Author 
Message 
TAGS:

Hide Tags

Director
Joined: 29 Nov 2012
Posts: 813

In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
19 Jan 2013, 01:43
Question Stats:
67% (00:53) correct 33% (01:06) wrong based on 495 sessions
HideShow timer Statistics
In the xyplane, points A, B and C are not on the same line. Is the slope of line BC negative? (1) The slope of line AB is 1. (2) The measure of angle ABC is 37 degrees.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html




Senior Manager
Joined: 27 Jun 2012
Posts: 390
Concentration: Strategy, Finance

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
19 Jan 2013, 12:53
Attachment:
Line AB with negative slope.jpg [ 348.17 KiB  Viewed 14841 times ]
Method 2(1) The slope of line AB is 1 INSUFFICIENT: This tells line AB has equation \(y = x + constant\) (with slope m=1) However, it does not give any information about point C. (2) The measure of angle ABC is 37 degrees. INSUFFICIENT: this statement doesn't give information about orientation/locations of points ABC Combining (1) & (2)  Here you solve it by plotting diagram SUFFICIENT: As line AB has 1 i.e. negative slope, it can be represented with equation \(y = x\) (assume constant zero). Plot line AB such that it makes \(45^{\circ}\) with X axis with negative slope. Plot point C such that BC makes \(37^{\circ}\) with AB. You can observe that the line BC shows negative slope. No matter where you plot point C (either left or right) w.r.t. line AB, the slope of the line is always negative. Same is the case, if you plot ABC in any quadrant. The line BC can make positive slope ONLY IF it makes MORE than \(45^{\circ}\) angle with AB. Hence choice(C) is the answer.
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here




Manager
Joined: 27 Feb 2012
Posts: 129

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
19 Jan 2013, 03:46
fozzzy wrote: In the xyplane, points A, B and C are not on the same line. Is the slope of line BC negative?
1. The slope of line AB is 1. 2. The measure of angle ABC is 37 degrees. Tricky one. A, B and C are not on the same line. 1) Slope of line AB is 1. No information on point C. Not sufficient. 2) Measure of Angle ABC Is 37 deg. Again no information on which way angle ABC orientation is. Combine We know angle ABC equals 37 degrees, which is the same as saying: lines AB and BC intersect at a 37 degree angle. This means, the orientation of BC must be 37 degrees different from the orientation of AB. There are two possibilities a) BC's slope is less negative than AB. b) BC's slope is more negative than AB In either case, BC is still oriented negative slope.
_________________

Please +1 KUDO if my post helps. Thank you.



Senior Manager
Joined: 27 Jun 2012
Posts: 390
Concentration: Strategy, Finance

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
19 Jan 2013, 12:36
Method 1 See next post for Method 2 (1) The slope of line AB is 1 INSUFFICIENT: This tells line AB has 1 negative slope and hence makes \(45^{\circ}\) angle with X axis. However, it does not give any information about point C. (2) The measure of angle ABC is 37 degrees. INSUFFICIENT: this statement doesn't give information about orientation/locations of points ABC Combining (1) & (2)  Here you can solve it even without drawing diagram. SUFFICIENT: With negative slope 1, line AB makes \(45^{\circ}\) angle with X axis. So any line (e.g. BC) making angle less than \(45^{\circ}\) with line AB will have negative slope, similarly line making more than \(45^{\circ}\) angle with AB will turn into positive slope. In this case BC makes angle \(37^{\circ}\) with AB, hence it has negative slope (regardless of which quadrants these points lies in) Hence choice(C) is the answer.
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Intern
Joined: 23 Jan 2013
Posts: 6

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
26 Jan 2013, 10:05
m still confused....wat is the concept of slope?How do we know that AB has a negative slope?can sum1 plz expalin



