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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] New post 17 Sep 2012, 04:54
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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.
Edited the question.
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Re: Set M contains numbers that satisfy the condition that, if [#permalink] New post 17 Sep 2012, 05:09
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] 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] 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] New post 03 Dec 2014, 05:56
Expert's post
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
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Set M contains numbers that satisfy the condition that, if   [#permalink] 03 Dec 2014, 05:56
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Set M contains numbers that satisfy the condition that, if

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