Reasoning-Number Series

Complete the following series

  1. 225,224,____,222,221
    a)220         b)223         c)219           d)226
Answer: b)

     2. 17,19,23,29,31,37,______
    a)41               b)43         c)40           d)42   

Answer: If you look at the above series they are all prime numbers, next series will be 41 

     3.225,196,169,____,121,100,81
    a)156              b)144         c)136           d)125

Answer: above series can be written as 15^2,14^2,13^2,____,11^2,10^2,9^2. The missing series is 12^2=144.

    4.12,14,15,16,18,20
    a)22              b)25         c)21           d)23

Answer: consider above series into two alternate parts. Like 12,15,18,____ & 14,16,20. Then the difference of two alternate series as follows: 3,3,3___ & 2,4. Next series after 18 need to be added with 3= 18+3=21.

   5.64,125,216,343,__
    a)64              b)424         c)317           d)512

Answer: The above series can be written, 4^3,5^3,6^3,7^3, then the next series is 8^3=512.

 6.  97,83,73,67,59,_____
    a)53              b)49         c)47           d)51
Answer:


7.57,60,63,66,69,_____
    a)72              b)73         c)70           d)74
Answer: From the above series the difference between consecutive series is 3. Therefor the next number is 72.

8.54,66,82,102,126,_____
    a)146              b)130         c)154           d)144
Answer: the difference of the above series is 12,16,20,24. so it is increasing in a trend of value 4. Next difference 28. next series is 154.


9.56.93,124,_____,176,195,212
    a)147              b)153         c)161           d)168
Answer: 


10.7,11,20,36,61,___,146
    a)25              b)91         c)97           d)92
Answer: The difference of the above series is 4,9,16,25,__, which can also be written as 2^2,3^2,4^2,5^2___.then the next difference would be 6^2=36. The next series is 61+36=97.

11.75,291,416,480,507,
    a)515              b)532         c)511           d)521
Answer: The difference of the above series is 216,125,64,27. Which can also be written as 6^3,5^3,4^3,3^3. Then the next difference is 2^3 i.e, 8. 507+8=515.


12.1027,1031,1037,1045,1054,___
    a)1065              b)1058         c)1064           d)1057
Answer: the difference of the above series are as follows: 4,6,8,9. The difference clearly states that these are non prime number series. The next difference series is 10. 1054+10=1064.


13.8,16,48,96,288,576,_____
    a)1152              b)1728         c)1052           d)1428
Answer: The above series can be written as 8*1,8*2,16*3,48*2,96*3,288*2. The next multiplied series is 576*3=1728.


14.75075,25025,5005,715,___,5
    a)225              b)365         c)156           d)65
Answer: The above series can be written as 25025*3,5005*5,715*7. Then next series will be multiplied by 11 in order to get 715. Because multiplied numbers are prime numbers. The missing series is 65*11=715. Therefore the missing number of continuation series is 65.


15.12,6,6,9,18,45,_____
    a)135              b)1475         c)1075           d)105

Answer: 


16. 5,5,10.30,120.600
    a)4200              b)1800         c)2400           d)3600

Answer: The above series can be written as 5*1,5*2,10*3,30*4,120*5.Then the next series is 600*6=3600.


17. 125,375,377,1131,1133,__
    a)3399              b)1136         c)1135           d)1234

Answer:The above series can be written as 125*1,125*3,375+2,377*3,1131+2. Then the next series 1133*3=3399.

18. 12,21,39,75,147,______
    a)272              b)291         c)283           d)263
Answer: The above series can be written as 12,12+12-3,21+21-3,39+39-3,75+75-3. . Then the next series would be 147+147-3=291.

19. 12,35,106,317,952,_____
    a)2851              b)2855         c)1851           d)1849
Answer: The above series can be written as 12,12*3-1,35*3+1,106*3-1,317*3+1. Then the next series is 952*3-1=2855.

20. 5,13,41,85,257,_____
    a)773              b)516         c)517           d)736
Answer: The above series can be written as 5*1, 5*2+3, 13*3+2, 41*2+3, 85*3+2. Then the next number is 257*2+3=517.

21. 13,39,118,356,1071,3217,_____
    a)9656              b)6459         c)6355           d)9651
Answer: The above series can be written as 13*1, 13*3+0, 39*3+1, 118*3+2, 356*3+3, 1071*3+4. Then the next number is 3217*3+5=9656.

22. 2,4,7,35,42,462,_____
    a)5016              b)470         c)4712           d)475
Answer: The above series can be written as 2*2=4+3=7*5=35+7=42*11=462 Then the next number is 462+13=475.

