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24 Oct 2016, 23:24
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:18) correct
38%
(02:03)
wrong
based on 598
sessions
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If x is an integer greater than 3, which of the following MUST be divisible by 3?
A. \(x^3+3x^2−10x\)
B. \(x^3+5x^2+6x\)
C. \(x(x+1)^2\)
D. \(x^3+3x^2−18x\)
E. \(x(x−1)^2\)
A. \(x^3+3x^2−10x\)
B. \(x^3+5x^2+6x\)
C. \(x(x+1)^2\)
D. \(x^3+3x^2−18x\)
E. \(x(x−1)^2\)
14 Jun 2018, 10:32
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Bunuel
We can simplify the expressions by removing multiples of 3 from them. For example, in choice A, the second term 3x^2 is a multiple of 3 regardless what x is. Similarly, -9x is also a multiple of 3 regardless what x is. Therefore, we can remove 3x^2 and -9x from choice A and it leaves us with x^3 - x.
Notice that x^3 - x can be factored as:
x(x^2 - 1)
x(x - 1)(x +1)
(x - 1)(x)(x + 1)
Notice that this is a product of three consecutive integers; thus it’s divisible by 3! = 6. If it’s divisible by 6, then it’s divisible by 3.
Answer: A
General Discussion
25 Oct 2016, 00:17
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When we factorize equation, x^3+3x^2−10x we get x(x+5)(x-2).
Whatever the value of x(eg 4,5,6), we will definitely get a number divisible by 3.
Hence Option A is the answer.
Whatever the value of x(eg 4,5,6), we will definitely get a number divisible by 3.
Hence Option A is the answer.
