Odd Numbers And Series
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ODD MAN OUT & SERIES
ODD MAN OUT & SERIES
In any type of problems, a set of numbers is given in such a way that each one except one satisfies a particular definite property. The one which does not satisfy that characteristic is to be taken out.
Some important properties of numbers are given below : 1.Prime Number Series Example: 2,3,5,7,11,.................
2.Even Number Series Example: 2,4,6,8,10,12,............
3.Odd Number Series: Example: 1,3,5,7,9,11,...................
4.Perfect Squares: Example: 1,4,9,16,25,..............
5.Perfect Cubes: Example: 1,8,27,64,125,.................
6.Multiples of Number Series: Example: 3,6,9,12,15,..............are multiples of 3
7.Numbers in Arithmetic Progression(A.P): Example: 13,11,9,7................
8.Numbers in G.P: Example: 48,12,3,..... SOME MORE PROPERTIES: 1. If any series starts with 0,3,.....,generally the relation will be (n2-1). 2. If any series starts with 0,2,.....,generally the relation will be (n2-n). 3. If any series starts with 0,6,.....,generally the relation will be (n3-n). 4. If 36 is found in the series then the series will be in n2 relation. 5. If 35 is found in the series then the series will be in n2-1 relation. 6. If 37 is found in the series then the series will be in n2+1 relation. 7. If 125 is found in the series then the series will be in n3 relation. 8. If 124 is found in the series then the series will be in n3-1 relation. 9. If 126 is found in the series then the series will be in n3+1 relation. 10. If 20,30 found in the series then the series will be in n2-n relation. 11. If 60,120,210,........... is found as series then the series will be in n3-n relation. 12. If 222,............ is found then relation is n3+n 13. If 21,31,.......... is series then the relation is n2-n+1. 14. If 19,29,.......... is series then the relation is n2-n-1. 15. If series starts with 0,3,............ the series will be on n2-1 relation.
EXAMPLE PROBLEMS: 13.Find the odd one out. 2,5,10,50,500,5000 SOLUTION: In the above series, the pattern as follows: 1st term * 2nd term = 3rd term 2nd term * 3rd term = 4th term 3rd term * 4th term = 5th term But 50*500=25000 which is not equal to 5000. so 5000 is odd one.
14.Find the odd one out. 582,605,588,611,634,617,600 SOLUTION: In the above series, alternatively 23 is added and 17 is subtracted from the terms. So 634 is odd one. 15.Find the odd one out. 46080,3840,384,48,24,2,1 SOLUTION: In the above series,the terms are successively divided by 12,10,8,6,..... so 24 is not in this pattern. so 24 is odd one. 16.Find the odd one out. 5,16,6,16,7,16,9 SOLUTION: In the above series, the terms at odd places are 5,6,7,8.......and at even places is 16. So 9 is odd one.
17.Find the odd one out. 6,13,18,25,30,37,40 SOLUTION: In the above series, the difference between two successive terms from the beginning are 7,5,7,5......... so 40 is odd one. 18.Find the odd one out. 56,72,90,110,132,150 SOLUTION: The above series as follows: 7*8,8*9,9*10,10*11,11*12,12*13. So it will be 56,72,90,110,132,156 so 150 is wrong. 19.Find the odd one out. 1,2,6,15,31,56,91 SOLUTION: Add 1square ,2square ,....,6square to the terms. so 91 is wrong. 20.Find the odd one out. 105,85,60,30,0,-45,-90 SOLUTION: Subtract 20,25,30,35,40,45 from the terms. So 0 is odd one. 21.Find out the odd one out. 3,10,21,36,55,70,105 SOLUTION: The pattern in the series is 1*3, 2*5, 3*7, 4*9, 5*11, 6*13, 7*15. So the series will be 3,10,21,36,55,78,105. So 70 is wrong term in the series.
22.Find out the odd one out. 4,9,19,39,79,160,319 SOLUTION: Double the number and add 1 to it. So the series will be 4,9,39,79,159,319. So 160 is wrong. 23.Find out the odd one out. 10,14,28,32,64,68,132. SOLUTION: Alternatively add 4 and double the next term. So 132 is wrong.