Senior Manager
Joined: 27 Jun 2012
Posts: 390
Concentration: Strategy, Finance

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
26 Jan 2013, 10:36
nimishasharma88 wrote: m still confused....wat is the concept of slope?How do we know that AB has a negative slope?can sum1 plz expalin Below is the snippet from GMAT Club Math book: mathcoordinategeometry87652.html a must read for deep dive in coordinate geometry. This topic should explain the concept of slope: Slope of a LineThe slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is: \(m=\frac{y_2y_1}{x_2x_1}\) If the equation of the line is given in the Pointintercept form: \(y=mx+b\), then \(m\) is the slope. This form of a line's equation is called the slopeintercept form, because \(b\) can be interpreted as the yintercept of the line, the ycoordinate where the line intersects the yaxis. If the equation of the line is given in the General form:\(ax+by+c=0\), then the slope is \(\frac{a}{b}\) and the y intercept is \(\frac{c}{b}\). SLOPE DIRECTIONThe slope of a line can be positive, negative, zero or undefined. Positive slopeHere, y increases as x increases, so the line slopes upwards to the right. The slope will be a positive number. The line below has a slope of about +0.3, it goes up about 0.3 for every step of 1 along the xaxis. Negative slopeHere, y decreases as x increases, so the line slopes downwards to the right. The slope will be a negative number. The line below has a slope of about 0.3, it goes down about 0.3 for every step of 1 along the xaxis. Zero slopeHere, y does not change as x increases, so the line in exactly horizontal. The slope of any horizontal line is always zero. The line below goes neither up nor down as x increases, so its slope is zero. Undefined slopeWhen the line is exactly vertical, it does not have a defined slope. The two x coordinates are the same, so the difference is zero. The slope calculation is then something like \(slope=\frac{15}{0}\) When you divide anything by zero the result has no meaning. The line above is exactly vertical, so it has no defined slope. SLOPE AND QUADRANTS:1. If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III. 2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV. 3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin \((0,0)\) OR is parallel to either of axis crosses only two quadrants. 4. If a line is horizontal it has a slope of \(0\), is parallel to Xaxis and crosses quadrant I and II if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect. 5. If a line is vertical, the slope is not defined, line is parallel to Yaxis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is \(x=a\), where a is xintercept. 6. For a line that crosses two points \((x_1,y_1)\) and \((x_2,y_2)\), slope \(m=\frac{y_2y_1}{x_2x_1}\) 7. If the slope is 1 the angle formed by the line is \(45\) degrees. 8. Given a point and slope, equation of a line can be found. The equation of a straight line that passes through a point \((x_1, y_1)\) with a slope \(m\) is: \(y  y_1 = m(x  x_1)\)
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Director
Joined: 29 Nov 2012
Posts: 813

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
26 Jan 2013, 23:29
nimishasharma88 wrote: m still confused....wat is the concept of slope?How do we know that AB has a negative slope?can sum1 plz expalin Prapon has provided the theory if you want a practice question check this link out below. Its a copy of a gmat prep question. inthexycoordinatesystemdoanypointsonlinekliein127635.html#p1169038
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 477
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
06 Mar 2013, 21:55
PraPon wrote: Attachment: Line AB with negative slope.jpg Method 2(1) The slope of line AB is 1 INSUFFICIENT: This tells line AB has equation \(y = x + constant\) (with slope m=1) However, it does not give any information about point C. (2) The measure of angle ABC is 37 degrees. INSUFFICIENT: this statement doesn't give information about orientation/locations of points ABC Combining (1) & (2)  Here you solve it by plotting diagram SUFFICIENT: As line AB has 1 i.e. negative slope, it can be represented with equation \(y = x\) (assume constant zero). Plot line AB such that it makes \(45^{\circ}\) with X axis with negative slope. Plot point C such that BC makes \(37^{\circ}\) with AB. You can observe that the line BC shows negative slope. No matter where you plot point C (either left or right) w.r.t. line AB, the slope of the line is always negative. Same is the case, if you plot ABC in any quadrant. The line BC can make positive slope ONLY IF it makes MORE than \(45^{\circ}\) angle with AB. Hence choice(C) is the answer.Just trying to cement my understanding: So if you have slope=1, line passes thru origin and makes 45 degree with X axis and line will be going upwards as you move from ve to +ve along teh x axis.. and if you have slope=  1, line passes thru origin and makes 45 degree with X axis and line will be going downwards as you move from ve to +ve along teh x axis right?
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Senior Manager
Joined: 27 Jun 2012
Posts: 390
Concentration: Strategy, Finance

