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# Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line

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Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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09 Mar 2016, 13:28
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95% (hard)

Question Stats:

39% (01:47) correct 61% (02:41) wrong based on 74 sessions

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Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q). Is p + q > 0?

(1) x-intercept of Line L is less than that of Line K
(2) y-intercept of Line L is less than that of Line K

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Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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11 Mar 2016, 04:59
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Quote:
Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q). Is p + q > 0?

(1) x-intercept of Line L is less than that of Line K
(2) y-intercept of Line L is less than that of Line K

Line K

Equation $$3y=4x+12$$

Point $$(p,q)$$ is on line L so $$3q=4p+12$$

X intercept is $$-3$$
Y intercept is $$4$$

Line L

Equation $$y-q=-\frac{3}{4}(x-p)$$
$$3x+4y=3p+4q$$

X intercept is $$\frac{3p+4q}{3}$$
Y intercept is $$\frac{3p+4q}{4}$$

Statement 1: x-intercept of Line L is less than that of Line K

$$\frac{3p+4q}{3}<-3$$

$$3p+4q<-9$$

Sum of p and q i.e., p+q is negative in all cases so sufficient.

Statement 2: y-intercept of Line L is less than that of Line K

$$\frac{3p+4q}{4}<4$$

$$3p+4q<16$$

Sum of p and q i.e., p+q can be both positive and negative hence statement 2 is insufficient.

A for me.
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Re: Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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09 Mar 2016, 23:26
Clue 1 and 2 only suggest that line L can meet K in either quadrant 1 or quadrant 3 as intercepts constraints apply in both the cases.Therefore meeting point p+q can be either positive or negative which can't be decided by given clues.
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Joined: 02 Aug 2009
Posts: 6549
Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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10 Mar 2016, 00:50
1
vardhanindaram wrote:
Clue 1 and 2 only suggest that line L can meet K in either quadrant 1 or quadrant 3 as intercepts constraints apply in both the cases.Therefore meeting point p+q can be either positive or negative which can't be decided by given clues.

Hi,
there is some info in statement 1, which can answer the Q..

Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q). Is p + q > 0?

INFO from this:-

A)the intercept on x axis is (3,0) and y axis is (0,4)..
B) the slope is 4/3, which tells us that y increases at a higher rate than x..

Inference:-

1)Since the Line L is perpendicular to K, If its x-intercept is less than 3, the two lines will intersect above x-axis and if more than 3, it will intersect below X-axis..

lets see the statements

(1) x-intercept of Line L is less than that of Line K
see att fig, p+q will be always negative
a) in Quad III, both p and q will be -ive, so p+q will be NEGAIVE.

Suff..

(2) y-intercept of Line L is less than that of Line K
not suff
insuff..

ans A

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
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Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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12 Mar 2016, 21:54
chetan2u wrote:
vardhanindaram wrote:
Clue 1 and 2 only suggest that line L can meet K in either quadrant 1 or quadrant 3 as intercepts constraints apply in both the cases.Therefore meeting point p+q can be either positive or negative which can't be decided by given clues.

Hi,
there is some info in statement 1, which can answer the Q..

Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q). Is p + q > 0?

INFO from this:-

A)the intercept on x axis is (3,0) and y axis is (0,4)..
B) the slope is 4/3, which tells us that y increases at a higher rate than x..

Inference:-

1)Since the Line L is perpendicular to K, If its x-intercept is less than 3, the two lines will intersect above x-axis and if more than 3, it will intersect below X-axis..

lets see the statements

(1) x-intercept of Line L is less than that of Line K
see att fig, p+q will be always negative
a) in Quad III, both p and q will be -ive, so p+q will be NEGAIVE.

Suff..

