Set M contains numbers that satisfy the condition that, if

Question

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

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

Bunuel · Accepted Answer

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.

Pansi · Answer

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.

evdo · Answer

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

thanks

Bunuel · Answer

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.

bumpbot · Answer

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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

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