Concept of Series-04

1.     2         9        30       105       ?        2195    [Ans :-(4) 436]

(1) 432     (2) 426     (3) 440    (4) 436     (5) None of these      

                                           

2.     3         4        12        45      ?     1005   [Ans :-(5) None of these (196)]

(1) 152      (2) 198      (3) 144      (4) 192      (5) None of these       

                                         

3.     1         3        9          31       ?      651    [Ans :-(3) 129]

(1) 97      (2) 127    (3) 129 (4) 109         (5) None of these      

                              

4.     5         ?        4         7.5        17        45   [Ans :-(2) 3]

(1) 3.5        (2) 3      (3) 2.5   (4) 2       (5) None of these      

                             

5.   15        30        ?        40        8         48    [Ans :-(1) 10]

(1) 10     (2) 20    (3) 18     (4) 12         (5) None of these       

Solution:

Detailed Explanation:

Concept: More than 90% questions can be classified on the basis of “slop”. Maximum Slop, Average Slop and Minimum Slop – these are the mainly three types or slop. There is one more type of slop - mean slop.

(1) In the Minimum Slop, the terms are obtained by adding some numbers. In this type of slop, terms are not become multiple.

(2) In other two types of slops, terms become multiple. In the Average Slop, terms become multiple equally, i. e., slops are as: ×2×2×2×2×2…. Or ×1.5×1.5×1.5×1.5×1.5…. or ×3×3×3×3×3×3×……., and something added or subtracted also.

 

(3) In the Maximum Slop, terms become multiple, but not equally. It is either increasing or decreasing  i. e., slops are as: ×1×2×3×4×5…. Or ×1.5×3×4.5×6×7.5…. or ×2×4×6×8×10×……., and something added or subtracted also.

(4) In the Mean Slop, terms become multiple, but not equally, but not so much sharp. It is either increasing or decreasing i. e., slops are as: ×0.5×1×1.5×2.5×3…. etc. and some thing added or subtracted also.

(5) There is an “Ups and down” series also. In this series there are two types; one, in which multiplication and division are in alternately used, and another, in which addition and subtraction are alternately used. If slop is sharp, then the case is of probably of multiplication and division and if the slop is less sharp, then the case is of probably of addition and subtraction.

(6) Some other rule may be associated in the series. Sometimes, any term in a series is the sum of its just previous two terms throughout the series. Or, any term in a series is the product of its just previous two terms throughout the series.     

Solution: 

1. Solution: This is type III series. Slop is “Maximum”. Terms are multiplied by 1, 2, 3, 4, 5, 6 respectively and added  a number which is the product of two numbers, complimentary to each other with respect to 8.  That is, 1+7 = 8,   2+6 = 8,    3+5 = 8, 4+4 = 8, 5+3 = 8, 6+2 = 8 and so on.

        ×1+1×7   ×2+2×6    ×3+3×5    ×4+4×4   ×5+5×3   ×6+6×2  

1)     2              9              30            105           ?              2195    [Ans :-(4) 436]

2. Solution: This is also of type III series. Slop is “Maximum”. Terms are multiplied by 1, 2, 3, 4, 5, 6 respectively and 1², 2², 3², 4², 5², 6² are successively added.

        ×1+1²   ×2+2²    ×3+3²   ×4+4²    ×5+5²    ×6+6²                                            

2)     3           4           12         45         ?            1005  

[Ans :-(5) None of these (196)]

3. Solution: This is also of type III series. Slop is “Maximum”. Terms are multiplied by 1, 2, 3, 4, 5, 6 respectively and 2, 3, 4, 5, 6, 7 are successively added.

        ×1+2    ×2+3    ×3+4     ×4+5   ×5+6    ×6+7                                   

3)     1           3           9          31        ?          651    [Ans :-(3) 129]

4. Solution: This series is an example of “Mean Slop” (Type IV). Terms are multiplied by 0.5, 1, 1.5, 2, 2.5 respectively; and then added 0.5, 1, 1.5, 2, 2.5 respectively also.

        ×0.5+0.5   ×1+1      ×1.5+1.5      ×2+2   ×2.5+2.5           

4)     5               ?            4               7.5           17            45   [Ans :-(2) 3]

1. Solution: This is an “Ups and down” series (type v). Here continuously multiplied by 2, then divided by and so on.

       ×2       ÷3       ×4        ÷5      ×6                             

5)   15        30        ?        40        8         48    [Ans :-(1) 10]