sanju09 wrote:GMATGuruNY wrote:sanju09 wrote:Cube of an integer is t less than the integer. Which of the following cannot be the value of t?
A. 120
B. 60
C. 24
D. 12
E. -6
[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
x³ = x - t
t = x - x³.
Since the answer choices are relatively small, |x| < 10.
Try integers close to 0.
If x=2, then t = -6. Eliminate E.
The remaining answer choices are positive, implying that x<0.
If x=-2, then t = 6.
If x=-3, than t = 24. Eliminate C.
As the value of x decreases, the value of t increases.
Given the results above, it is not possible that t=12.
The correct answer is
D.
Can we say that the product of three consecutive integers [spoiler]
cannot be 12, hence D[/spoiler]?
Almost.
t = x - x³ = x(1-x²) = x(1+x)(1-x).
The factors of t are NOT 3 consecutive integers.
To illustrate:
If x=2, t = 2(3)(-1).
If x=(-2), t = (-2)(-1)(3).
In neither case are the factors of t consecutive.
The ABSOLUTE VALUES of these factors, however, ARE consecutive.
With this reasoning in mind -- once we've seen that t=-6 is possible -- we could scan the remaining answer choices for a value that is not the product of 3 consecutive integers.
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