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Set M contains numbers that satisfy the condition that, if

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Set M contains numbers that satisfy the condition that, if [#permalink]

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Set M contains numbers that satisfy the condition that, if integer x is in the set then x+3 will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.

I. -7
II. -1
III. 2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II and III
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Sep 2012, 05:50, edited 1 time in total.
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Re: Set M contains numbers that satisfy the condition that, if [#permalink]

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New post 17 Sep 2012, 05:53
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Vamshi8411 wrote:
Set M contains numbers that satisfy the condition that, if integer x is in the set then x+3 will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.

I. -7
II. -1
III. 2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II and III


Notice that we are asked "which of the following numbers MUST also be present in the set M" not "COULD be in the set".

Now, if -4 is in the set, then -4+3=-1 must be in the set. Since -1 is in the set then -1+3=2 must be in the set. Could -7 be in the set? Certainly, but we don't know that for sure.

Answer: D.

Hope it's clear.
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Re: Set M contains numbers that satisfy the condition that, if [#permalink]

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New post 17 Sep 2012, 05:09
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If -4 is part of the list, then -4+3(i.e -1) & -1+3(i.e 2) "MUST" be part of the set. Whereas -4-3(i.e -7) "COULD" be a part of the list
Hence D is the answer.
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Re: Set M contains numbers that satisfy the condition that, if [#permalink]

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New post 03 Dec 2014, 04:10
Pansi wrote:
If -4 is part of the list, then -4+3(i.e -1) & -1+3(i.e 2) "MUST" be part of the set. Whereas -4-3(i.e -7) "COULD" be a part of the list
Hence D is the answer.


why -7 could be in the list? Why not must? why can't we use the rule backward?

thanks
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Re: Set M contains numbers that satisfy the condition that, if [#permalink]

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New post 03 Dec 2014, 05:56
evdo wrote:
Pansi wrote:
If -4 is part of the list, then -4+3(i.e -1) & -1+3(i.e 2) "MUST" be part of the set. Whereas -4-3(i.e -7) "COULD" be a part of the list
Hence D is the answer.


why -7 could be in the list? Why not must? why can't we use the rule backward?

thanks


If integer x is in the set then x+3 will also be in the set does NOT mean that the reverse must be true.

If integer x is in the set then x+3 will also be in the set does NOT mean that if integer x+3 is in the set then x must also be in the set.

Check similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-both-161920.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
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if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html
k-is-a-set-of-numbers-such-that-166908.html

Hope this helps.
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Collection of Questions:
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Re: Set M contains numbers that satisfy the condition that, if [#permalink]

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Re: Set M contains numbers that satisfy the condition that, if   [#permalink] 16 Dec 2015, 06:58
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