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

 It is currently 23 Jul 2018, 02:23

### 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

# The slope of line n in the xy-plane is not 0 and the y-inter

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 434
The slope of line n in the xy-plane is not 0 and the y-inter  [#permalink]

### Show Tags

Updated on: 12 Jan 2014, 05:14
2
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:50) correct 44% (02:05) wrong based on 61 sessions

### HideShow timer Statistics

The slope of line n in the xy-plane is not 0 and the y-intercept of line n in the xy-plane is not 0. The equation of line n is y = mx + b, where m and b are constants. What is the value of m + b?

(1) The y-intercept is equal to the square of the x-intercept.
(2) The line goes through the point (−8, −16).

OE
(1): By definition, y-intercept of a line in form y = mx + b is equal to b. x-intercept is value of x when y = 0.
y = mx + b → 0 = mx + b → mx = −b → x = -(b/m)
Thus, y-intercept is b & x-intercept is –(b/m).
Since y-intercept is square of x-intercept, we can create equation: b = (-b/m)^2 → m^2*b= b^2
Since we are told in question stem that b does not equal 0, we can divide both sides by b. m^2= b
Since we know that b is equal to m^2, we can substitute that value into equation of line n.
y = mx + b → y = mx + m^2
"what is value of m + b?" Different values of m lead to different values for b.
So different values for m lead to different values for m + b.
For example,
if m = 1, then b = 1^2 = 1 → m + b = 1 + 1 = 2
If m = 2, then b = m^2 = 4 → m + b = 2 + 4 = 6
Insufficient.

(2): In order to determine equation of a line, it's necessary to have either two points, or one point and slope. Therefore, it is impossible to derive an equation of a line from simply one point on line. There are infinitely many different lines that go through point (−8, −16). So there are infinitely many different possible values of m + b.
Insufficient.

Combined: From (1), equation of line n is of form y = mx + m^2, where m is slope and m≠ 0.
(2) says that line goes through point (−8, −16). Remember that any paired point in form (x, y) represents a pair of values that could satisfy equation. In other words, first term in ordered pair can substitute in for x, and second term can be substituted in for y. Substituting −8 for x and −16 for y, we have:
−16 = m(−8) + m^2 → −16 = −8m + m^2 → 16 − 8m + m^2 = 0
With quadratics, it's difficult to tell sufficiency without solving.
This is because sometimes quadratics yield a single repeated root, and sometimes they yield two different values.
m^2 − 8m + 16 = (m − 4)(m − 4) = (m − 4)^2
If (m − 4)^2 = 0, then m = 4
As b = m^2 → b = 4^2 → b = 16
Able to determine m + b = 4 + 16 = 20
Sufficient.

Hi, I want to know if we have simpler solution for this question, please.

Originally posted by goodyear2013 on 12 Jan 2014, 03:56.
Last edited by Bunuel on 12 Jan 2014, 05:14, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 47202
Re: The slope of line n in the xy-plane is not 0 and the y-inter  [#permalink]

### Show Tags

12 Jan 2014, 06:49
2
1
goodyear2013 wrote:
The slope of line n in the xy-plane is not 0 and the y-intercept of line n in the xy-plane is not 0. The equation of line n is y = mx + b, where m and b are constants. What is the value of m + b?

(1) The y-intercept is equal to the square of the x-intercept.
(2) The line goes through the point (−8, −16).

OE
(1): By definition, y-intercept of a line in form y = mx + b is equal to b. x-intercept is value of x when y = 0.
y = mx + b → 0 = mx + b → mx = −b → x = -(b/m)
Thus, y-intercept is b & x-intercept is –(b/m).
Since y-intercept is square of x-intercept, we can create equation: b = (-b/m)^2 → m^2*b= b^2
Since we are told in question stem that b does not equal 0, we can divide both sides by b. m^2= b
Since we know that b is equal to m^2, we can substitute that value into equation of line n.
y = mx + b → y = mx + m^2
"what is value of m + b?" Different values of m lead to different values for b.
So different values for m lead to different values for m + b.
For example,
if m = 1, then b = 1^2 = 1 → m + b = 1 + 1 = 2
If m = 2, then b = m^2 = 4 → m + b = 2 + 4 = 6
Insufficient.

(2): In order to determine equation of a line, it's necessary to have either two points, or one point and slope. Therefore, it is impossible to derive an equation of a line from simply one point on line. There are infinitely many different lines that go through point (−8, −16). So there are infinitely many different possible values of m + b.
Insufficient.

Combined: From (1), equation of line n is of form y = mx + m^2, where m is slope and m≠ 0.
(2) says that line goes through point (−8, −16). Remember that any paired point in form (x, y) represents a pair of values that could satisfy equation. In other words, first term in ordered pair can substitute in for x, and second term can be substituted in for y. Substituting −8 for x and −16 for y, we have:
−16 = m(−8) + m^2 → −16 = −8m + m^2 → 16 − 8m + m^2 = 0
With quadratics, it's difficult to tell sufficiency without solving.
This is because sometimes quadratics yield a single repeated root, and sometimes they yield two different values.
m^2 − 8m + 16 = (m − 4)(m − 4) = (m − 4)^2
If (m − 4)^2 = 0, then m = 4
As b = m^2 → b = 4^2 → b = 16
Able to determine m + b = 4 + 16 = 20
Sufficient.

Hi, I want to know if we have simpler solution for this question, please.

The slope of line n in the xy-plane is not 0 and the y-intercept of line n in the xy-plane is not 0. The equation of line n is y = mx + b, where m and b are constants. What is the value of m + b?

(1) The y-intercept is equal to the square of the x-intercept. The y-intercept is the value of y for x=0, so b, and the x-intercept is the value of x for y=0, so -b/m. Thus we are given that $$b=\frac{b^2}{m^2}$$ --> reduce by b, which we know is not 0 to get: $$m^2=b$$. Not sufficient to get the value of m+b.

(2) The line goes through the point (−8, −16). Clearly insufficient: one point of a line cannot give neither the slope nor the y-intercept of it.

(1)+(2) From (2) we have that $$-16=-8m+b$$ and from (1) we have that $$m^2=b$$ --> substitute: $$-16=-8m+m^2$$ --> $$(m-4)^2=0$$ --> $$m=4$$ --> $$b=m^2=16$$ --> $$m+b=20$$. Sufficient.

Hope it helps.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 7335
Re: The slope of line n in the xy-plane is not 0 and the y-inter  [#permalink]

### Show Tags

22 Oct 2017, 02:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The slope of line n in the xy-plane is not 0 and the y-inter &nbs [#permalink] 22 Oct 2017, 02:44
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.