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02 Apr 2016, 09:34
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
30% (01:38) correct
70%
(01:37)
wrong
based on 186
sessions
History
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If x is positive, is x prime?
(1) \(x^3\) has exactly four distinct factors
(2) \(x^2-x-6=0\)
(1) \(x^3\) has exactly four distinct factors
(2) \(x^2-x-6=0\)
02 Apr 2016, 09:49
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krodin
Hi,
1 is not suff because we do not know if x is an integer..
1) Say x^3 =6..
Factors of 6 are 1,2,3,6...
But x here is \(\sqrt[3]{6}\)..
Insuff
2)\(x^2-x-6=0\)
X=-2and 3...
X is positive so x=3
Suff
B
General Discussion
04 Apr 2016, 06:01
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
If x is positive, is x prime?
(1) x^3 has exactly four distinct factors
(2) x^2−x−6=0
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make the answer D.
For 1), the number of factors is 3+1=4 and x must be prime, which is yes and sufficient.
For 1), from (x-3)(x+2)=0, x=3 is only possible, which is yes and sufficient.
Thus, D is the answer.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
If x is positive, is x prime?
(1) x^3 has exactly four distinct factors
(2) x^2−x−6=0
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make the answer D.
For 1), the number of factors is 3+1=4 and x must be prime, which is yes and sufficient.
For 1), from (x-3)(x+2)=0, x=3 is only possible, which is yes and sufficient.
Thus, D is the answer.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