23. 440,360,288,224,____
    a)170              b)169         c)168           d)171
Answer: The above series can be written as 21^2-1, 19^2-1, 17^2-1, 15^2-1. Then the next number is 13^2-1=168.


24. 132,182,306,380,552,870,____
    a)930              b)1010         c)992           d)1142
Answer: The above series can be written as 11*12,13*14,17*18,19*20,23*24,29*30. Then the next prime number is 31. 31*32=992.

25. 2,10,30,68,130,_____
    a)216              b)222         c)250           d)210
Answer:   The above series can be written as 1^3+1,2^3+2,3^3+3,4^3+4,5^3+5.Then the next term is 6^3+6=222.

26. 95,126.5,138,175.5,189,232.5,____
    a)256              b)272         c)247.5           d)248
Answer:  The difference from the series 138-95=43,189-138=51, 175.5-126.5=49,232.5-175.5=57. The common differences among the alternate difference is 8. Then the next term is as follows. 51+8=59.  189+59=248.

27. 6,24,60,120,210,_____
    a)336              b)343         c)368           d)322
Answer:  The above series can be written as 1*2*3,2*3*4,3*4*5,4*5*6,5*6*7. Then the next series is 6*7*8=336.


28. 150,392,810,1452,2366
    a)3375              b)3600         c)2800           d)3000
Answer: The above series can be written as 5^2+5^3,7^2+7^3,9^+9^3,11^2+11^3,13^2+13^3. Then the next term is 15^2+15^3=3600.

29. 29,29,27,23,25,19,23,17,____,_____
    a)19,13              b)19,15         c)21,13           d)19,13
Answer: Divide the above series into alternate series as follows; 29,27,25,23 & 29,23,19,17. The difference of first series is 2. But the difference of second series is 6,4,2, 

30. 24,625,26,729,28,841,______
    a)30              b)29         c)900           d)961
Answer: Consider alternate series as 24,26,28, & 625,729,841. The difference of first alternate series is 2. next number is 30. another alternate series can be written as 25^2, 27^2, 29^2 the next would be 31^2=961.

31. 50/500,40/1200,30/1500,20/1400,_____
    a)10/1000              b)100/1900         c)10/900           d)10/800
Answer:  The above series can be written as 1/10, 1/30, 1/50, 1/70. Then the next term is 1/90=10/900.


32. 5,12,13,7,14,17,9,16,19,11,18,23,____,_____,______
    a)25,27,25             b)20,25,27         c)17,23,29           d)13,20,29
Answer: from the above series pick 1st number of 3 set of numbers. i.e,. 5,7,9,11. Then the next term is 13.
 Second number series are 12,14,16,18, are all even numbers next term is 20.
The numbered series are 13,17,19,23, are all prime numbers next term is 29.
Then the final combined series is 13,20,29. 

33. 6+√216, 7+√343,8+√512,9+√729
    a)10+√100            b)10+√1000        c)100+√1000          d)100+√10
Answer:  The above series can be written as 6+√6^3,7+√7^3,8+√8^3,9+√9^3. Then the next term is 10+√10^3=10+√1000

34. (14,272),(17,182),____(23,56),(26,20)
    a)(19,10)             b)(20,150)         c)(20,110)           d)(21,462)
Answer: 

35. 1,8,27,16.125,36,343,64,___,_____
    a)729,1000             b)81,1000         c)729,100           d)81,100
Answer: The above series need to be divided into alternates as 1,27,125,343,... & 8,16,36,64....

1,27,125,343=1^3,3^3,5^3,7^3. Then the next series is 9^3=729. since this series is cube of odd numbers.

8,16,36,64=2^2*2, 2^2*2^2, 2^2*3^2, 2^2*4^2. Then the next series will succession of next numbers i.e., 2^2*5^2=100
729,100.


36. 10,200,3000,40000,___
    a)500000             b)400000         c)50000           d)6000000
Answer: The above series can be written as 10*1, 100*2, 1000*3, 10,000*4. The next series is 100,000*5=500,000.

37. 7,66,555,____,33333,222222
    a)444             b)44444         c)444444           d)4444
Answer: The above series can be written as 7*1, 11*6, 111*5,____,11111*3, 111111*2. Then the missing series is 1111*4=4444.

38. 5/7,11/13,17/19,23/29,____
    a)31/33         b)31/35         c)31/37           d)33/37
Answer: The above series it is clear that, series is prime number. Every denominator in the series are followed by immediate prime number. Then the next series is written as 31/37.

39. 11,28,327,464,____
    a)525             b)5625         c)5125           d)5250
Answer: 

40. 3731,2923,1917,1311,_____
    a)117          b)119         c)917           d)75
Answer: 



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