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
06 Mar 2013, 22:30
Sachin9 wrote: PraPon wrote: Attachment: Line AB with negative slope.jpg Method 2(1) The slope of line AB is 1 INSUFFICIENT: This tells line AB has equation \(y = x + constant\) (with slope m=1) However, it does not give any information about point C. (2) The measure of angle ABC is 37 degrees. INSUFFICIENT: this statement doesn't give information about orientation/locations of points ABC Combining (1) & (2)  Here you solve it by plotting diagram SUFFICIENT: As line AB has 1 i.e. negative slope, it can be represented with equation \(y = x\) (assume constant zero). Plot line AB such that it makes \(45^{\circ}\) with X axis with negative slope. Plot point C such that BC makes \(37^{\circ}\) with AB. You can observe that the line BC shows negative slope. No matter where you plot point C (either left or right) w.r.t. line AB, the slope of the line is always negative. Same is the case, if you plot ABC in any quadrant. The line BC can make positive slope ONLY IF it makes MORE than \(45^{\circ}\) angle with AB. Hence choice(C) is the answer.Just trying to cement my understanding: So if you have slope=1, line passes thru origin and makes 45 degree with X axis and line will be going upwards as you move from ve to +ve along teh x axis.. and if you have slope=  1, line passes thru origin and makes 45 degree with X axis and line will be going downwards as you move from ve to +ve along teh x axis right? That is correct. Consider line with positive slope as positive slash '/' and negative slope as backward slash '\'.
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 615

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
06 Mar 2013, 23:27
fozzzy wrote: In the xyplane, points A, B and C are not on the same line. Is the slope of line BC negative?
(1) The slope of line AB is 1. (2) The measure of angle ABC is 37 degrees. The angle (x) between two lines L1 and L2 with respective slopes as m1 and m2 : tanx = mod[(m1m2)/(1+m1*m2)] From F.S 1, we have m1=1. Clearly Insufficient. From F.S 2, we have x= 37 degrees. We know that value of tan(30) = 1/\(\sqrt{3}\). So tan 37 will be a little more in value than this. But we don't know anything about m1 and m2. Insufficient. Combining both, we have tan(37) = mod[m1+1/(1m1)]. As tan(37) has a positive value and less than 1, lets represent it by a constant value P and 0<P<1. Now, removing the mod sign, we have either (m1+1)/(1m1) = P or P. In either case, we have the value of m1 as negative. Sufficient. C.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Retired Moderator
Joined: 19 Apr 2013
Posts: 643
Concentration: Strategy, Healthcare
GPA: 4

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
16 Dec 2014, 05:25
Bunuel, would be glad to know your solution for this question.
_________________
If my post was helpful, press Kudos. If not, then just press Kudos !!!



Manager
Joined: 26 May 2013
Posts: 61

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
09 Jul 2015, 18:16
Why can't the line AB be at a different degree? The slope is given as 1. Is it not possible to have the line/slope(1) AB at any other degree other than 45? Thanks.



Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
09 Jul 2015, 18:33
Amit0507 wrote: Why can't the line AB be at a different degree? The slope is given as 1. Is it not possible to have the line/slope(1) AB at any other degree other than 45? Thanks. No, as slope = tan (angle) where 'angle' = angle that a line makes with the positive direction of the xaxis, i.e. if \(m_{AB}\) = Slope of line AB, then, based on the attached figure, tan (45 deg) = 1 and tan (45) or tan (135) = 1. Thus, if you are given that slope of a line is 1 or 1, the line MUST be inclined at 45 degrees or 135 degrees respectively to the positive direction of the Xaxis. I have shown in the 2nd figure, why the angle will be 45 degrees, if the slope of a line is 1. Let me know if anything is not clear.
Attachments
IMG_1224.JPG [ 60.52 KiB  Viewed 9509 times ]
IMG_1223.JPG [ 49.07 KiB  Viewed 9512 times ]



Senior Manager
Status: Always try to face your worst fear because nothing GOOD comes easy. You must be UNCOMFORTABLE to get to your COMFORT ZONE
Joined: 15 Aug 2014
Posts: 322
Concentration: Marketing, Technology
GMAT 1: 570 Q44 V25 GMAT 2: 600 Q48 V25
WE: Information Technology (Consulting)

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
11 Jul 2016, 09:36
fozzzy wrote: In the xyplane, points A, B and C are not on the same line. Is the slope of line BC negative?
(1) The slope of line AB is 1. (2) The measure of angle ABC is 37 degrees. Hi Bunuel, Can you please provide your solution for this question! Many thanks in advance
_________________
"When you want to succeed as bad as you want to breathe, then you’ll be successful.”  Eric Thomas
I need to work on timing badly!!



Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 580

In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
11 Jul 2016, 11:16
This is a fantastic example of a 'just draw it and look at it' DS geometry problem! You can get away with almost no math here. Try drawing a couple of lines with a slope of 1, and labeling the points A, B, and C accordingly. You'll find that it's impossible to draw a set of points where BC has a positive slope. Critically, on test day, you don't have to understand mathematically why that's the case, as long as you can convince yourself that it's true. Complex diagrams and explanations like the ones above are really great when you're reviewing, but they also sometimes make people think that you'll have to go through all of that math within 2 minutes on the test, which makes this problem look impossible. You don't! It's okay to just draw it, try a couple of cases, and look at it. That's just as valid a solution as the 'mathematical' one, and it gives you the same correct answer. Here's what my scratch work looked like  this one took me about 45 seconds:
Attachments
slope_abc.png [ 9.64 KiB  Viewed 6052 times ]
_________________



Senior Manager
Status: Always try to face your worst fear because nothing GOOD comes easy. You must be UNCOMFORTABLE to get to your COMFORT ZONE
Joined: 15 Aug 2014
Posts: 322
Concentration: Marketing, Technology
GMAT 1: 570 Q44 V25 GMAT 2: 600 Q48 V25
WE: Information Technology (Consulting)

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
12 Jul 2016, 01:53
Hi ccooley, Thanks for the explanation!
_________________
"When you want to succeed as bad as you want to breathe, then you’ll be successful.”  Eric Thomas
I need to work on timing badly!!



CEO
Joined: 12 Sep 2015
Posts: 2702
Location: Canada

Re: In the xyplane, points A, B and C are not on the same line.
[#permalink]
Show Tags
17 Jul 2018, 08:33
fozzzy wrote: In the xyplane, points A, B and C are not on the same line. Is the slope of line BC negative?
(1) The slope of line AB is 1. (2) The measure of angle ABC is 37 degrees. We can quickly see that statements 1 and 2 (alone) are NOT SUFFICIENT. This brings us to... Statements 1 and 2 combined If we draw the line segment AB with slope 1, then we get something like this: If we add some lines parallel to the x and yaxes, we need to recognize that we get 45degree angles at point B So, if we add a 37degree angle at point B, we get two possible scenarios: Scenario #1or Scenario #2In BOTH possible scenarios, the slope of line BC is definitely negative. Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer = C Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com




Re: In the xyplane, points A, B and C are not on the same line. &nbs
[#permalink]
17 Jul 2018, 08:33






