Equations, Inequalities and VICs - Chapter 6, Q#28

[guest]

Q#28) If x not equal to 0, is x^2 + 1 / x > y (reads x square plus 1 divided by x greater than y) ?

1) x = y
2) y > 0

The answer is C. I thought the answer was A because, no matter what the sign of x, since we are squaring that variable, we should always get a positive number and so, we do not need to flip the sign. So, when x = y, if x = -2 or x = 2, x^2 + 1 is always greater than x^2. I am not able to understand why this explanation is wrong.

In the explanation it is mentioned that considering the case of x>0, x^2 + 1 > x^2
and when x<0, x^2 + 1 < x^2. The one thing I did not understand was the reason we need to flip the sign. So, Statement 1 is not sufficient.

Could anyone please explain this confusing topic ?

Thanks,
Sonu

[kylo]

IMO E.



Thanks!

[guest]

Sorry, the official answer is 'C'.

[JonathanSchneider]

You are confusing two different points about pos/neg values. The first is that whenever a value is squared, the result cannot be negative. The second is that, in an inequality, multiplying by a negative flips the sign. Notice here that we are multiplying by an x (the denominator). We are NOT multiplying by an x^2. Although there is an x^2 in the problem, don't let that throw you off. It is the fact that we multiplied by a single x that makes the difference here.

Make sense?

[Shradha]

For statement 1 :
a. When x = 2 equation results in 2.5 > 2. Which makes the statement true.
b. When x= -2 equation results in -2.5 > -2 which is NOT the case. Because for negative numbers smaller is greater :)

Statement 1 is NOT sufficient.

For statement 2 :
a. Knowing y>0 does not help us with solving the equation by itself.

Statement 2 is NOT sufficient.

Try Combining Statement 1 and Statement 2.
Using statement 2 we can get rid of 1b ambiguity as x=y and y>0
This helps us is getting a unique answer.

Hence answer is C.

Hope it helps.

[esledge]

Nice use of number plugging, Shradha. I like that method for inequalities that really seem to be about sign (i.e. a positive case and a negative case will usually do the trick.)