[GMAT math practice question]
In the x-y plane, does the parabola y=ax^2+bx+c have x-intercepts?
1) b^2-4ac<0
2) a<0
In the x-y plane, does the parabola y=ax^2+bx+c have x-inter
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
For any parabola of the form y = ax² + bx + c, the DISCRIMINANT is equal to b² - 4ac.Max@Math Revolution wrote:[GMAT math practice question]
In the x-y plane, does the parabola y=ax^2+bx+c have x-intercepts?
1) b^2-4ac<0
2) a<0
If the discriminant is positive, then the parabola has two x-intercepts.
If the discriminant is equal to 0, then the parabola has one x-intercept.
If the discriminant is negative, then the parabola has no x-intercepts.
Statement 1:
Since the discriminant is negative, the parabola has no x-intercepts.
Thus, the answer to the question stem is NO.
SUFFICIENT.
Statement 2:
No way to determine whether the discriminant is positive, negative, or equal to 0.
INSUFFICIENT.
The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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
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
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
For y=ax^2+bx+c to have an x-intercept, we must have b^2-4ac ≥ 0.
Thus, condition 1) gives the answer of 'no'. Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.
Condition 2)
If a = -1, b = 0, c = 0, we have y = -x, which has an x-intercept of zero, so the answer is 'yes'.
If a = -1, b = 0, c = -1, we have y = -x^2 - 1, which has no x-intercept. The answer is 'no' in this case.
Since we don't have a unique solution, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
For y=ax^2+bx+c to have an x-intercept, we must have b^2-4ac ≥ 0.
Thus, condition 1) gives the answer of 'no'. Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.
Condition 2)
If a = -1, b = 0, c = 0, we have y = -x, which has an x-intercept of zero, so the answer is 'yes'.
If a = -1, b = 0, c = -1, we have y = -x^2 - 1, which has no x-intercept. The answer is 'no' in this case.
Since we don't have a unique solution, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]