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# Which of the following describes all the values of y for whi

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Senior Manager
Joined: 19 Oct 2012
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Which of the following describes all the values of y for whi  [#permalink]

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Updated on: 14 Oct 2013, 10:21
10
24
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Difficulty:

85% (hard)

Question Stats:

48% (01:45) correct 52% (01:44) wrong based on 332 sessions

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Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

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Citius, Altius, Fortius

Originally posted by TheMechanic on 14 Oct 2013, 10:15.
Last edited by Bunuel on 14 Oct 2013, 10:21, edited 1 time in total.
Renamed the topic and edited the question.
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Posts: 53800
Re: Which of the following describes all the values of y for whi  [#permalink]

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14 Oct 2013, 10:23
12
1
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

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##### General Discussion
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Posts: 93
Re: Which of the following describes all the values of y for whi  [#permalink]

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15 Oct 2013, 07:40
Bunuel wrote:
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

Hi bunuel, Your method is really easy but could you look at what i did just to tell me where i'm making a mistake?
$$y<y^2$$
$$y^2-y>0$$
$$y(y-1)>0$$
Two cases arise:-
Case I: When both are positive
either$$y>0$$ or $$Y>1$$, Thus $$y>1$$

Case II: When both are negative
$$Y<0$$ and $$y<1$$ thus $$Y<0$$

From the above two cases$$Y<0$$ and $$Y>1$$.

Where am I going wrong????
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Joined: 02 Sep 2009
Posts: 53800
Re: Which of the following describes all the values of y for whi  [#permalink]

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15 Oct 2013, 08:56
2
1
mahendru1992 wrote:
Bunuel wrote:
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

Hi bunuel, Your method is really easy but could you look at what i did just to tell me where i'm making a mistake?
$$y<y^2$$
$$y^2-y>0$$
$$y(y-1)>0$$
Two cases arise:-
Case I: When both are positive
either$$y>0$$ or $$Y>1$$, Thus $$y>1$$

Case II: When both are negative
$$Y<0$$ and $$y<1$$ thus $$Y<0$$

From the above two cases$$Y<0$$ and $$Y>1$$.

Where am I going wrong????

Yes, y < y^2 means that either y < 0 or y > 1.

If y < 0, then 1/y = negative < 0 < 1.
If y > 1, then 1/y < 1.

So, D is correct.
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Re: Which of the following describes all the values of y for whi  [#permalink]

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15 Oct 2013, 09:00
Oh Thanks! I expected a verbatim answer because usually that is the case. I'll have to be careful in evaluating the choices from now on.
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Joined: 09 Aug 2013
Posts: 2
Re: Which of the following describes all the values of y for whi  [#permalink]

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16 Oct 2013, 07:37
Bunuel wrote:
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

Hi Bunnel

I got your method of solving the equation. But could you please tell me why answer choice C is incorrect , won't y < -1 lead to all values for which y < y^2 ?

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Joined: 02 Sep 2009
Posts: 53800
Re: Which of the following describes all the values of y for whi  [#permalink]

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16 Oct 2013, 07:38
1
SN30 wrote:
Hi Bunnel

I got your method of solving the equation. But could you please tell me why answer choice C is incorrect , won't y < -1 lead to all values for which y < y^2 ?

We are given that y < 0 or y > 1. So, y, for example can be 2, thus y < -1 is not always true.
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Concentration: Finance
Re: Which of the following describes all the values of y for whi  [#permalink]

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01 Jan 2014, 07:27
Bunuel wrote:
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

I also solved it factorizing y^2-y>0
y(y-1)>0

Two cases:
y<0 or y>1

Now if y>0

Then 1/y<1 is y>1, by reciprocal. So we have case 1 checked

Then if y<0

We have that 1/y<1, do not flip inequality. y<1<0

So we have second case

Therefore D is the correct answer

PS. Its fine not to flip inequality in second case no? Just wanted to confirm this

Thanks

Cheers!
J
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Posts: 97
Location: India
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Re: Which of the following describes all the values of y for whi  [#permalink]

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14 Mar 2014, 23:42
1
jlgdr wrote:
Bunuel wrote:
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

I also solved it factorizing y^2-y>0
y(y-1)>0

Two cases:
y<0 or y>1

Now if y>0

Then 1/y<1 is y>1, by reciprocal. So we have case 1 checked

Then if y<0

We have that 1/y<1, do not flip inequality. y<1<0

So we have second case

Therefore D is the correct answer

PS. Its fine not to flip inequality in second case no? Just wanted to confirm this

Thanks

Cheers!
J

Mr J

Could you why did u get Two cases:y<0 or y>1 after factorization .?
I did the factorization lets c... Y^2-Y>0
=>Y(Y-1)>0
=>Y>0 and Y>1
Then i have checked the answer and landed upon D...

Rgds
Prasannajeet
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Location: India
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Re: Which of the following describes all the values of y for whi  [#permalink]

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14 Mar 2014, 23:43
jlgdr wrote:
Bunuel wrote:
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

I also solved it factorizing y^2-y>0
y(y-1)>0

Two cases:
y<0 or y>1

Now if y>0

Then 1/y<1 is y>1, by reciprocal. So we have case 1 checked

Then if y<0

We have that 1/y<1, do not flip inequality. y<1<0

So we have second case

Therefore D is the correct answer

PS. Its fine not to flip inequality in second case no? Just wanted to confirm this

Thanks

Cheers!
J

Mr J

Could you why did u get Two cases:y<0 or y>1 after factorization .?
I did the factorization lets c... Y^2-Y>0
=>Y(Y-1)>0
=>Y>0 and Y>1
Then i have checked the answer and landed upon D...

