**Directions(1-2): In each of the following questions a number series is given. Below the series, a number along with (1), (2), (3) (4) and (5) is given. You have to complete the series following the same sequence as that of the given series. Then answer the question that follows.**

**Q1. 5 , 7, 10, 36, 136, 690**

**2 ,(1), (2) , (3), (4), (5)**

**What will come in place of (3)?**

(a) 26

(b) 64

(c) 18

(d) 46

**Ans.(c)**

**Sol. The series is based on the following pattern:**

**5 × 1 + 2 = 7**

**7 × 2 – 4 = 10**

**10 × 3 + 6 = 36**

**36 × 4 – 8 = 136**

**136 × 5 + 10 = 690**

**Similarly, the new series is as follows:**

**2 × 1 + 2 = 4 .... (1)**

**4 × 2 – 4 = 4 .... (2)**

**4 × 3 + 6 = 18 .... (3)**

**Therefore, the number 18 will come in place of (3).**

**Q2. 8, 4, 6, 15, 52.5, 236.25**

**4, (1), (2), (3), (4), (5)**

**What will come in place of (4)?**

(a) 36.25

(b) 26.25

(c) 16.25

(d) 32.75

**Ans.(b)**

**Sol. The series is based on following pattern:**

**8 × 0.5 = 4,**

**4 × 1.5 = 6,**

**6 × 2.5 = 15,**

**15 × 3.5 = 52.6,**

**52.5 × 4.5 = 236.25**

**Similarly,**

**4 × 0.5 = 2 .... (1)**

**2 × 1.5 = 3 .... (2)**

**3 × 2.5 = 7.5 .... (3)**

**7.5 × 3.5 = 26.25 . ...(4)**

**Therefore, the number 26.25 will come in place of (4).**

**Directions(3-5): In each of the following questions a number is missing. Find this missing number from the following alternatives.**

**Q3. 512, 49, 216, 25, ?**

(a) 8

(b) 27

(c) 64

(d) 36

**Ans.(c)**

**Sol.**

**512, 49, 216, 25, 64**

**(8**

^{3}), (7^{2}), (6^{3}), (5^{2}), (4^{3})

**Q4. 15, 24, 43, 71, (?), 154**

(a) 114

(b) 108

(c) 100

(d) 140

**Ans.(b)**

**Sol. The pattern of the number series is as given below:**

**15 + 9 = 24**

**24 + 19 (= 10 + 9) = 43**

**43 + 28 (= 19 + 9) = 71**

**71 + 37 (= 28 + 9) = 108**

**108 + 46 (= 37 + 9) = 154**

**Q5. 3, 7, 16, 32, ?, 93**

(a) 53

(b) 57

(c) 54

(d) 60

**Ans.(b)**

**Sol.**

**= 32 + 5**

^{2}

**= 32 + 25**

**= 57**

**Directions(6-10): In these questions, which of the following number complete the given sequence?**

**Q6. 8, 24, 12, 36, 18, 54, (....)**

(a) 27

(b) 108

(c) 68

(d) 72

**Ans. (a)**

**Sol. Numbers are alternatively multiplied by 3 and divided by 2.**

**So, the next number = 54 ÷ 2 = 27.**

**Q7. 2, 6, 12, 20, 30, 42, 56, (....)**

(a) 61

(b) 64

(c) 72

(d) 70

**Ans.(c)**

**Sol. The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8.**

**So, the next number is 8 x 9 = 72.**

**Q8. 4, -8, 16, -32, 64, (....)**

(a) 128

(b) -128

(c) 192

(d) -192

**Ans.(b)**

**Sol. Each number is the proceeding number multiplied by -2.**

**So, the required number is -128.**

**Q9. 122 , 170 , 290 , ?**

(a) 369

(b) 255

(c) 432

(d) 362

**Ans.(d)**

**Sol. (11)**

^{2}= 121+1= 122,**(13)**

^{2}= 169+1= 170**(17)**

^{2}= 289 + 1= 290,**Similarly**

**(19)**

^{2}= 361 + 1 = 362

**Q10. 2 ,3 , 8 , 63, ?**

(a) 3900

(b) 3636

(c) 3968

(d) 3988

**Ans.(c)**

**Sol. 2**

^{2}= 4-1= 3**3**

^{2}= 9-1 = 8**8**

^{2}= 64-1= 63**63**

^{2}=3969-1 = 3968

**Direction (11-13): In each of these questions, a number series is given. In each series, only one number is wrong. Find out the wrong number from the given alternatives?**

**Q11. 32, 16, 24, 65, 210, 945, 5197.5**

(a) 16

(b) 210

(c) 65

(d)5197.5

**Ans.(c)**

**Sol.**

**So, wrong number is 65, it must be replaced by 60.**

**Q12. 6, 91, 584, 2935, 11756, 35277, 70558**

(a) 35277

(b) 584

(c) 2935

(d) 91

**Ans.(b)**

**Sol. The pattern of number series is as follows:**

**6 × 7 + 72 = 42 + 49 = 91**

**91 × 6 + 62 = 546 + 36 = 582 [584]**

**582 × 5 + 52 = 2910 + 25 = 2935**

**2935 × 4 + 42 = 11740 + 16 = 11756**

**11756 × 3 + 32 = 35268 + 9 = 35277**

**So, wrong number is 584, it must be replaced by 582.**

**Q13. 3601, 3602, 1803, 604, 154, 36, 12**

(a) 3601

(b) 154

(c) 604

(d) 1803

**Ans.(b)**

**Sol.**

**So, wrong number is 154, it must be replaced by 155.**

**Directions(14-15): What should come in place of question mark (?) in the following number series?**

**Q14. 656, 352, 200, 124, 86, (?)**

(a) 97

(b) 49

(c) 67

(d) 57

**Ans.(c)**

**Sol. The pattern of the number series is as given below:**

**Missing term is 67.**

**Q15. 4.5, 18, 2.25, ? , 1.6875, 33.75**

(a) 35

(b) 25.5

(c) 27

(d) 43

**Ans.(c)**

**Sol. The series is**

**× 4, ÷ 8, × 12, ÷ 16, × 20**

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