Number Series Prime Number Series: Example 1. 4, 9, 25, 49, 121, 169,… (a) 324 (b) 289 (c) 225 (d) 196 Solution. (b) The given series is a consecutive square of prime number series. The next prime number is 289. Example 2. 5, 7, 13, 23, … (a) 25 (b) 27 (c) 29 (d) 41 Solution. (d) The difference between prime numbers is increasing. 7 is next prime to 5; 13 is second to next prime to 7; 23 is third to next to 13. Hence, next should be fourth to next prime to 23. Hence, required number is 41. Multiplication Series: Example 3. 4, 8, 16, 32, 64… 256 (a) 96 (b) 98 (c) 86 (d) 106 Solution. (a) The numbers are multiplied by 2 to get the next number. 64 × 2 = 128 Example 4. 5, 20, 80, 320, … 1280 (a) 5120 (b) 5220 (c) 4860 (d) 3642 Solution. (a) The numbers are multiplied by 4 to get the next number. 1280 × 4 = 5120 Difference Series: Example 5. 3,6,9,12,15,…. 21 (a) 16 (b) 17 (c) 20 (d) 18 Solution. (d) The difference between the numbers is 3. 15 + 3 = 18 Example 6. 55, 50, 45, 40,….30 (a) 33 (b) 34 (c) 35 (d) 36 Solution. (c) The difference between the numbers is -5. 40 – 5 = 35 Division Series: Example 7. 5040, 720, 120, 24, ….2,1 (a) 8 (b) 7 (c) 6 (d) 5 Solution. (c) Example 8. 16, 24, 36,… 81 (a) 52 (b) 54 (c) 56 (d) 58 Solution. (b) Previous number × = Next number n2 Series Example 9. 4, 16, 36, 64, …. 144 (a) 112 (b) 78 (c) 100 (d) 81 Solution. (c) The series is square of consecutive even numbers. 22, 42,62, 82 Next number is 102 = 100 Example 10. 1, 4, 9, 16, 25, 36, 49, … 81 (a) 100 (b) 121 (c) 64 (d) 144 Solution. (c) The series is 12, 22, 32, 42, 52,62, 72,…. The next number is 82 = 64 (n2 + 1) Series Example 11. 17, 26, 37, 50, 65,….101 (a) 82 (b) 75 (c) 78 (d) 90 Solution. (a) The series is 42 + 1, 52 +1, 62 + 1, 72 + 1, 82 + 1. The next number is 92 + 1 = 82 Example 12. 101, 401, 901, 1601, 2501, …. 4901 (a) 2201 (b) 3301 (c) 4401 (d) 3601 Solution. (d) The series is 102 + 1, 202 +1, 302 + 1, 402 + 1, 502 + 1, etc. The next number is 602 + 1 = 3601 (n2 -1) Series Example 13. 3, 8, 15, 24,…48 (a) 32 (b) 33 (c) 34 (d) 35 Solution. (d) The series is 22 – 1, 32 –1, 42 – 1,52 – 1. etc. The next number is 62 – 1 =35 Example 14. 99, 80, 63,….35 (a) 48 (b) 84 (c) 46 (d) 64 Solution. (a) The series is 102 -1, 92 -1, 82 -1, etc. The next number is 72 – 1 = 48 (n2 + n) Series Example 15. 2, 6, 12, 20, 30,…. 56 (a) 32 (b) 34 (c) 42 (d) 24 Solution. (c) The series is 12 + 1, 22 + 2, 32 + 3, 42 + 4, 52 + 5, etc. The next number is 62 + 6 = 42 Example 16. 110, 132, 156, 182,…. (a) 212 (b) 201 (c) 211 (d) 210 Solution. (d) The series is 102 + 10, 112 + 11, 122 + 12, etc. The next number is 142 + 14 = 210 (n2 – n) Series Example 17. 0, 2, 6, 12, 20,….42 (a) 25 (b) 30 (c) 32 (d) 40 Solution. (b) The series is 12 – 1 = 0, 22 – 2 = 2, 32 – 3 = 6, etc. The next number is 62 – 6 = 30 Example 18. 90, 380, 870, 1560,….. (a) 2405 (b) 2450 (a) 2400 (d) 2455 Solution. (b) The series is 102 – 10, 202 – 20, 302 – 30, etc. The next number is 502 – 50 = 2450 n3 Series Example 19. 1, 8, 27, 64,…. 216 (a) 125 (b) 512 (c) 215 (d) 122 Solution. (a) The series is 13, 23, 33 , 43, etc. The next number is 53 = 125 Example 20. 1000, 8000, 27000, 64000,…. (a) 21600 (b) 125000 (c) 152000 (d) 261000 Solution. (b) The series is 103 , 203, 303, 403, etc. The next number is 503 = 125000 (n3 + 1) Series Example 21. 2, 9, 28, 65,…217 (a) 123 (b) 124 (c) 125 (d) 126 Solution. (d) The series is 13 +1, 23 + 1, 33 + 1, etc. The next number is 53 + 1 = 126 Example 22. 1001, 8001, 27001, 64001, 125001,…. (a) 261001 (b) 216001 (c) 200116 (d) 210016 Solution. (b) The series is 103 + 1, 203 + 1, 303 + 1, etc. The next number is 603 + 1 = 216001 (n3 -1) Series Example 23. 0, 7, 26, 63, 124,… (a) 251 (b) 125 (c) 215 (d) 512 Solution. (c) The series is 13 – 1, 23 – 1, 33 – 1, etc. The next number is 63 – 1 = 215 Example 24. 