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GATE CS 2015 Set 3 · General Aptitude

Question 5

MCQPrinted as GA Q.51 markWrong answer: −1/3Easy (estimate)

Question

A function f(x)f(x) is linear and has a value of 29 at x=−2x = -2 and 39 at x=3x = 3. Find its value at x=5x = 5.

Choose one option
Official answer and solution
Official answer
C
From
Official GATE 2015 answer key

Solution

Use the two given points to find the slope of the linear function and extrapolate to the target coordinate.

A linear function can be written as f(x)=mx+cf(x) = mx + c, where mm is the slope and cc is the y-intercept.

We are given two coordinates:

  • Point 1: (−2,29)  ⟹  f(−2)=29(-2, 29) \implies f(-2) = 29
  • Point 2: (3,39)  ⟹  f(3)=39(3, 39) \implies f(3) = 39

Calculate the slope mm:

m=f(3)−f(−2)3−(−2)=39−293+2=105=2m = \frac{f(3) - f(-2)}{3 - (-2)} = \frac{39 - 29}{3 + 2} = \frac{10}{5} = 2

Calculate f(5)f(5) using point-slope form from x=3x = 3:

f(5)=f(3)+m⋅(5−3)=39+2(2)=39+4=43f(5) = f(3) + m \cdot (5 - 3) = 39 + 2(2) = 39 + 4 = 43
Final answer

C

Common trap

Making an arithmetic error in subtracting the negative coordinate in the denominator, e.g., 3−2=13 - 2 = 1 instead of 3−(−2)=53 - (-2) = 5.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2015 Computer Science and Information Technology (CS) Session 3
Question
5 of 65, printed as GA Q.5
Section
General Aptitude

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