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GMATH practice exercise (Quant Class 20)



If c is a nonzero constant such that x*f(x) = c, variables x and y=f(x) are said to be inversely proportional. If the dotted curve shown above, defined by the points (x,y) where x>0 and y=f(x), represents a relationship between two inversely proportional variables, what is the value of the proportionality constant c?

(A) 0.5
(B) 0.625
(C) 0.8
(D) 1.25
(E) 1.5

Using the congruent triangles approach,
(sq.rt of 6.25)/2=y/1
ie., y=(sq.rt of 6.25)/2
Given, c=x*f(x)=c*y
=0.5*y
=0.625

Answer: B
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My method:

Given that f(x)*x=c and y=f(x)

we can say that y*x=c

We have been given the value of X as 0.5 but we don't have the value for y

Using slope property we know that the slope of the line is same across the length

So slope of the line:

Rise / run = 1/2

Similarly for the outer triangle run is 2.5 (2+0.5) and therefore the rise will be 1.25 (based on slope)

therefore, y=1.25

Substituting the value of y and x in y*x=c

1.25*0.5 = 0.625 Ans
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