Series-02

1.             4       2.25        3.25        7.125          18.25        51.875                  

7         (a)           (b)           (c)              (d)             (e)

What will come in place of (b)?   [Ans:-(4)]

(1) 4.125     (2) 5.25     (3) 6.75   (4) 4.75    (5) None of these

                                                                                          

2.             3         40      176        537          1078            1079    

 1         (a)      (b)          (c)            (d)                (e)      

What will come in place of (e)?   [Ans:-(1)]

(1) 839     (2) 738    (3) 829      (4) 938        (5) None of these

                                                                             

3.               3            5            22         13.5            35             19      

  5           (a)          (b)           (c)            (d)             (e)

What will come in place of (c)?    [Ans:-(3)]

(1) 16      (2) 15.5     (3) 14.5    (4) 13       (5) None of these

                                                                                      

4.               9           10           16        57           212         1085

                  2           (a)           (b)        (c)         (d)            (e)

What will come in place of (c)?   [Ans:-(2)]

(1) 37         (2) 15       (3) 18          (4) 25    (5) None of these

                                                                 

5.       7            20            46              98         202              410

          4           (a)            (b)              (c)         (d)              (e)

What will come in place of (d)?    [Ans:-(5)]

(1) 166       (2) 184     (3) 146     (4) 162     (5) None of these

Solution:

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 some thing 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 some thing 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.

Detailed Explanation: Now we will solve the given series in detail as:

1) Here the case is of “Mean slop” (type 4). Slop is ×0.5×1×1.5×2.5×3…. and 0.5, 1, 1.5, 2, 2.5… are added respectively. The rule is: ×0.5+0.5   ×1+1     ×1.5+1.5   ×2+2      ×2.5+2.5

2) This is a case of “Decreasing Maximum Slop”. The slop is as ×5×4×3×2×1…. Also,  5²,  4², 3², 2², 1² are added respectively. Final rule is: ×5+5²   ×4+4²    ×3+3²    ×2+2²    ×1+1²   

3) This is typical type of series. It can be explained in two ways.

First Rule: 7 is added to the term and then divided by 2; 6 is added to the next term and multiplied by 2; 5 is added to the next term and divided by 2; 4 is added to the next term and multiplied by 2 and so on.      (3+7)÷2  (5+6)×2   (22+5)÷2   (13.5+4)×2   (35+3)÷2

Second Rule is as: ÷2+3.5   ×2+12     ÷2+2.5      ×2+8           ÷2+1.5        The given series can be solved as:  

       ÷2+3.5   ×2+12     ÷2+2.5      ×2+8           ÷2+1.5                                                                                                                            

      3            5              22             13.5               35            19

      5           (a)            (b)             (c)?                (d)          (e)

                                         Ans. is (c) = 14.5   

4) This is a case of “Increasing Maximum Slop”. The slop is as ×1×2×3×4×5…. Also,  1²,  -2², 3², -4², 5² are added respectively. Final rule is: ×1+1²   ×2-2²   ×3+3²   ×4-4²    ×5+5²                                                                                                                                                                                                                                                                  

5)  Here the case is of “Average slop”. Slop is ×2×2×2×2×2…. and 6 is added to each of the term. The rule is: ×2+6, ×2+6, ×2+6, ×2+6, ×2+6.......