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In the xycoordinate plane, line A is defined by the equation j*xy=7
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Updated on: 01 Sep 2015, 08:30
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In the XYcoordinate plane, line A is defined by the equation j*xy=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)
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Originally posted by Tornikea on 01 Sep 2015, 08:21.
Last edited by ENGRTOMBA2018 on 01 Sep 2015, 08:30, edited 1 time in total.
Formatted the question




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In the xycoordinate plane, line A is defined by the equation j*xy=7
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Updated on: 03 Sep 2015, 04:23
Tornikea wrote: In the XYcoordinate plane, line A is defined by the equation j*xy=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) Please follow the posting guidelines. 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 = 14k and y = 2k21. 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 x, we get 1.5x+7=jx+7 > x(j+1.5) =0 > either x =0 or j=1.5 but as per (a) above, j \(\neq\)1.5 The only case possible is for x=0 > y =7 to be the actual point of intersection. B is the correct answer. Alternately, you can see that once you get the equations of A and B as B: y = 1.5x+7 A: y = jx+7, Xcoordinate 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.
Originally posted by ENGRTOMBA2018 on 01 Sep 2015, 08:44.
Last edited by ENGRTOMBA2018 on 03 Sep 2015, 04:23, edited 1 time in total.
Edited the wording to make it clearer.




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Re: In the xycoordinate plane, line A is defined by the equation j*xy=7
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02 Sep 2015, 06:23
Engr2012 wrote: Tornikea wrote: In the XYcoordinate plane, line A is defined by the equation j*xy=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) Please follow the posting guidelines. 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 = 14k and y = 2k21. 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.B is the correct answer. 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



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Re: In the xycoordinate plane, line A is defined by the equation j*xy=7
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02 Sep 2015, 06:36
anupamadw wrote: Engr2012 wrote: Tornikea wrote: In the XYcoordinate plane, line A is defined by the equation j*xy=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) Please follow the posting guidelines. 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 = 14k and y = 2k21. 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.B is the correct answer. 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, Xcoordinate 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.



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In the xycoordinate plane, line A is defined by the equation j*xy=7
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Updated on: 06 Sep 2015, 20:50
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 XYcoordinate plane, line A is defined by the equation j*xy=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, jxy=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), 3j1=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 jxy=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.
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Re: In the xycoordinate plane, line A is defined by the equation j*xy=7
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03 Sep 2015, 07:24
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 XYcoordinate plane, line A is defined by the equation j*xy=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, jxy=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), 3j1=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 jxy=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.



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Re: In the xycoordinate plane, line A is defined by the equation j*xy=7
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28 Jun 2017, 20:54
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 xy 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":'(



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Re: In the xycoordinate plane, line A is defined by the equation j*xy=7
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25 Jun 2018, 21:00
Hi All, We're told that In the XYcoordinate plane, line A is defined by the equation (J)(X)  Y = 7 and line B is defined by the equation 3X + 2Y = K and that the two lines are NOT parallel. We're asked at what point they intersect. to start, with graphing questions, it usually helps to convert the given equations into slopeintercept format (re: Y = MX + B). In this case, the lines would be: Y = (J)(X) + 7 Y = 3x/2 + K/2 We have to figure out at what point will X and Y be the same for BOTH equations. 1) Line A passes through the point (3,1) With the coordinate in Fact 1, we can plug in and get.... 1 = J(3) + 7 6 = 3J 2 = J Now our two equations are: Y = 2X + 7 Y = 3X/2 + K/2 Unfortunately, we still have an unknown (K) and that keeps us from figuring out where the lines intersect. Fact 1 is INSUFFICIENT 2) Line B passes through the point (0,7) With the coordinate in Fact 2, we can plug in and get.... 7 = 0 + K/2 K = 14 Now, the two lines are; Y = 3X/2 + 7 Y = (J)(X) + 7 Notice how the yintercepts are the same in both equations? We now KNOW where the two lines intersect: at (0,7) Fact 2 is SUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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In the xycoordinate plane, line A is defined by the equation j*xy=7
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21 Jul 2018, 10:48
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: jxy=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=(y1y2/x1x2) >> 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.



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In the xycoordinate plane, line A is defined by the equation j*xy=7
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21 Jul 2018, 16:17
To those who struggle with questions about xyplane: 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.
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In the xycoordinate plane, line A is defined by the equation j*xy=7 &nbs
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