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What are the coordinates of point S?

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Bunuel
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What are the coordinates of point S? [#permalink] New post   04 Feb 2020, 04:10
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Question Stats:

78% (01:20) correct 22% (01:38) wrong based on 133 sessions
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What are the coordinates of point S?

(1) The slope of OS is 1/3
(2) The slope of ST is 1/2


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C
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Re: What are the coordinates of point S? [#permalink] New post   04 Feb 2020, 04:39
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What are the coordinates of point S?

(1) The slope of OS is 1/3
(2) The slope of ST is 1/2

y = mx + C

i) For line OS, \(y =0\), \(x=0\), \(m=\frac{1}{3}\) -> \(C =0\) -> \(y=\frac{x}{3}\) -> Not Sufficient

ii) For line ST, \(y=0\), \(x=5\), \(m=\frac{1}{2}\) -> \(0=\frac{5}{2} + C \) -> \(C = \frac{-5}{2}\) -> Not Sufficient

Combining i) and ii), substituting value of y in ii) from i)
\(\frac{x}{3} = \frac{x}{2 }- \frac{5}{2 }\)-> \(x=15\) and therefore \(y=5\) coordinates of S -> Sufficient

Answer - C
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What are the coordinates of point S? [#permalink] New post   04 Feb 2020, 05:55
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Bunuel wrote:

What are the coordinates of point S?

(1) The slope of OS is 1/3
(2) The slope of ST is 1/2


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Solution


Step 1: Analyse Question Stem


    • O is point (0,0) and T is point (5, 0)
    • Let us assume that the point S is (x, y)
Thus, we need to find the values of x and y.

Step 2: Analyse Statements Independently


Statement 1: The slope of OS is \(\frac{1}{3}\)
    • According to this statement: \(\frac{(y-0)}{(x-0)} = \frac{1}{3}\)
      o Or, \(\frac{y}{x} = \frac{1}{3}\)
      o Or, \(x = 3y\)
Now, we have two variables and only one equation. So, we won’t be able to find x and y from this statement.
Hence, statement 1 is not sufficient and we can eliminate answer options A and D
Statement 2: The slope of ST is \( \frac{1}{2}\)
    • According to this statement: \(\frac{(y-0)}{(x-5) }= \frac{1}{2}\)
      o Or, \(\frac{y}{(x-5)} = \frac{1}{2}\)
      o Or, \(x = 2y + 5\)
Again, we have two variables and only one equation. So, we won’t be able to find x and y from this statement too.
Hence, statement 2 is also not sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining.


    • From statement 1: \( x = 3y\)
    • From statement 2: \(x = 2y +5 \)
Now, we have two equations and two variables. We can easily solve these equations to get the values of x and y (in this case, we will get, x = 15 and y =5)
Thus, the correct answer is Option C.
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Re: What are the coordinates of point S? [#permalink] New post   04 Feb 2020, 08:21
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Bunuel wrote:

What are the coordinates of point S?

(1) The slope of OS is 1/3
(2) The slope of ST is 1/2


Coordinate of S is where both lines, OS and ST, meet

(1) The slope of OS is 1/3 insufic

y=mx+b: y=x/3+b
point (0,0): 0=0+b
Line OS: y=x/3

(2) The slope of ST is 1/2 insufic

y=mx+b: y=x/2+b
point (5,0): 0=5/2+b, b=-2.5
Line ST: y=x/2-2.5

(1&2) sufic

Line ST = Line OS
x/2-2.5=x/3
-x=6*-2.5
x=15, y=15/3=5

Ans (C)
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Re: What are the coordinates of point S? [#permalink]
04 Feb 2020, 08:21
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Bunuel
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