If x varies as y then x2 + y2 varies as

Given, x = y Or, x - y = 0 Or, (x - y)2 = 0 Or, x2 + y2 - 2xy = 0 Or, x2 + y2 = 2xy It means that, x2 + y2 varies as xy

This question belongs to Arithmetic Ability Ratio

Ratio

If x varies as y then x² + y² varies as

A) x + y B) x - y C) x² - y² D) x³ - y³ E) None of these

Answer & Solution

Correct Answer: Option E

Given,
x = y
Or, x - y = 0
Or, (x - y)² = 0
Or, x² + y² - 2xy = 0
Or, x² + y² = 2xy
It means that, x² + y² varies as xy

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Azazel Demon 8 years ago

The answer is c
If x proportional to y then,
x=ky(where k is proportionality constant
x/y=k
x²/y²=k²
x²+y²/x²-y²=k²+1/k²-1 (componendo Dividendo)
x²+y²=(k²+1/k²-1)(x²-y²)
I.e. x²+y² is proportional to x²-y² where k²+1/k²-1 is new proportionality constant

Tapojoy De 8 years ago

@Onno Jogot : Yes , you are correct.

Onno Jogot 8 years ago

Btw, (x2 + y2) is proportional to y2 means, (x2 + y2) varies with y2.

Onno Jogot 8 years ago

In the answer they wrote x=y. It kind of confuses me. I think it should be x is proportional to y.

Thus,we can write:
x= ky [ where, k is a constant ]

Therefore, x2 + y2
= k2y2 + y2 [ since x= ky]
= y2 * (k2+1)

Therefore, x2 + y2 is proportional to y2, since (k2+1) is a constant.

The answer will be E.
Thanks.

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