Complex Problems
EXAMPLE PROBLEMS: 1.Find the missing term in the series: 4,-8,16,-32,64,( ) SOLUTION: The terms are doubled and change the sign. So the next term is -128 2.16,33,65,131,261,(
)
SOUTION: The terms are doubled and 1 is added. So 261*1+1=522+1=523 So the missing term is 523. 3.2,6,12,20,30,42,56,(
)
SOLUTION: The pattern is 1 * 2 , 2 * 3 , 3 * 4 , 4 * 5 , 5 * 6 , 6 * 7 , 7*8,8*9. So the series is 2,6,12,20,30,42,56,72. So 72 is the missing term. 4. 8,24,12,36,18,54,(
)
SOLUTION: Numbers are alternatively multiplied by 3 and divided by 2. So the next term is 54 / 2 = 27. 5. 165,195,255,285,345,(
)
SOLUTION: Each number is 15 multiplied by a prime number. i.e the series is 15*11,15*13,15*17,15*19,15*23,15*29. So series is 165,195,255,285,345,435. So 435 is the missing term. 6. 7,16,63,124,215,342,(
).
SOLUTION: Numbers are 23 -1,33-1,43-1,....................so 83-1=511. So 511 is the missing term. 7.2,4,12,48,240,(
)
SOLUTION: Go on multiplying by 2,3,4,5,6. So the last term in the series is 240*6=1440. 8.8,7,11,12,14,17,17,22,(
)
SOLUTION: There are two series 8,11,14,17,20 and 7,12,17,22 So increasing by 3 and 5.So 20 the missing term. 9.71,76,69,74,67,72,(
)
SOLUTION: Alternately add 5 and subtract 7. so the series is 71+5=76 10.2,5,9,19,37 SOLUTION: Second number is one more than twice the first,Third number is one less than twice the second,Forth is one more than twice the third and so on. So the next number is 2 * 37 + 1 = 74+1 = 75. 11. Find the wrong number in the given series. 3,8,15,24,34,48,63 SOLUTION: The difference between consecutive terms are respectively 5,7,9,11,13. So 34 is the wrong number in the series. 12. 125,106,88,76,65,58,53 SOLUTION: Subtract 24,21,18,15,12,9 from the numbers to get the next number. So 128 is wrong. 13. 1,1,2,6,24,96,720 SOLUTION: Multiply with 1,2,3,4,5,6 to get the next number. So 96 is wrong. 14 . 32,36,41,61,86,122,171,235 SOLUTION: Second term = First term + 22 Third term = Second term + 32 Fourth term = Third term + 42 Fifth term = Forth term + 52 Sixth term = Fifth term + 62
Seventh term = Sixth term + 72 So the third term should be 45 instead of 41. 15 . 15,16,34,105,424,2124,12576 SOLUTION: Second term = First term * 1 + 1 = 16 Third term = Second term * 2 + 2 = 34 Forth term = Third Term * 3 + 3 = 105 Fifth term = Forth term * 4 + 4 = 424 Sixth term = Fifth term * 5 + 5 =2125 Seventh term = Sixth term * 6 + 6 = 12576. So 2124 is wrong. 16 . 40960,10240,2560,640,200,40,10 SOLUTION: Go on dividing by 4 ,the series will be 40960,10240,2560,640,160,40,10. So 200 is wrong. 17.7,8,18,57,228,1165,6996 SOLUTION: Let the numbers be A,B,C,D,E,F,G then A,A*1+1,B*2+2,C*3+3,............ so 288 is wrong. 18. 19,26,33,46,59,74,91 SOLUTION: Go on adding 7,9,11,13,15,17. So 33 is wrong. 19 . 10,26,74,218,654,1946,5834. SOLUTION: Second term = first term * 3 – 4 = 26. Third term = Second term * 3 – 4 =74 Forth term = Third term * 3 – 4 =218
Fifth term = Forth term * 3 – 4 =650 So 654 is wrong .
