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

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

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New post 19 Dec 2015, 10:26
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]

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

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New post 15 Feb 2017, 22:38
Why cant it be be 'A'?
if we try with cases, for 1<y, y can be 1.1, 1.2,2,3,4 etc...
so here square any of these y terms will always be greater than the original y term.

Can anyone throw some light on this?
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Re: Which of the following describes all the values of y for whi [#permalink]

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New post 16 Feb 2017, 02:10
kkrrsshh wrote:
Why cant it be be 'A'?
if we try with cases, for 1<y, y can be 1.1, 1.2,2,3,4 etc...
so here square any of these y terms will always be greater than the original y term.

Can anyone throw some light on this?


y < y^2 means that either y < 0 or y > 1. Thus y > 1 is not always true.
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Re: Which of the following describes all the values of y for whi [#permalink]

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New post 11 Mar 2017, 22:37
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. 8-)

Kudos if you like the question. :-D


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.

Answer: D.



What is the difference between option A and D?
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Re: Which of the following describes all the values of y for whi [#permalink]

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New post 12 Mar 2017, 02:57
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gauraha 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. 8-)

Kudos if you like the question. :-D


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.

Answer: D.



What is the difference between option A and D?


1/y < 1 translates to y<0 or y>1.
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Re: Which of the following describes all the values of y for whi [#permalink]

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New post 24 Mar 2017, 13:25
I understand this as below:

From Question Infer: y is either y<0 or y > 1. So we need to choose a value from options which satisfies both the ranges.

Except D all values violate one of range.

For D) 1/y = -ve if y < 0
& 1/y < 1 if y > 1. So satisfies both ranges. Tricky One.
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Re: Which of the following describes all the values of y for whi   [#permalink] 24 Mar 2017, 13:25

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