GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2019, 06:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 03 Mar 2018
Posts: 204
In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis?  [#permalink]

### Show Tags

06 Mar 2018, 11:40
5
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:04) correct 41% (01:23) wrong based on 87 sessions

### HideShow timer Statistics

In x-y plane, does parabola y=$$ax^2$$+bx+c intersect to x-axis?

1) b= -2
2) c<0

_________________
Retired Moderator
Joined: 22 Aug 2013
Posts: 1409
Location: India
Re: In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis?  [#permalink]

### Show Tags

07 Mar 2018, 02:47
1
1
itisSheldon wrote:
In x-y plane, does parabola y=$$ax^2$$+bx+c intersect to x-axis?

1) b= -2
2) c<0

In case of a parabola(quadratic expression) ax^2 + bx + c:
If parabola intersects x-axis at two distinct points, it means the quadratic expression has two distinct real roots, and this happens when (b^2 - 4ac) > 0
If parabola intersects x-axis at one point only, it means the quadratic expression has one real root, and this happens when (b^2 - 4ac) = 0
If parabola does not intersect x-axis at all, it means the quadratic expression has no real root, and this happens when (b^2 - 4ac) < 0

So we need to know the sign of (b^2 - 4ac).

Statement 1
b is negative, but we don't know anything about a and c. Not sufficient.

Statement 2
c is negative, but we don't know anything about a and b. Not sufficient.

Combining the two statements,
b and c are negative, but we don't know the sign of a.
If a is positive, then - 4ac will be positive, and then (b^2 - 4ac) will also be positive and the parabola will intersect x-axis.
If a is negative, then -4ac will be negative, and (b^2 - 4ac) could be either negative or positive or 0 depending on the magnitudes of a, b, c. So we cant say whether parabola will intersect x-axis or not.

So not sufficient to determine.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis?  [#permalink]

### Show Tags

19 Mar 2018, 13:06

SOLUTION

In $$x-y$$ plane, the parabola intersects the $$x$$-axis if the equation of the parabola has real roots.
Thus, we have to find:
• Whether $$y=ax^2+bx+c$$ has real roots or not.

Per our conceptual understanding of quadratic equation, a quadratic equation has real roots if the value of discriminant is greater or equal to zero.
For equation $$y= ax^2+bx+c$$, the value of $$D$$ is:
• $$D= b^2-4ac$$
Thus, we have to find if the value of $$(b^2-4ac) >=0$$.
Statement-1 "$$b= -2$$"

Since we don’t know the value of $$a$$ and $$c$$, statement 1 alone is not sufficient to answer the question.

Statement-2 "$$c<0$$"

Let us assume $$c=-k$$.
Since we don’t know the value of $$b$$ and $$a$$, statement 2 alone is not sufficient to answer the question.

Combining both the statements:
From both the statements combined, the value of $$D$$ is:
• $$D= (-2)^2 – 4*a*(-k)$$
• $$D= 4+4ak$$
We still do not have the value of “$$a$$”.
Hence, “Statement (1) and (2) together are not sufficient to answer the question”.

_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis?  [#permalink]

### Show Tags

30 Nov 2019, 00:09
itisSheldon wrote:
In x-y plane, does parabola y=$$ax^2$$+bx+c intersect to x-axis?

1) b= -2
2) c<0

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The question asks if the discriminant b^2 - 4ac ≥ 0.

Since we have 3 variables (a, b and c) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

If $$a = 1, b = -2, c = -1$$, then $$b^2-4ac = (-2)^2-4 \cdot 1 \cdot (-1) = 4 + 4 > 0$$ and it has an intersection.
If $$a = -2, b = -2, c = -1$$, then $$b^2-4ac = (-2)^2-4 \cdot (-2) \cdot (-1) = 4 - 8 < 0$$ and it doesn't an intersection.

Since both conditions together do not yield a unique solution, they are not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis?   [#permalink] 30 Nov 2019, 00:09
Display posts from previous: Sort by