Explanation With Answers Key:
1). C)The series is -4, -10, -28, -82, -244,
476 – (31 + 1) = 472, 472 – (32 + 1) = 462, 462 – (33+ 1) = 434, 434 – (34 + 1) = 352, 352 – (35 + 1) = 108, …
2). E)The series is ÷25, ÷20, ÷15, ÷10, ÷5, •••
ie 45000 ÷ 25 = 1800, 1800 ÷ 20 = 90, 90 ÷ 15 = 6, 6 ÷ 10 = 0.6, 0.6 ÷ 5 = 0.12,
3). A)The series is x1 – 1, x2 – 2, x3 – 3, x4 – 4, x5 – 5, …
ie 9 x 1 – 1 = 8, 8 x 2 – 2 = 14, 14 x 3 – 3 =39, 39 x 4 – 4 = 152, 152 x 5 – 5 = 755, …
4). B) The series is ÷2 + 12, ÷2 + 10, ÷2 + 8, ÷2+6, …
192 ÷ 2 +12 = 108, 108 ÷ 2 + 10 = 64, 64 ÷ 2 + 8 = 40, 40 ÷ 2 + 6 = 26, 26 ÷ 2 + 4 = 17, …
5). D)The series is x0.5 — 1, x1 — 1, x1.5 — 1, x2 — 1, x2.5 — 1, …
ie 18 x 0.5 — 1 = 8, 8 x 1 — 1 = 7, 7 x 1.5 — 1 = 9.5, 9.5 x 2 — 1 = 18, 18 x 2.5 — 1 = 44, …
6). B) Reqd ratio
= Kathakali (A + D) males / Kathakali (A + D) females
= [450 × (30/100) × (7/15)] + [400 × (18/100) × (5/12)] / [450 × (30/100) × (8/15)] + [400 × (18/100) × (7/12)]
= (63+30)/(72+42) = 93/114 = 31/38 = 31 : 38
7). E)Total number of students who are learning Kathakali in School B 200 x (38/100) = 76
Number of male students who are learning Kathakali = 76 x (9/19) = 36 19
Number of female students who are learning Kathakali = 76 x (10/19) = 40
Both males and females below 15 years = 76 × (1/19) = 4
Number of females below 15 years = 4 × (50/100) = 2
Number of female students learning kathakali who are 15 years or above = 40 – 2 = 38
8). B)Total number of male students learning kathakali in school B and C together
= 200 × (38/100) × (9/19) + 500 × (24/100) × (5/24)
= 36 + 25 = 61
Total number of female students learning Kathakali in school B and C together
= 200 × (38/100) × (10/19) + 500 × (24/100) × (19/24)
= 40 + 95 = 135
Reqd difference = 135 — 61 = 74
9). E) Reqd average
={ 450 × (70/100) + 200 × (62/100) + (500 × 76) /100} / 3
= (315+124+380) / 3 = 819/3 = 273
10). B)The number of students (both male and female) who are learning Kathakali in School B and D together
= 200 x (38/100) + 400 × (18/100) = 76 + 72 = 148
The number of students (both males and females) who are learning Kathakali in School A and C together
= 450 × (30/100) + (500 × 24)/100 = 135 + 120 = 255
Difference = 255 -148 = 107
Reqd %=(107/255) × 100 = 42