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A student draws 35 lines in the XY plane, none of which are vertical
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09 Jul 2018, 03:29
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A student draws 35 lines in the XY plane, none of which are vertical and 15 of which have a positive slope. Of those with positive slope, 1/3 also have a positive Yintercept. If 23 lines have a Yintercept less than or equal to zero, how many lines contain no point in Quadrant I? A: 0 B: 7 C: 13 D: 20 E: 35
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A student draws 35 lines in the XY plane, none of which are vertical
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09 Jul 2018, 03:56
Raksat wrote: A student draws 35 lines in the XY plane, none of which are vertical and 15 of which have a positive slope. Of those with positive slope, 1/3 also have a positive Yintercept. If 23 lines have a Yintercept less than or equal to zero, how many lines contain no point in Quadrant I? A: 0 B: 7 C: 13 D: 20 E: 35 Hi... 35 lines.. 15 positive slope that if x increases y increases and vice versa.. So 1/3 have a positive y intercept, so remaining 2/3 or 10 have negative y intercept or y is 0 But total 23 have negative or zero y intercept, so 2310=13 of these have negative slope.. So these 13 will never cross the quad I Ans 13
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A student draws 35 lines in the XY plane, none of which are vertical
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09 Jul 2018, 04:02
chetan2u wrote: So 1/3 have a positive y intercept, so remaining 2/3 or 10 have negative y intercept..
Ans 13 chetan2uShouldn't the remaining 10 lines have zero or negative yintercept ? The final answer doesn't change anyway.
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Re: A student draws 35 lines in the XY plane, none of which are vertical
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09 Jul 2018, 04:07
workout wrote: chetan2u wrote: So 1/3 have a positive y intercept, so remaining 2/3 or 10 have negative y intercept..
Ans 13 chetan2uShouldn't the remaining 10 lines have zero or negative yintercept ? The final answer doesn't change anyway. Yes , it will be 0 or negative... You are correct. Doesn't effect the answer so didn't mention it.
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Re: A student draws 35 lines in the XY plane, none of which are vertical
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09 Jul 2018, 11:45
Raksat wrote: A student draws 35 lines in the XY plane, none of which are vertical and 15 of which have a positive slope. Of those with positive slope, 1/3 also have a positive Yintercept. If 23 lines have a Yintercept less than or equal to zero, how many lines contain no point in Quadrant I? A: 0 B: 7 C: 13 D: 20 E: 35 There are 8 categories of lines (i) positive slope, positive yintercept  x (ii) positive slope, passing through origin  y (iii) positive slope, negative yintercept  z (iv) negative slope & positive yintercept  a (v) negative slope & passing through origin  b (vi) negative slope & negative yintercept  c (vii) parallel to x  axis & with positive yintercept  p (viii) parallel to x  axis & with negative yintercept  q Lines x, y, z, a, p pass through Quadrant I, we are asked to find (b + c + q) Given x + y + z + a + b + c + p + q = 35 x + y + z = 15 x = 15/3 = 5, hence y + z = 10 y + z + b + c + q = 23 hence b + c + q = 23  10 = 13 Answer C. Thanks, GyM
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Re: A student draws 35 lines in the XY plane, none of which are vertical
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17 Aug 2018, 07:36
chetan2u wrote: Raksat wrote: A student draws 35 lines in the XY plane, none of which are vertical and 15 of which have a positive slope. Of those with positive slope, 1/3 also have a positive Yintercept. If 23 lines have a Yintercept less than or equal to zero, how many lines contain no point in Quadrant I? A: 0 B: 7 C: 13 D: 20 E: 35 Hi... 35 lines.. 15 positive slope that if x increases y increases and vice versa.. So 1/3 have a positive y intercept, so remaining 2/3 or 10 have negative y intercept or y is 0 But total 23 have negative or zero y intercept, so 2310=13 of these have negative slope.. So these 13 will never cross the quad I Ans 13 Total 35 lines 23 of those lines have y intercept \(\leq\) 0 5 of those lines have y intercept \(>\) 0 what about the remaining seven lines ? if they don't have a zero y intercept, or negative y intercept or positive y intercept , what kind of intercept do they have ? Is it possible to have a line with NO y intercept? Isn't it the same as having a zero Y intercept? if those 7 lines pass through the origin , then y intercept should be 0 and we should have 23 +7 lines having y intercept \(\leq\)0 Please account for those 7 lines . Thanks.
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Re: A student draws 35 lines in the XY plane, none of which are vertical
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19 Aug 2018, 10:12
Raksat wrote: A student draws 35 lines in the XY plane, none of which are vertical and 15 of which have a positive slope. Of those with positive slope, 1/3 also have a positive Yintercept. If 23 lines have a Yintercept less than or equal to zero, how many lines contain no point in Quadrant I? A: 0 B: 7 C: 13 D: 20 E: 35 Here is my approach. Line contains no point in Quadrant I means Line has Yintercept ≤ 0 AND negative slope Of the 15 lines with positive slope, 1/3 also have a positive Yintercept > remaining 2/3 * 15 = 10 lines have Yintercept ≤ 0 Of the 23 lines have Yintercept ≤ 0, 10 lines have Yintercept ≤ 0 AND positive slope > remaining 2310 = 13 lines Yintercept ≤ 0 and negative slope Answer C.
