Statement Choices Eliminated

　　（1） is sufficient B， C， E

　　（1） is not sufficient A， D

　　（2） is sufficient A， C， E

　　（2） is not sufficient B， D

　　（1） is not sufficient and （2） is not sufficient A， B， D

　　Example 1： What is the 1st term in sequence S？

　　（1） The 3rd term of S is 4.

　　（2） The 2nd term of S is three times the 1st， and the 3rd term is four times

　　the 2nd.

　　（1） is no help in finding the first term of S. For example， the following se

　　quences each have 4 as their third term， yet they have different first terms

　　：

　　0， 2， 4

　　-4， 0， 4

　　This eliminates choices A and D. Now， even if we are unable to solve this pr

　　oblem， we have significantly increased our chances of guessing correctly——fr

　　om 1 in 5 to 1 in 3.

　　Turning to （2）， we completely ignore the information in （1）。 Although （2） co

　　ntains a lot of information， it also is not sufficient. For example， the fol

　　lowing sequences each satisfy （2）， yet they have different first terms：

　　1， 3， 12

　　3， 9， 36

　　This eliminates B， and our chances of guessing correctly have increased to 1

　　in 2.

　　Next， we consider （1） and （2） together. From （1）， we know “the 3rd term of S

　　is 4.“ From （2）， we know ”the 3rd term is four times the 2nd.“ This is equi

　　valent to saying the 2nd term is 1/4 the 3rd term： （1/4）4 = 1. Further， from

　　（2）， we know “the 2nd term is three times the 1st.” This is equivalent to s

　　aying the 1st term is 1/3 the 2nd term： （1/3）1 = 1/3. Hence， the first term

　　of the sequence is fully determined： 1/3， 1， 4. The answer is C.

　　Example 2： In the figure to the right， what is the area of the triangle？