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]
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t less than the integer
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sanju09
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GMATGuruNY
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x³ = x - tsanju09 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]
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.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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sanju09
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Can we say that the product of three consecutive integers [spoiler]cannot be 12, hence D[/spoiler]?GMATGuruNY wrote:x³ = x - tsanju09 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]
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.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
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Almost.sanju09 wrote:Can we say that the product of three consecutive integers [spoiler]cannot be 12, hence D[/spoiler]?GMATGuruNY wrote:x³ = x - tsanju09 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]
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.
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