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Re: A student draws 35 lines in the XY plane, none of which are vertical
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19 Aug 2018, 10:22
Izzyjust5 wrote: Raksat wrote: A student draws 35 lines in the XY plane, none of which are vertical and 15 of which have a positive slope. Of those with positive slope, 1/3 also have a positive Yintercept. If 23 lines have a Yintercept less than or equal to zero, how many lines contain no point in Quadrant I? A: 0 B: 7 C: 13 D: 20 E: 35 Here is my approach. Line contains no point in Quadrant I means Line has Yintercept ≤ 0 AND negative slope Of the 15 lines with positive slope, 1/3 also have a positive Yintercept > remaining 2/3 * 15 = 10 lines have Yintercept ≤ 0 Of the 23 lines have Yintercept ≤ 0, 10 lines have Yintercept ≤ 0 AND positive slope > remaining 2310 = 13 lines Yintercept ≤ 0 and negative slope Answer C. That can be easily understood , can you help me understand , about the y intercept of the remaining 7 lines , positive 5 y intercept ,zero and less = 23 Y intercept , that makes 28, what about the y intercept of the remaining 7 lines ?
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Re: A student draws 35 lines in the XY plane, none of which are vertical
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19 Aug 2018, 10:28
stne wrote: chetan2u wrote: Raksat wrote: A student draws 35 lines in the XY plane, none of which are vertical and 15 of which have a positive slope. Of those with positive slope, 1/3 also have a positive Yintercept. If 23 lines have a Yintercept less than or equal to zero, how many lines contain no point in Quadrant I? A: 0 B: 7 C: 13 D: 20 E: 35 Hi... 35 lines.. 15 positive slope that if x increases y increases and vice versa.. So 1/3 have a positive y intercept, so remaining 2/3 or 10 have negative y intercept or y is 0 But total 23 have negative or zero y intercept, so 2310=13 of these have negative slope.. So these 13 will never cross the quad I Ans 13 Total 35 lines 23 of those lines have y intercept \(\leq\) 0 5 of those lines have y intercept \(>\) 0 what about the remaining seven lines ? if they don't have a zero y intercept, or negative y intercept or positive y intercept , what kind of intercept do they have ? Is it possible to have a line with NO y intercept? Isn't it the same as having a zero Y intercept?if those 7 lines pass through the origin , then y intercept should be 0 and we should have 23 +7 lines having y intercept \(\leq\)0 Please account for those 7 lines . Thanks. 5 of the 15 lines which have a positive slope have y intercept \(>\) 0, not 5 of the total 35 lines have y intercept \(>\) 0 In general, it is possible to have lines with NO yintercept. Those lines never intersect the yaxis, or in other words, those lines are vertical (parallel to the yaxis). It is not the same as having a zero yintercept. If a line is vertical and has a zero yintercept, it is yaxis. In this question, the stem clearly states that "A student draws 35 lines in the XY plane, none of which are vertical..." so it's not possible to have lines with NO yintercept in this case. Hope it's clear.
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A student draws 35 lines in the XY plane, none of which are vertical
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19 Aug 2018, 10:45
Izzyjust5 wrote: 5 of the 15 lines which have a positive slope have y intercept >> 0, not 5 of the total 35 lines have y intercept >> 0
In general, it is possible to have lines with NO yintercept. Those lines never intersect the yaxis, or in other words, those lines are vertical (parallel to the yaxis). It is not the same as having a zero yintercept. If a line is vertical and has a zero yintercept, it is yaxis. In this question, the stem clearly states that "A student draws 35 lines in the XY plane, none of which are vertical..." so it's not possible to have lines with NO yintercept in this case.
Hope it's clear.
I think you did not understand my question correctly. May be I am missing something total 35 lines , 15 have positive slope and 20 have 0 or negative slope ( 20 + 15 = 35) out of 15 having positive slope, 5 have positive Y intercept So 10 having positive slope have 0 or negative Y intercept So total 15 lines have positive slope = 5 lines have positive y intercept and 10 lines have , zero or negative y intercept. also we know total 23 lines have y intercept \(\leq\) 0 so 23 + 5 = 28 , what kind of y intercept do the remaining 7 lines have ? hope now my question is clear. Edit:Thank you , understood it , the answer I was looking for was this : Those 7 lines have positive y intercept but negative slope . So here is the break up Total 12 have positive y intercept out of which 5 have positive slope and 7 have zero or negative slope total 23 have zero or negative Y intercept out of which 10 have positive slope and 13 have 0 or negative slope . total 35 lines are now accounted for .
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Re: A student draws 35 lines in the XY plane, none of which are vertical
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19 Aug 2018, 11:11
stne wrote: Izzyjust5 wrote: 5 of the 15 lines which have a positive slope have y intercept >> 0, not 5 of the total 35 lines have y intercept >> 0
In general, it is possible to have lines with NO yintercept. Those lines never intersect the yaxis, or in other words, those lines are vertical (parallel to the yaxis). It is not the same as having a zero yintercept. If a line is vertical and has a zero yintercept, it is yaxis. In this question, the stem clearly states that "A student draws 35 lines in the XY plane, none of which are vertical..." so it's not possible to have lines with NO yintercept in this case.
Hope it's clear.
I think you did not understand my question correctly. May be I am missing something total 35 lines , 15 have positive slope and 20 have 0 or negative slope ( 20 + 15 = 35) out of 15 having positive slope, 5 have positive Y intercept So 10 having positive slope have 0 or negative Y intercept So total 15 lines have positive slope = 5 lines have positive y intercept and 10 lines have , zero or negative y intercept. also we know total 23 lines have y intercept \(\leq\) 0 so 23 + 5 = 28 , what kind of y intercept do the remaining 7 lines have ? hope now my question is clear. Edit:Thank you , understood it , the answer I was looking for was this : Those 7 lines have positive y intercept but negative slope . So here is the break up Total 12 have positive y intercept out of which 5 have positive slope and 7 have negative slope total 23 have zero or negative Y intercept out of which 10 have positive slope and 13 have 0 or negative slope . total 35 lines are now accounted for . Drawing a 2x2 table may help you see it easier
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