ODD MAN OUT & SERIES
In any type of problems, a set of numbers is given in such a way that each one except one satisfies a particular definite property. The one which does not satisfy that characteristic is to be taken out.
Some important properties of numbers are given below : 1.Prime Number Series Example: 2,3,5,7,11,.................
2.Even Number Series Example: 2,4,6,8,10,12,............
3.Odd Number Series: Example: 1,3,5,7,9,11,...................
4.Perfect Squares: Example: 1,4,9,16,25,..............
5.Perfect Cubes: Example: 1,8,27,64,125,.................
6.Multiples of Number Series: Example: 3,6,9,12,15,..............are multiples of 3
7.Numbers in Arithmetic Progression(A.P): Example: 13,11,9,7................
8.Numbers in G.P: Example: 48,12,3,..... SOME MORE PROPERTIES: 1. If any series starts with 0,3,.....,generally the relation will be (n2-1). 2. If any series starts with 0,2,.....,generally the relation will be (n2-n). 3. If any series starts with 0,6,.....,generally the relation will be (n3-n). 4. If 36 is found in the series then the series will be in n2 relation. 5. If 35 is found in the series then the series will be in n2-1 relation. 6. If 37 is found in the series then the series will be in n2+1 relation. 7. If 125 is found in the series then the series will be in n3 relation. 8. If 124 is found in the series then the series will be in n3-1 relation. 9. If 126 is found in the series then the series will be in n3+1 relation. 10. If 20,30 found in the series then the series will be in n2-n relation. 11. If 60,120,210,........... is found as series then the series will be in n3-n relation. 12. If 222,............ is found then relation is n3+n 13. If 21,31,.......... is series then the relation is n2-n+1. 14. If 19,29,.......... is series then the relation is n2-n-1. 15. If series starts with 0,3,............ the series will be on n2-1 relation.
EXAMPLE PROBLEMS: 13.Find the odd one out. 2,5,10,50,500,5000 SOLUTION: In the above series, the pattern as follows: 1st term * 2nd term = 3rd term 2nd term * 3rd term = 4th term 3rd term * 4th term = 5th term But 50*500=25000 which is not equal to 5000. so 5000 is odd one.
14.Find the odd one out. 582,605,588,611,634,617,600 SOLUTION: In the above series, alternatively 23 is added and 17 is subtracted from the terms. So 634 is odd one. 15.Find the odd one out. 46080,3840,384,48,24,2,1 SOLUTION: In the above series,the terms are successively divided by 12,10,8,6,..... so 24 is not in this pattern. so 24 is odd one. 16.Find the odd one out. 5,16,6,16,7,16,9 SOLUTION: In the above series, the terms at odd places are 5,6,7,8.......and at even places is 16. So 9 is odd one.
17.Find the odd one out. 6,13,18,25,30,37,40 SOLUTION: In the above series, the difference between two successive terms from the beginning are 7,5,7,5......... so 40 is odd one. 18.Find the odd one out. 56,72,90,110,132,150 SOLUTION: The above series as follows: 7*8,8*9,9*10,10*11,11*12,12*13. So it will be 56,72,90,110,132,156 so 150 is wrong. 19.Find the odd one out. 1,2,6,15,31,56,91 SOLUTION: Add 1square ,2square ,....,6square to the terms. so 91 is wrong. 20.Find the odd one out. 105,85,60,30,0,-45,-90 SOLUTION: Subtract 20,25,30,35,40,45 from the terms. So 0 is odd one. 21.Find out the odd one out. 3,10,21,36,55,70,105 SOLUTION: The pattern in the series is 1*3, 2*5, 3*7, 4*9, 5*11, 6*13, 7*15. So the series will be 3,10,21,36,55,78,105. So 70 is wrong term in the series.
22.Find out the odd one out. 4,9,19,39,79,160,319 SOLUTION: Double the number and add 1 to it. So the series will be 4,9,39,79,159,319. So 160 is wrong. 23.Find out the odd one out. 10,14,28,32,64,68,132. SOLUTION: Alternatively add 4 and double the next term. So 132 is wrong.
