Which of the following describes all the values of y

vishalpathak wrote:Which of the following describes all the values of y for which y < y²?

A) 1 < y
B) −1 < y < 0
C) y < −1
D) 1/y < 1
E) 0 < y < 1

The questions asks us to find all values of y that satisfy the condition that y < y²
Answer choices B and C describe some values of y that satisfy the condition, but they don't describe all of them.

For example, y = 2 satisfies the condition that y < y² (since 2 < 2²)
When we check the answer choices, we see that y = 2 is NOT included in answer choices B, C or E, so we can ELIMINATE these 3 answer choices.

Another value of y that satisfies the condition that y < y² is y = -3
When we check the two remaining answer choices (A and D), we see that y = -3 is not included in answer choice A, so we can ELIMINATE this answer choice.

This leaves us with D, the correct answer.

Cheers,
Brent

vishalpathak wrote:Which of the following describes all the values of y for which y < y²?

1 < y
−1 < y < 0
y < −1
1/y < 1
0 < y < 1

Another approach is to first recognize that y² is > 0 for all values of y
Also recognize that, from the given inequality, y cannot equal 0 (since 0 is NOT less than 0²)
So, from the given inequality, we can be certain that y² is positive.

Now that we've ensured that y² is positive, we can rewrite the given inequality (y < y²) by dividing both sides by y² to get y/y² < 1.
This simplifies to be 1/y < 1, which matches answer choice D

IMPORTANT TAKEAWAY: We can safely divide both sides of an inequality by a VARIABLE, once we have ensured that the variable does not equal 0, AND we have ensured that the variable cannot have both positive AND negative values.

Cheers,
Brent