Last visit was: 03 Aug 2024, 07:08 It is currently 03 Aug 2024, 07:08
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# In the xy-coordinate plane, line A is defined by the equation j*x-y=-7

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 19 May 2015
Posts: 6
Own Kudos [?]: 252 [121]
Given Kudos: 4
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11811 [19]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
SVP
Joined: 20 Mar 2014
Posts: 2356
Own Kudos [?]: 3653 [9]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
General Discussion
Manager
Joined: 31 Jul 2014
Posts: 107
Own Kudos [?]: 126 [0]
Given Kudos: 373
GMAT 1: 630 Q48 V29
Re: In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
Engr2012 wrote:
Tornikea wrote:
In the XY-coordinate plane, line A is defined by the equation j*x-y=-7 and line B is defined by the equation 3*x+2*y=k

If line A and line B are not parallel, at what point do they intersect?

(1) Line A passes through the point (3,1)

(2) Line B passes through the point (0,7)

Given: A: y = jx+7, B : y = -1.5x+k/2

As A is NOT parallel to B ---> j $$\neq$$-1.5 ....(a)

Per statement 1, A passes through (3,1), without complete equation of B, we will not be able to solve this question. Not sufficient.

Check: solving the 2 equations y = -2x+7 and y = -1.5x+k/2, we get x = 14-k and y = 2k-21. Thus without the value 'k' we dont know the exact point of intersection.

Per statement 2, B passes through (0,7), thus 7 = 0+k/2 ---> k = 14. Thus, equation of B is y = -1.5x+7.

Solving for A and B , we get j = -1.5 but as per (a) above, j can not be = -1.5 The only case possible is for (0,7) to be the actual point of interesection. Sufficient.

Hope this helps.

Sorry, red part is not clear, you solved A and B , got j=-1.5 --> The only case possible is for (0,7) to be the actual point of interesection, can you please elaborate ..please
B: y = -1.5x+7
A: y = jx+7
SVP
Joined: 20 Mar 2014
Posts: 2356
Own Kudos [?]: 3653 [1]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Re: In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
1
Kudos
Engr2012 wrote:
Tornikea wrote:
In the XY-coordinate plane, line A is defined by the equation j*x-y=-7 and line B is defined by the equation 3*x+2*y=k

If line A and line B are not parallel, at what point do they intersect?

(1) Line A passes through the point (3,1)

(2) Line B passes through the point (0,7)

Given: A: y = jx+7, B : y = -1.5x+k/2

As A is NOT parallel to B ---> j $$\neq$$-1.5 ....(a)

Per statement 1, A passes through (3,1), without complete equation of B, we will not be able to solve this question. Not sufficient.

Check: solving the 2 equations y = -2x+7 and y = -1.5x+k/2, we get x = 14-k and y = 2k-21. Thus without the value 'k' we dont know the exact point of intersection.

Per statement 2, B passes through (0,7), thus 7 = 0+k/2 ---> k = 14. Thus, equation of B is y = -1.5x+7.

Solving for A and B , we get j = -1.5 but as per (a) above, j can not be = -1.5 The only case possible is for (0,7) to be the actual point of interesection. Sufficient.

Hope this helps.

Sorry, red part is not clear, you solved A and B , got j=-1.5 --> The only case possible is for (0,7) to be the actual point of interesection, can you please elaborate ..please
B: y = -1.5x+7
A: y = jx+7

Sure, look below.

From statement 2, you get the equation of line B: y = -1.5x+7 and A: y= jx+7

Now,when you plot A and B such that j $$\neq$$-1.5, you will see that

y = -1.5x+7 and
y = jx+7 (with j = anything BUT -1.5)

will intersect at (0,7) ONLY. Try with j = 2 or 5 or 10 or -4.

Case 1: j = 2 ---> A: y = 2x+7 and B: y = -1.5x+7 ---> (0,7) is the ONLY point of intersection.

Case 2: j = 10 ---> A: y = 10x+7 and B: y = -1.5x+7 ---> (0,7) is the ONLY point of intersection.

Case 3: j = -10 ---> A: y = -10x+7 and B: y = -1.5x+7 ---> (0,7) is the ONLY point of intersection.

Alternately, you can see that once you get the equations of A and B as

B: y = -1.5x+7
A: y = jx+7,

X-coordinate of intersection ----> -1.5x+7=jx+7 ---> x = 0. Put this value of x back into any 1 of the 2 equations, you will get y = 7 . Finally, note that the point of intersection is a constant/unique value without 'j' or 'k'

Hence B is sufficient to arrive at a unique answer.

Hope this helps.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17105 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

In the XY-coordinate plane, line A is defined by the equation j*x-y=-7 and line B is defined by the equation 3*x+2*y=k

If line A and line B are not parallel, at what point do they intersect?

(1) Line A passes through the point (3,1)

(2) Line B passes through the point (0,7)

Transforming the original condition and question, jx-y=-7, 3x+2y=k and we have 2 variable (j,k), 1 equation. Since we need to match the number of variables and equations, we need 1 more equation and sine we have 1 each in 1) and 2), D is likely the answer.

In case of 1), 3j-1=-7, j=-2 but we don't know what k is, thus we can't find the point of interaction
In case of 2), 3*0+2*7=k gives us k=14 and line B: 3x+2y=14, y=-1.5x+7. Since line A cross (0,7) in jx-y=-7, line A and line B are not parallel and they meet in (0,7). Thus the condition is sufficient.Therefore the answer is B.