Complex Problems
EXAMPLE PROBLEMS: 1.Find the missing term in the series: 4,-8,16,-32,64,( ) SOLUTION: The terms are doubled and change the sign. So the next term is -128 2.16,33,65,131,261,(
)
SOUTION: The terms are doubled and 1 is added. So 261*1+1=522+1=523 So the missing term is 523. 3.2,6,12,20,30,42,56,(
)
SOLUTION: The pattern is 1 * 2 , 2 * 3 , 3 * 4 , 4 * 5 , 5 * 6 , 6 * 7 , 7*8,8*9. So the series is 2,6,12,20,30,42,56,72. So 72 is the missing term. 4. 8,24,12,36,18,54,(
)
SOLUTION: Numbers are alternatively multiplied by 3 and divided by 2. So the next term is 54 / 2 = 27. 5. 165,195,255,285,345,(
)
SOLUTION: Each number is 15 multiplied by a prime number. i.e the series is 15*11,15*13,15*17,15*19,15*23,15*29. So series is 165,195,255,285,345,435. So 435 is the missing term. 6. 7,16,63,124,215,342,(
).
SOLUTION: Numbers are 23 -1,33-1,43-1,....................so 83-1=511. So 511 is the missing term. 7.2,4,12,48,240,(
)
SOLUTION: Go on multiplying by 2,3,4,5,6. So the last term in the series is 240*6=1440. 8.8,7,11,12,14,17,17,22,(
)
SOLUTION: There are two series 8,11,14,17,20 and 7,12,17,22 So increasing by 3 and 5.So 20 the missing term. 9.71,76,69,74,67,72,(
)
SOLUTION: Alternately add 5 and subtract 7. so the series is 71+5=76 10.2,5,9,19,37 SOLUTION: Second number is one more than twice the first,Third number is one less than twice the second,Forth is one more than twice the third and so on. So the next number is 2 * 37 + 1 = 74+1 = 75. 11. Find the wrong number in the given series. 3,8,15,24,34,48,63 SOLUTION: The difference between consecutive terms are respectively 5,7,9,11,13. So 34 is the wrong number in the series. 12. 125,106,88,76,65,58,53 SOLUTION: Subtract 24,21,18,15,12,9 from the numbers to get the next number. So 128 is wrong. 13. 1,1,2,6,24,96,720 SOLUTION: Multiply with 1,2,3,4,5,6 to get the next number. So 96 is wrong. 14 . 32,36,41,61,86,122,171,235 SOLUTION: Second term = First term + 22 Third term = Second term + 32 Fourth term = Third term + 42 Fifth term = Forth term + 52 Sixth term = Fifth term + 62
Seventh term = Sixth term + 72 So the third term should be 45 instead of 41. 15 . 15,16,34,105,424,2124,12576 SOLUTION: Second term = First term * 1 + 1 = 16 Third term = Second term * 2 + 2 = 34 Forth term = Third Term * 3 + 3 = 105 Fifth term = Forth term * 4 + 4 = 424 Sixth term = Fifth term * 5 + 5 =2125 Seventh term = Sixth term * 6 + 6 = 12576. So 2124 is wrong. 16 . 40960,10240,2560,640,200,40,10 SOLUTION: Go on dividing by 4 ,the series will be 40960,10240,2560,640,160,40,10. So 200 is wrong. 17.7,8,18,57,228,1165,6996 SOLUTION: Let the numbers be A,B,C,D,E,F,G then A,A*1+1,B*2+2,C*3+3,............ so 288 is wrong. 18. 19,26,33,46,59,74,91 SOLUTION: Go on adding 7,9,11,13,15,17. So 33 is wrong. 19 . 10,26,74,218,654,1946,5834. SOLUTION: Second term = first term * 3 – 4 = 26. Third term = Second term * 3 – 4 =74 Forth term = Third term * 3 – 4 =218
Fifth term = Forth term * 3 – 4 =650 So 654 is wrong .
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