32. A set of numbers has the property that for any number t in the set, t + 2 is in the set. If –1 is in the set, which of the following must also be in the set?
I. –3 II. 1 III. 5
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
Soln: Series property: t => t+2. (Note: for any given number N, ONLY N + 2 is compulsory. N - 2 is not a necessity as N could be the first term...this can be used as a trap.)
Given: -1 belongs to the series. => 1 => 3 =>5. DOES NOT imply -3.
Hence, II and III (D).
*****
I thought it was (B). I thought that since it didn't specify how many items are in the set, then I can't assume how extensive the set is in terms of the number of items...i.e., I can't assume that the set goes further than t+2. If that is the case, then 5 would not be absolutely necessary.
Thoughts? Where am I mistaken?
I. –3 II. 1 III. 5
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
Soln: Series property: t => t+2. (Note: for any given number N, ONLY N + 2 is compulsory. N - 2 is not a necessity as N could be the first term...this can be used as a trap.)
Given: -1 belongs to the series. => 1 => 3 =>5. DOES NOT imply -3.
Hence, II and III (D).
*****
I thought it was (B). I thought that since it didn't specify how many items are in the set, then I can't assume how extensive the set is in terms of the number of items...i.e., I can't assume that the set goes further than t+2. If that is the case, then 5 would not be absolutely necessary.
Thoughts? Where am I mistaken?
