If the Points (a, 0) , (0, b) and (1, 1) are Collinear, What is the Value of 1/a + 1/b? GMAT Problem Solving

Question: If the points (a, 0) , (0, b) and (1, 1) are collinear, what is the value of 1/a + 1/b?

(A) −1
(B) 0
(C) 1
(D) 2
(E) 3

Correct Answer: C
Solution and Explanation:
Approach Solution 1:
The slope of the line that goes through two points (a, 0) and (1, 1) is 1−a/1

The slope of the line that goes through two points (0, b) and (1, 1) is 1/1−b

Since those 3 points are collinear, we have
1−a/1 = 1/1−b⟹(1−a)(1−b)=1⟹a+b=ab⟹1/a+1/b= 1

Approach Solution 2:
Points are collinear: Suppose (0,b) is mid-point of the other two-points.
=> (a+1)2=0 and (0+1)2=b
=> a = -1 and b = ½
=>1/a+1/b = -1 + 2 = 1

Approach Solution 3:
Let A= (a,0), B= (0,b) and C- (1,1) and B divides the line segment AC in the ratio of k : 1

Then by section formula,
(k+a/k+1, k/k+1)= (0,b)
=> k= -a

Now, k/k+1= b
=> -a/ 1-a= b

=> a-1/a= 1/b
Therefore 1/a+1/b= 1

“If the points (a, 0) , (0, b) and (1, 1) are collinear, what is the”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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