999, 7999, 26999, 63999,…. (a) 199924 (b) 124999 (c) 129994 (d) 999124 Solution. (b) The series is 103 – 1, 203 – 1, 303 – 1, etc. The next number is 503 – 1 = 124999 (n3 + n) Series Example 25. 2, 10, 30, 68,….222 (a) 130 (b) 120 (c) 110 (d) 100 Solution. (a) The series is 13 + 1, 23 + 2, 33 + 3, etc. The next number is 53 + 5 = 130 Example 26. 1010, 8020, 27030, 64040,…. (a) 125500 (b) 125050 (c) 100255 (d) 120055 Solution. (b) The series is 103 + 10 = 1010, 203 + 20 = 8020, etc. The next number is 503 + 50 = 125050 (n3 – n) Series Example 27. 0, 6, 24, 60,…. 210 (a) 012 (b) 210 (c) 201 (d) 120 Solution. (d) The series is 13 – 1 = 0, 23 – 2 = 6, 33 – 3 = 24, etc. The next number is 53 – 5 = 120 Example 28. 990, 7980, 26970, 63960,…. (a) 124500 (b) 124005 (c) 120045 (d) 124950 Solution. (d) The series is 103 – 10, 203 – 20, 303 – 30 etc. The next number is 503 – 50 = 124950 Letter Series - Type 1 One Letter Series Such series consists of one letter in each term and this series is based on increasing or decreasing positions of corresponding letters according to English alphabet. Example 1: B, C, A, D, Z, E, … F, X, G (a) U (b) Y (c) W (d) V Solution. (b) The sequence consists of two series B, A, Z, Y, X and C, D, E, F, G. The missing letter is Y. Example 2: P, U, Z, … J, 0, T (a) E (b) U (c) S (d) P Solution. (a) The sequence is P+ 5, U+ 5,Z+ 5. The missing letter is Z + 5 = E Example 3: B, D, G, I, … N, Q, S (a) I (b) J (c) L (d) K Solution. (c) The sequence is B + 2, D+ 3, G + 2, I + 3 and so on. Letter Series - Type 12 Two Letter Series The first letters of the series follow one logic and the second letters follow another logic. Example 4: EZ, DX, CV,..., AR, ZP (a) CS (b) AM (c) BT (d) TG Solution. (c) First and second letters follow a sequence of-1 and -2 respectively. Example 5: DG, HK, LO, PS, TW,… (a) XA (b) ZA (c) XB (d) None of these Solution. (a) First and second letters follow a sequence of + 4. Example 6: DX, EY FV, ... : ; HT, IU (a) HV (b) IX (c) GW (d) BZ Solution. (c) First, -third and fifth terms follow a sequencee and second, fourth and sixth terms follow another sequence. (DX, FV, HT, etc) and (EY, GW, IU, etc). Letter Series - Type 3 Three Letter Series: :Such series consist of three letters in each term. The first letters follow one logic, the second letters follow another logic and the third letters follow some other logic. Example 7: DIE, XCY, RWS, ... (a) LQN (b) QMP (c) LMS (d) LQM Solution. (d) First, second and third letters of each group follow a sequence of -6 series. Example 8: VPG, UQF, ..., SSD, RTC (a) SQD (b) TRE (c) TRS (d) QDT Solution. (b) First, second and third letters follow a sequence of –1, + 1, –1 series respectively. Example 9: DJS, HNW, LRA, PVE, ..., XDM (a) TZI (b) SAF (c) UXH (d) None of these Solution. (a) First, second and third letters follow a sequence of + 4 series. Letter Series - Type 4 A series of letters is given with one or more missing letters. From the choices, the choice that gives the letters that go into the blanks has to be selected as answer. Example 10: In the following series some letters are missing. From the choices, select the choice that gives that letters that can fill the blanks in the given sequence. a_ c_ b_ab_a_ca_c (a) abaccb (b) accbab (c) aabbcc (d) baccbb Solution. (d) First of all, notice that there are 6 blanks in the given sequence and each choice gives six letters to fill the six blank in order. Now, we have to select an alternative which if placed in the blanks of the series in order, we get a complete series of letters which follow some particular pattern. The best way is to try with each option. Inserting the letters of option (d) in place of the blanks, we get a series like “abc abc abc abc abc” which is a repetition of the group of letters “abc”. Letter Series - Type 5
Posted on: Sun, 31 Aug 2014 06:16:27 +0000
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