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06 Apr 2021, 07:00
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (01:09) correct
28%
(01:33)
wrong
based on 124
sessions
History
Date
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Not Attempted Yet
A set is such that if m is in the set, (m^2 + 3) is also in the set. If −1 is in the set, which of the following is also in the set?
I. −2
II. 4
III. 19
(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and III
(E) I, II and III
I. −2
II. 4
III. 19
(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and III
(E) I, II and III
11 Apr 2021, 03:01
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Bunuel
Is there maybe a typo in the question stem (m^2 instead of m^3)? Otherwise, I don't get an answer.
My approach: since -1 is in the set, -1 could be m or \(m^3+3\)
Let's first check what we can get if m = -1
That means, that \(-1^3+3=2\) and \(2^3+3=11\) are in the set as well.
From this point, I won't check any more numbers, because \(11^3+3\) would already result in a number that is bigger than any answer choice.
Now check what would happen if \(m^3+3 = -1\)
\(m^3+3 = -1\) --> \(m=\sqrt[3]{-4}\)
From this point, I don't see how we could get to any of the answer choices?
Can you help Bunuel ?
12 Apr 2021, 08:10
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Bunuel
If -1 is in the set, then \((-1)^3 + 3 = 2\) is in the set, then \(2^3 + 3 = 8 + 3 = 11\) is also in the set. From there we can see the numbers only get bigger so seems like there is a typo with the question.
Note that this does not mean the value of x for \(x^3 + 3 = -1\) is in the set, the if statement we were given is a one-way statement. ("if and only if" would work two-ways)
