Question
Statements:Some pencils are erasers. All erasers
are pens. Some pens are sharpeners. Conclusions:I. some sharpeners are erasers. II. Some pens are pencils. III. Some pencils are sharpeners. In each of the questions below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of given conclusions logically follows from the given  statements disregarding commonly known facts.Solution
A + I = No conclusion. Hence, conclusion I and III will not follow. Some pencils are erasers (I) + All erasers are pens (A) = some pencils are pens (I) ⇒ conversion ⇒ some pens are pencils (I). Hence, conclusion II will follow. Alternative method: 
97 106 121 138 157 180
...37    59    103    191    ?     719
51     53     109     332     ?     6686
...30 27 20 9 ? - 25
32, 8, 4, ?, 3, 3.75
13 24 75 134 447 892
...19   20   42   129   ?    2605  . Â
Select the number from among the given options that can replace the question mark (?) in the following series.
64, 60, 52, 40, ?, 4
1001, 728, 513, 342, 217, ?
The question below is based on the given series I. The series I satisfy a certain pattern, follow the same pattern in series II and answer the question...
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