x

Therefore A’s income = 150 / 100 * x = Rs. 3x / 2

C’s income = 120 / 100 * 3x / 2

= Rs. 9x / 5

Therefore x + 3x / 2 + 9x / 5 = 86000

=> 10x + 15x + 18x / 10 = 86000

=> 43x = 860000

=> x = 860000 / 43 = 20000

Therefore C’s income

= Rs. (9 / 5 * 20000) = Rs. 36000