Rgds
Prasannajeet
Math Expert
Joined: 02 Sep 2009
Posts: 53800
Which of the following describes all the values of y for whi  [#permalink]

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15 Mar 2014, 05:32
1
prasannajeet wrote:
Could you why did u get Two cases:y<0 or y>1 after factorization .?
I did the factorization lets c... Y^2-Y>0
=>Y(Y-1)>0
=>Y>0 and Y>1
Then i have checked the answer and landed upon D...

Rgds
Prasannajeet

If you think about it, you should understand that y>0 and y>1 does not make any sense. What could be the values of y in this case?

y(y-1)>0 --> the "roots" are 0 and 1, this gives us 3 ranges:

y<0;
0<y<1;
y>1.

Next, test some extreme value for y: if y is some large enough number, say 10, then both multiples will be positive which gives the positive result for the whole expression, so when y>1 the expression is positive. Now the trick: as in the 3rd range expression is positive then in the 2nd it'll be negative and finally in the 1st it'll be positive again: + - + . So, the ranges when the expression is positive are: y<0 and y>1.

Check this for more: x2-4x-94661.html#p731476

Hope it helps.
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Which of the following describes all the values of y for  [#permalink]

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30 Jun 2014, 03:22
Which of the following describes all the values of y for which y < y^2?
A) 1 < y
B) −1 < y < 0
C) y < −1
D) 1/y < 1
E) 0 < y < 1
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Joined: 02 Sep 2009
Posts: 53800
Re: Which of the following describes all the values of y for whi  [#permalink]

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30 Jun 2014, 03:24
1
goodyear2013 wrote:
Which of the following describes all the values of y for which y < y^2?
A) 1 < y
B) −1 < y < 0
C) y < −1
D) 1/y < 1
E) 0 < y < 1

Merging similar topics. Please refer to the discussion above.

Hope it helps.
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Re: Which of the following describes all the values of y for whi  [#permalink]

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30 Jun 2014, 14:18
What is y = -4. Then y<-1 holds true but y>1 does not....
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Re: Which of the following describes all the values of y for whi  [#permalink]

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30 Jun 2014, 14:24
bankerboy30 wrote:
What is y = -4. Then y<-1 holds true but y>1 does not....

Sorry, but I don't understand what you mean... Can you pleas elaborate?
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Re: Which of the following describes all the values of y for whi  [#permalink]

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30 Jun 2014, 14:31
If we have two solutions : y<0 and y>1, and the above comment was if y is equal to 2, Y<0 does not hold up. But if y=-3 then y>1 does not hold up.... maybe I'm not understanding the explanation completely. I still don't understand why choice C won't work
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Re: Which of the following describes all the values of y for whi  [#permalink]

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30 Jun 2014, 14:59
bankerboy30 wrote:
If we have two solutions : y<0 and y>1, and the above comment was if y is equal to 2, Y<0 does not hold up. But if y=-3 then y>1 does not hold up.... maybe I'm not understanding the explanation completely. I still don't understand why choice C won't work

$$y < 0$$ and $$y > 1$$ are the ranges for which $$y < y^2$$ holds true. For any $$y$$ from these ranges, $$y$$ is less than $$y^2$$.

Option C is not true because the question asks to find ALL the values of $$y$$ for which $$y$$ is less than $$y^2$$. And while for $$y < -1$$, $$y$$ is indeed less than $$y^2$$, this range ($$y < -1$$) does not cover ALL the values of $$y$$ for which $$y$$ is less than $$y^2$$. Namely it does not cover range $$-1\leq{y}<0$$ and range $$y>1$$.

I think you need to brush up fundamentals on inequality:

Hope it helps.
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Re: Which of the following describes all the values of y for whi  [#permalink]

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07 Jul 2014, 03:17
Bunuel wrote:
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

Hi Bunnel,

I have a query for ans. choice A

here it is mentioned y<1 i.e. y >1. if y>1 then always y<y^2.

Please clarify this. What is the issue in this logic

Thanks.
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Joined: 02 Sep 2009
Posts: 53800
Re: Which of the following describes all the values of y for whi  [#permalink]

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07 Jul 2014, 03:24
PathFinder007 wrote:
Bunuel wrote:
vabhs192003 wrote:
Which of the following describes all the values of y for which y < y^2 ?

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

I wanted an algebraic approach to solve this question. Any pointers are welcomed.

Kudos if you like the question.

From y < y^2, it follows that y is not 0, thus y^2>0. Divide both parts by it: y/y^2 < 1 --> 1/y < 1.

Hi Bunnel,

I have a query for ans. choice A

here it is mentioned y<1 i.e. y >1. if y>1 then always y<y^2.

Please clarify this. What is the issue in this logic

Thanks.

The question does not ask for the option which must be true. The question asks to find ALL the values of y for which y is less than y^2. Please check here: which-of-the-following-describes-all-the-values-of-y-for-whi-161602.html#p1378717
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Re: Which of the following describes all the values of y for whi  [#permalink]

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19 Dec 2015, 11:26
Which of the following describes all the values of y for which y < y^2 ?

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

I solved it as per below and plucked the wrong answer. Can anyone please explain where i am wrong:

y < y^2
Or, y^2>y
Or, y^2/y>y/y
Or, y>1
Or, 1<y

Hereby, I choose "A".
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Re: Which of the following describes all the values of y for whi   [#permalink] 19 Dec 2015, 11:26

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