If a line K passes through (1, 5) and the line K intersects with the

Question

If a line K passes through (1, 5) and the line K intersects with the other line L at (5, t), what is the value of t?

(1) The y-intercept of the line K is 5
(2) The slope of the line L is positive

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
  • Let’s say line K is  y=m_1x+c_1  , and line L is  y = m_2x+c_2  , where  
   o  m_1   and  m_2  are slopes of K and L respectively, and 
 o  c_1  and  c_2   are y intercepts of K and L respectively.    
 • Line K passes through (1,5), so 
  o  1=m_1*5+c_1 ……………..Eq.(1)   
 • Lines K and L intersect each other at (5,t) 
  o So, point (5,t) will satisfy equation of line K as well as L.  
We need to find the value of t; which can be found if we know the equation of any one of the lines K and L.

Step 2: Analyse Statements Independently  
 Statement 1 :  The y-intercept of the line K is 5 
 • According to this statement,   c_1 = 5 
• On substituting the value of  c_1  in Eq.(1) , we get :  m_1 = \frac{-4}{5} 
• So , Equation of line K is  y=\frac{-4}{5}x+5  
Since, we got equation of line K, then we can substitute x=5 and y=t in it and can easily find the value of t.
Hence, statement 1 is sufficient and we can eliminate answer options B, C and E
 Statement 2 :  The slope of the line L is positive 
 • According to this statement  m_2 >0   
From above information only, we can not find exact value of  m_2  and  c_2 .Hence we can neither find equation of L nor the equation of K from this statement alone.
Therefore, statement 2 is not sufficient.
Thus, the correct answer is Option A.

Jbbaille · Answer

Let me know if I'm wrong, but if line K passes through (1,5) and its y-intercept is 5, it just means that line K is a horizontal line (y = 5) that will intercept line L at (5,5).

Bunuel · Answer

________________________
Yes, that's absolutely correct.

Kinshook · Answer

Asked: If a line K passes through (1, 5) and the line K intersects with the other line L at (5, t), what is the value of t?

(1) The y-intercept of the line K is 5
Equation of line k: y = mx + 5
Since it passes through (1,5)
5 = m + 5
m = 0
y = 5
Since it intersects at (5,t)
t = 5
SUFFICIENT

(2) The slope of the line L is positive
y = mx + c ; where m>0
5 = m + c
c = 5 - m
y = mx + (5-m)
Since it intersects at (5,t)
t = 5m + (5-m)
t = 4m + 5
But m may take multiple values
NOT SUFFICIENT

IMO A

GMATinsight · Answer

Question : t = ?

We have one point on the line, (1,5)
To find the equation of line K, we need either one more point on line K OR Y-intercept OR X-intercept OR Slope value

If we have the equation of line K, then we can substitute x=5 and value of y will be the value of t because (5, t) also lies on the same like K

Statement 1 : The y-intercept of the line K is 5

We can find exact equation of Line k and hence we can find value of t by substituting x=5 hence

SUFFICIENT

Statement 2 : The slope of the line L is positive

Like K is still not fixed on graph hence

NOT SUFFICIENT

Answer: Option A

If a line K passes through (1, 5) and the line K intersects with the

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