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Set $M$ contains numbers that satisfy the condition that, if integer x
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18 Mar 2025, 01:13
18 Mar 2025, 01:13
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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 value in the set, which of the following values 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
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Re: Set $M$ contains numbers that satisfy the condition that, if integer x
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22 Mar 2025, 04:15
22 Mar 2025, 04:15
Expert Reply
OFFICIAL EXPLANATION
We know that 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 $M$ in other words we can say that if an elements ' $a$ ' is there in the set all other elements that are multiple of 3 steps away from ' $a$ ' i.e. $a+3 k$, where $k$ is any positive integer, would also be there in the set.
We know that -4 is there in set M ; we need to check that which of the given numbers must also be present in set M.
I. -7 - which might not be there in the set as the set may start with the minimum value of -4 only.
II. -1 - which must be there as $-4+3=-1$
III. 2 - which must be there as $-4+3=-1 \&-1+3=2$ or we can say $-4+2 \times 3=-4+6=2$
Hence only II \& III numbers must be there in the set M, so the answer is (D).
We know that 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 $M$ in other words we can say that if an elements ' $a$ ' is there in the set all other elements that are multiple of 3 steps away from ' $a$ ' i.e. $a+3 k$, where $k$ is any positive integer, would also be there in the set.
We know that -4 is there in set M ; we need to check that which of the given numbers must also be present in set M.
I. -7 - which might not be there in the set as the set may start with the minimum value of -4 only.
II. -1 - which must be there as $-4+3=-1$
III. 2 - which must be there as $-4+3=-1 \&-1+3=2$ or we can say $-4+2 \times 3=-4+6=2$
Hence only II \& III numbers must be there in the set M, so the answer is (D).
gmatclubot
Re: Set $M$ contains numbers that satisfy the condition that, if integer x [#permalink]
22 Mar 2025, 04:15
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