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A set is such that if m is in the set, (m + 3) is also in the set. If

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A set is such that if m is in the set, (m + 3) is also in the set. If  [#permalink]

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New post 20 Sep 2018, 00:02
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A set is such that if m is in the set, (m + 3) is also in the set. If −3 is in the set, which of the following is also in the set?

I. −6
II. 0
III. 6

(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and III
(E) I, II and III

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A set is such that if m is in the set, (m + 3) is also in the set. If  [#permalink]

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New post Updated on: 20 Sep 2018, 14:11
Bunuel wrote:
A set is such that if m is in the set, (m + 3) is also in the set. If −3 is in the set, which of the following is also in the set?

I. −6
II. 0
III. 6

(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and III
(E) I, II and III


As we are explicitly given a rule to follow, we'll follow it.
This is a Precise approach

If -3 is in the set, (-3)+3 = 0 is in the set. So II is true.
Since 0 is in the set, 0+3 = 3 is in the set and since 3 is in the set, 3 +3 = 6 is in the set.
So III is also true. We do not have information about numbers smaller than -3 and cannot conclude if I is true or not.

(D) is our answer.

Note that a different, Logical approach would have been to recognize that what we are doing is creating a set out of an arithmetic sequence with a difference of 3. Since one of the elements is -3, a multiple of 3, then the set contains all multiples of 3 starting from some number. The first number has to be at least -3 so II and III are true but we do not know if the first number in the set is smaller/equal to -6 or not so cannot conclude if I is true.
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Originally posted by DavidTutorexamPAL on 20 Sep 2018, 00:10.
Last edited by DavidTutorexamPAL on 20 Sep 2018, 14:11, edited 1 time in total.
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A set is such that if m is in the set, (m + 3) is also in the set. If  [#permalink]

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New post 20 Sep 2018, 03:58
Bunuel wrote:
A set is such that if m is in the set, (m + 3) is also in the set. If −3 is in the set, which of the following is also in the set?

I. −6
II. 0
III. 6

(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and III
(E) I, II and III


NOTE: This is forward progressing series i.e. if m is in set (m+3) also will be in the set but please NOTE that if m is in the set (m-3) will not essentially be in set which is what is misunderstood by many test takers

i.e. if -3 is in set then {0,3,6,9,12,15....} will also be in the set hence

II and III will always be in the set

Answer: option D
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A set is such that if m is in the set, (m + 3) is also in the set. If &nbs [#permalink] 20 Sep 2018, 03:58
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