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

Question

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

Nevernevergiveup · Accepted Answer

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.

vardhanindaram · Answer

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.
Hence Answer E

chetan2u · Answer

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

vardhanindaram · Answer

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.

chetan2u · Answer

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..

rohit8865 · Answer

Please refer fig. with above solution for better understanding

kplusprinja1988 · Answer

can you explain how did you deduce 3p+4q<-9

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

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

Crytiocanalyst · Answer

First of let us pen down the equation of the lines
k-3y = 4x + 12(given)
=>y=-3/4x+c since it's perpendicular to k
now we have to figure out whether p+q point of intersection of k and l that is p+q>0

state 1 provides :
c*4/3<-3 that is let us assume c=-10/4 <-9/4
gives us p+q<0 when substitued in L
sufficient

state 2 provides :
in a similar method of substitution provides c<-3
however when finding out for p and q provides both p+q>0
and p+q<0
hence Insuff

IMO A

Nidanyr · Answer

Hi, please tell me what assumption that I am making is wrong here. I don't seem to need any of the statements to find a value for p and q.

Can we not form the following equations based on the info given? Info given in the question stem- Lines L and K intersect at point (p,q), so this pair should follow the equations of both Line K and line L Line K equation is : y=4/3x +12 Line L equation b = -3/4a + k, where k is a constant Now, since (p,q) satisfies both the equations, q = 4/3p +12 = -3/4p + k Using these three equations, we can find out p and k and q. We don't seem to need the Statements. Pls tell me where I am wrong. I am making an unfair assumption somewhere. (how i did it was, using the last two terms of the equation in bold, i calculated the ratio of p and k. Then I put the value of k in terms of p in the equation of first and last terms and found out the ratio of p and q and finally, put this ratio in the first two terms and found out p =1.) Thanks

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

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