**Directions (1-10): In the following number series only one number is wrong. Find out the wrong number.**

1. 9050, 5675, 3478, 2147, 1418, 1077, 950

(a) 3478

(b) 1418

(c) 5675

(d) 2147

(e) 1077

2. 71, 90, 128, 185, 261, 365

(a) 365

(b) 128

(c) 185

(d) 90

(e) 261

3. 484 240 120 57 26.5 11.25 3.625

(a) 240

(b) 120

(c) 57

(d) 26.5

(e) 11.25

4. 3 5 13 43 176 891 5353

(a) 5

(b) 13

(c) 43

(d) 176

(e) 891

5. 12 25 52 55 57 115 117

(a) 55

(b) 117

(c) 25

(d) 52

(e) None of these

**Directions (6-10): The following pie chart shows the percentage distribution of marks obtained by Shalini and Bikas in Mains exams of UPSC constituting of seven papers of equal maximum marks. It is known that Bikas obtained 50 marks more in GS I paper than GS III paper.**

Study the chart carefully to answer the questions asked below.

6. Find the difference in the marks obtained by Bikas in GS I and GS III papers together and that by Shalini in Optional I and Essay papers together.

(a) 25

(b) 20

(c) 35

(d) 22

(e) None of these

7. By what percent the total marks obtained by Shalini in Essay is more or less than that by Bikas in GS I? (Approximately)

8. Find the overall approximate percentage of marks scored by Shalini.

(a) 51%

(b) 54%

(c) 57%

(d) 59%

(e) 62%

9. In Optional I paper Shalini was unable to clear the cutoff by only 5 marks. Find by what percent the cutoff marks in Optional I paper is less than marks obtained by Bikas in GS II paper. (rounded up to 1 decimal place)

(a) 18.5%

(b) 17.2%

(c) 15.8%

(d) 20.4%

(e) 19.4%

10. Find the ratio of marks obtained by Bikas in Essay, GS II and Optional II together and that by Shalini in GS III, GS I and Optional I together?

(a) 89 : 80

(b) 80 : 89

(c) 87 : 80

(d) 89 : 79

(e) None of these

Answers

1- Ans.(e)

Sol.

The pattern of number series is as follows:

9050 - 〖15〗^3 = 9050 – 3375 = 5675

5675 - 〖13〗^3= 5675 – 2197 = 3478

3478 - 〖11〗^3= 3478 – 1331 = 2147

2147 - 9^3= 2147 – 729 = 1418

1418 - 7^3= 1418 – 343 = 1075 ≠ 1077

2-Ans.(a)

Sol.

The series is 71 +19 = 90

90 + 38 = 128, 128 + 57 = 185

185 + 76 = 261, 261 + 95 = 356

Hence there should be 356 in place of 365

3-Ans.(b)

Sol.

The series is :

÷2-2,÷2-2.......

So, 240 ÷ 2 - 2 = 118 ≠ 120

4-Ans.(d)

Sol.

Series is : ×1+2,×2+3,×3+4…………….

So, 43 × 4 + 5 = 177

∴ 176 should be replaced by 177.

5-Ans.(d)

Sol.

The series is ×2 + 1, × 1 + 2 alternately

6-Ans.(b)

Sol.

Marks obtained by Bikas = (70 + 50) % of 250 = 300

Marks obtained by Shalini = (64 + 48) % of 250 = 280

∴ Required difference = 20

7-

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