ProperSanity? May be Proportionality!

Algebra Level pending

Given that x x can only attain values of negative integers. In how many of the following equations, y y is not directly proportional to x x ?

A) x + y = 1 x+y=1

B) x + y = 0 x+y=0

C) x / y = 1 x/y=1

D) x y = 1 xy=1


AYWC?

3 3 2 2 1 1 4 4

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1 solution

Soumo Mukherjee
Apr 2, 2015

y y is said to be directly proportional to x x if y = k x y=kx . Now let us examine the options given. Do they agree with the form y = k x y=kx

A) x + y = 1 x+y=1 or y = 1 x y=1-x , isn't of the form y = k x y=kx

B) x + y = 0 x+y=0 or y = x y=-x , is of the form y = k x y=kx . Where k = 1 k=-1 .

C) x / y x/y ) or y = x y=x , is of the form y = k x y=kx . Where k = 1 k=1 .

D) x y = 1 xy=1 or y = 1 / x y=1/x , isn't of the form y = k x y=kx

So there are only two option, (A) & (D), in which y y isn't directly proportional to x x . Hence, the answer is 2 2 .

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