(2) y-intercept of Line L is less than that of Line K
not suff
insuff..

ans A

The line that you drew in the picture is wrong.It has to meet x axis at -3.
And I would like someone to clarify if intercept is said to be less than -3,does that mean intercept of line should be between 3 and -3 considering the definition of intercept to be distance between origin and point where line meets axis.This is if we ignore the sign as it's the convention to denote the direction.
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Joined: 02 Aug 2009
Posts: 6549
Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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12 Mar 2016, 22:09
vardhanindaram wrote:
chetan2u wrote:
vardhanindaram wrote:
Clue 1 and 2 only suggest that line L can meet K in either quadrant 1 or quadrant 3 as intercepts constraints apply in both the cases.Therefore meeting point p+q can be either positive or negative which can't be decided by given clues.

Hi,
there is some info in statement 1, which can answer the Q..

Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q). Is p + q > 0?

INFO from this:-

A)the intercept on x axis is (3,0) and y axis is (0,4)..
B) the slope is 4/3, which tells us that y increases at a higher rate than x..

Inference:-

1)Since the Line L is perpendicular to K, If its x-intercept is less than 3, the two lines will intersect above x-axis and if more than 3, it will intersect below X-axis..

lets see the statements

(1) x-intercept of Line L is less than that of Line K
see att fig, p+q will be always negative
a) in Quad III, both p and q will be -ive, so p+q will be NEGAIVE.

Suff..

(2) y-intercept of Line L is less than that of Line K
not suff
insuff..

ans A

The line that you drew in the picture is wrong.It has to meet x axis at -3.
And I would like someone to clarify if intercept is said to be less than -3,does that mean intercept of line should be between 3 and -3 considering the definition of intercept to be distance between origin and point where line meets axis.This is if we ignore the sign as it's the convention to denote the direction.

Hi,
Thanks for pointing out..
Firstly less than -3 should mean <-3 in literal sense..
now the point of intersection would be in III quad, where both x and y are -ive, so the SUM will always be -ive..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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Updated on: 23 Oct 2016, 08:09
Bunuel wrote:
Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q). Is p + q > 0?

(1) x-intercept of Line L is less than that of Line K
(2) y-intercept of Line L is less than that of Line K

Please refer fig. with above solution for better understanding
Attachments

coordinate (1).png [ 12.68 KiB | Viewed 1981 times ]

Originally posted by rohit8865 on 10 Oct 2016, 10:21.
Last edited by rohit8865 on 23 Oct 2016, 08:09, edited 1 time in total.
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Joined: 13 Apr 2015
Posts: 32
Re: Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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10 Oct 2016, 10:52
Nevernevergiveup wrote:
Quote:
Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q). Is p + q > 0?

(1) x-intercept of Line L is less than that of Line K
(2) y-intercept of Line L is less than that of Line K

Line K

Equation $$3y=4x+12$$

Point $$(p,q)$$ is on line L so $$3q=4p+12$$

X intercept is $$-3$$
Y intercept is $$4$$

Line L

Equation $$y-q=-\frac{3}{4}(x-p)$$
$$3x+4y=3p+4q$$

X intercept is $$\frac{3p+4q}{3}$$
Y intercept is $$\frac{3p+4q}{4}$$

Statement 1: x-intercept of Line L is less than that of Line K

$$\frac{3p+4q}{3}<-3$$

$$3p+4q<-9$$

Sum of p and q i.e., p+q is negative in all cases so sufficient.

Statement 2: y-intercept of Line L is less than that of Line K

$$\frac{3p+4q}{4}<4$$

$$3p+4q<16$$

Sum of p and q i.e., p+q can be both positive and negative hence statement 2 is insufficient.

A for me.

can you explain how did you deduce 3p+4q<-9[/m]

Sum of p and q i.e., p+q is negative in all cases so sufficient.
and
3p+4q<16[/m]

Sum of p and q i.e., p+q can be both positive and negative hence statement 2 is insufficient.
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Re: Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line  [#permalink]

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30 Oct 2017, 14:52
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Re: Line L is perpendicular to line K whose equation is 3y = 4x + 12; Line &nbs [#permalink] 30 Oct 2017, 14:52
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