Originally posted by MathRevolution on 03 Sep 2015, 04:47.
Last edited by MathRevolution on 06 Sep 2015, 20:50, edited 1 time in total.
SVP
Joined: 20 Mar 2014
Posts: 2356
Own Kudos [?]: 3653 [0]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Re: In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

In the XY-coordinate plane, line A is defined by the equation j*x-y=-7 and line B is defined by the equation 3*x+2*y=k

If line A and line B are not parallel, at what point do they intersect?

(1) Line A passes through the point (3,1)

(2) Line B passes through the point (0,7)

Transforming the original condition and question, jx-y=-7, 3x+2y=k and we have 2 variable (j,k), 1 equation. Since we need to match the number of variables and equations, we need 1 more equation and sine we have 1 each in 1) and 2), D is likely the answer.

In case of 1), 3j-1=-7, j=-2 but we don't know what k is, thus we can't find the point of interaction
In case of 2), 3*0+2*7=k gives us k=14 and line B: 3x+2y=14, y=-1.5x+7. Since line A cross (0,7) in jx-y=-7, line A and line B are not parallel and they meet in (0,7). Thus the condition is sufficient.Therefore the answer is B.

IMO, your quote "Remember equal number of variables and equations ensures a solution." is a bit misleading as it should be stated as "Remember equal number of variables and DISTINCT equations ensures a solution.".

Case in point,

2a+3b =16
4a+6b=-3.5. Although you have 2 equations and 2 variables, you still can not find the solution as the 2 equations are necessarily the same.
Manager
Joined: 24 Jan 2017
Posts: 121
Own Kudos [?]: 328 [2]
Given Kudos: 106
GMAT 1: 640 Q50 V25
GMAT 2: 710 Q50 V35
GPA: 3.48
Re: In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
1
Kudos
1
Bookmarks
Good question. Just learn my own lesson that never ever overlook a single detail of information provided that is, in this case, (0,7)

General equation for any line on x-y coordinate: y=ax+b
--> Line A: y=j*x+7
Line B: y=-1.5x + 0.5k

(0,7) is definitely a turning point, which helps 0.5k=7 matched exactly with 7 in equation of line A. Remember (0,7) is the one and only point that makes statement (2) become sufficient. Otherwise, if that is another value, let's say (0,5), we cannot find intersect point with only statement (2), because j*x+7=-1.5x+5, then (j+1.5)x = -2. In this case, we cannot find out a consistent answer.

Well in the first place, I just thought we cannot work out intersect point without knowing proper equations of lines A and B. That's why I ended up with option (C) in only 20s. Oh goshhhh too fast too "dangerous":'(
Director
Joined: 20 Sep 2016
Posts: 556
Own Kudos [?]: 959 [1]
Given Kudos: 632
Location: India
Concentration: Strategy, Operations
GPA: 3.6
WE:Operations (Consumer Products)
In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
1
Kudos
Cool Cool Cool..

First lets absorb the info and infer as much as we can >
equation of line >> y=mx+b >> m=slope >> b = y intercept (0,b)
line A: jx-y=-7 >> y=jx+7 >> get y intercept>> put x=0 > y=7 (y intercept)> Line A intersects Y axis at (0,7).
Line B: 3x+2y=k >> y= -1.5x+k/2 >> K is the Y intercept of line B.

Line A NOT PARALLEL to line B >> slopes of parallel lines are equal>> given- lines not parallel. Therefore slopes are not equal >> slope of B =-1.5 >> slope of A CANNOT BE -1.5.

Question- Point of intersection of lines A & B.

St 1. line A passes through the point (3,1) >> we can get the slope of line A >> m=(y1-y2/x1-x2) >> but line B can pass through anywhere . INSUFFICIENT.

st2. Line B passes through point (0,7) >> but (0,7) is also a point on Line A as (0,7) is y intercept of line A >> Therefore point of intersection = (0,7) >> SUFFICIENT.
Senior Manager
Joined: 29 Dec 2017
Posts: 302
Own Kudos [?]: 313 [0]
Given Kudos: 273
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE:Marketing (Telecommunications)
In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
To those who struggle with questions about xy-plane: 99% of such questions can be solved drawing lines on xy plane, without messing with formulae. Just start drawing, and the answer will jump on you.
Director
Joined: 29 Jun 2017
Posts: 776
Own Kudos [?]: 403 [0]
Given Kudos: 2198
Re: In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
this is tricky. we do not need to have 2 identified lines. we need just that the two line intersect at a specific point. mayber one line is unidentifie or mayby both lines are unidentified but both of them need to intersect at one specific point for us to find out the point.

with this thinking in mind, we anticipate that we need to find the specific point, not find 2 identified lines.

i dont think that we can do so on test day
VP
Joined: 11 Aug 2020
Posts: 1245
Own Kudos [?]: 209 [1]
Given Kudos: 332
Re: In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
1
Bookmarks
In the XY-coordinate plane, line A is defined by the equation j*x-y=-7 and line B is defined by the equation 3*x+2*y=k

A: y = jx + 7
B: y = -3/2x + k/2

If line A and line B are not parallel, at what point do they intersect?

(1) Line A passes through the point (3,1)
y = jx + 7
1 = 3j + 7
j = -2

y = -2x + 7

Insufficient

(2) Line B passes through the point (0,7)
y = -3/2x + k/2
7= -3/2(0) + k/2
k = 14

y = -3/2x + 7

Sufficient (A and B each have the same y-intercept: 0,7)

B
Non-Human User
Joined: 09 Sep 2013
Posts: 34222
Own Kudos [?]: 857 [0]
Given Kudos: 0
Re: In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
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: In the xy-coordinate plane, line A is defined by the equation j*x-y=-7 [#permalink]
Moderator:
Math Expert
94776 posts