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Which of the following describes all the values of y

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by ganeshrkamath » Wed Nov 20, 2013 6:18 am
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

OA D

All values of B and C also satisfy the given condition. Somebody please explain
I'm assuming y2 = y^2

y < y^2

This is true for all positive values of y > 1 ____________(set 1)

It is also true for all negative values y < 0 ____________(set 2)

Now look at the options:
Option A : 1 < y
Represents only the first set.
Eliminate

Option B : −1 < y < 0
Represents only part of the second set.
Eliminate

Option C : y < −1
Represents only part of the second set.
Eliminate

Option D : 1/y < 1
Case 1: y is positive
y > 1
This represents set 1.
Case 2: y is negative
1/(-p) < 1 ______________(p is a positive number)
-1/p < 1
1 > -p
1 > y
Since y is negative, y < 0.
This represents set 2.
Select

Option E : 0 < y < 1
Does not represent the required set.
Eliminate

Choose D

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by Brent@GMATPrepNow » Wed Nov 20, 2013 6:18 am
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
Last edited by Brent@GMATPrepNow on Wed Nov 20, 2013 6:27 am, edited 2 times in total.
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by Brent@GMATPrepNow » Wed Nov 20, 2013 6:24 am
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
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by theCodeToGMAT » Wed Nov 20, 2013 10:04 am
y < y^2

y^2 - y > 0

y(y-1) > 0

(y-0)(y-1)>0

y<0 & y>1

From this we can eliminate {A}, {B}, {C}, {E}

Answer [spoiler]{D}[/spoiler]

Testing {D}
Let y = -1
-1 < 1 YES
Let y = 2
1/2 < 1 YES
R A H U L
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