¡¡¡¡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£º 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
¡¡¡¡£º
¡¡¡¡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¡ª¡ªfr
¡¡¡¡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£º
¡¡¡¡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£º £¨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£º £¨1/3£©1 = 1/3. Hence£¬ the first term
¡¡¡¡of the sequence is fully determined£º 1/3£¬ 1£¬ 4. The answer is C.
¡¡¡¡Example 2£º In the figure to the right£¬ what is the area of the triangle£¿
