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]

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.

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]?

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.