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Question is 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?
Doubt 1 - Lets say t= -1 ; then t+2 is is set = i.e. 1 is in set.
Since question stem is Must be True, how do we make sure that this pattern will continue. i.e if 1 is in set, then 3 will be in set and so on.. Also
Doubt 2 - Cant we assume that t+2 = -1 then t= -3(should also be in set)
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
The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Now, about your questions: 1. The question says "a set of numbers has the property that for ANY number t in the set, t + 2 is in the set", so if 1 is in the set then 1+2=3 MUST be in the set.
2. We don't know which is the source integer in the set, if it's -1 than odd number less than it won't be in the set but if source integer is let's say -11 than -3 will be in the set. So -3 may or may not be in the set.
"B"....ques says for a number t , t+2 shd be there we know -1 is there so -1+2 = 1 MUST be there. I don't think we can extrapolate this and make this an infinite series. Surya do u have the OA ?
Hey Baner, but we already have this as an infinite series in one direction (positive). But I agree with you - this could be an infinite series in one direction, starting with -1. So we cannot assume the presence of numbers lower than -1. _________________
I was thinking B first. but, what does "A set of numbers has the property that for any number t in the set, t + 2 is in the set"?
i think any number indicates to an infinite series. if so, it should be E.
t could be any number in the series. if t is in the series, t+2 is also in the series. if t=t+2, then t+2=t+4. then if t+2=t, then t=t-2.
Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...