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19 May 2021, 06:46
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
81% (01:16) correct
19%
(01:32)
wrong
based on 119
sessions
History
Date
Time
Result
Not Attempted Yet
sherxon
Joined: 28 May 2021
Last visit: 09 Nov 2025
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14 Jun 2021, 21:11
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sm1510
S1: solving for x we find three values for x: 0, 1 and -3
insuff
S2: here we find x=5 and x=-3
insuff
S1&2: it becomes clear that x=-3
Answer is C
14 Jun 2021, 23:47
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This is a value kind of DS question, so we need a unique value of x.
From statement I alone, \(x^3 + 2x^2\) = 3x.
This is a cubic equation. Although cubic equations are not tested extensively on the GMAT, they may be tested at a basic level, like the one here. A cubic equation is a 3rd-degree polynomial equation in one variable (on the GMAT) and therefore has 3 roots.
Therefore, the given equation has 3 possible values for x and not only one. Let us try to factorise the given equation to find these 3 roots.
\(x^3 + 2x^2\) = 3x can be written as \(x^3 + 2x^2 – 3x\) = 0.
Factoring out x, we have x (\(x^2 + 2x – 3\)) = 0. This means, x = 0 or (\(x^2 + 2x – 3\)) = 0.
Factorising \(x^2 + 2x – 3\) = 0, we have (x+3) (x-1) = 0 which means x = 1 or x = -3.
Statement I alone is insufficient to answer the question. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, \(x^2 – 2x – 15\) = 0.
Factorising, we have (x-5) (x+3) = 0, which means x = 5 or x = -3.
Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, we see that the common value that satisfies both equations is x = -3.
The combination of statements is sufficient to answer the question. Answer option E can be eliminated.
The correct answer option is C.
Hope that helps!
Aravind B T
From statement I alone, \(x^3 + 2x^2\) = 3x.
This is a cubic equation. Although cubic equations are not tested extensively on the GMAT, they may be tested at a basic level, like the one here. A cubic equation is a 3rd-degree polynomial equation in one variable (on the GMAT) and therefore has 3 roots.
Therefore, the given equation has 3 possible values for x and not only one. Let us try to factorise the given equation to find these 3 roots.
\(x^3 + 2x^2\) = 3x can be written as \(x^3 + 2x^2 – 3x\) = 0.
Factoring out x, we have x (\(x^2 + 2x – 3\)) = 0. This means, x = 0 or (\(x^2 + 2x – 3\)) = 0.
Factorising \(x^2 + 2x – 3\) = 0, we have (x+3) (x-1) = 0 which means x = 1 or x = -3.
Statement I alone is insufficient to answer the question. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, \(x^2 – 2x – 15\) = 0.
Factorising, we have (x-5) (x+3) = 0, which means x = 5 or x = -3.
Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, we see that the common value that satisfies both equations is x = -3.
The combination of statements is sufficient to answer the question. Answer option E can be eliminated.
The correct answer option is C.
Hope that helps!
Aravind B T
