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If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y =

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If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y = [#permalink]

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New post 02 Oct 2011, 13:59
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:06) correct 48% (01:01) wrong based on 33 sessions

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If yz not equal to 0, is 0<y<1 ?

(1) \(y< 1/y\)
(2) \(y\)=\(z^2\)

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-yz-not-eq ... 39571.html
[Reveal] Spoiler: OA

Last edited by shashankp27 on 04 Oct 2011, 10:52, edited 1 time in total.

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Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y = [#permalink]

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New post 02 Oct 2011, 16:08
shashankp27 wrote:
If yz not equal to 0, is 0<y<1 ?

(1) \(y< 1/y\)
(2) \(y\)=\(z^2\)



My answer is A.

Dont find any relevance to 2nd statement.
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Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y = [#permalink]

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New post 02 Oct 2011, 21:06
IMO E

Stmt A: the statement satisfies when y is negative or between 0 and 1. Not sufficient
Stmt B: Nothing is known about Z. Not Sufficient

Combining the statement also not suffient to conclude.

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Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y = [#permalink]

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New post 02 Oct 2011, 21:55
divyakatas wrote:
IMO E

Stmt A: the statement satisfies when y is negative or between 0 and 1. Not sufficient
Stmt B: Nothing is known about Z. Not Sufficient

Combining the statement also not suffient to conclude.



i think from 2nd stmt, we know y is not negative. so it shud be between 0 and 1.

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Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y = [#permalink]

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New post 02 Oct 2011, 22:49
1)

y < -1, or 0 < y < 1

NS

2)

y = z^2

y > 0

NS

1+2)

Given y < -1 or 0 < y < 1
and y > 0

then, 0 < y < 1

C

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Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y = [#permalink]

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New post 03 Oct 2011, 00:12
(1)
\(y<1/y\)

\(y^2<1, y>0\)
\(y^2>1, y<0\)

\(0<y<1, y<-1\)
So, we could not say whether 0<y<1.

(2)
\(y=z^2\)
This means that y>0 (since yz is not 0), but we do not know whether y>1 or not.

(1) and (2) together
\(y<-1, 0<y<1 and y>0\)
\(0<y<1\)

So, tho statements together are sufficient.
The answer is (C)
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Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y = [#permalink]

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New post 26 Nov 2017, 22:34
If yz not equal to zero is 0 < y < 1?

\(yz\neq{0}\) means that neither of them is zero.

(1) y < 1/y --> \(\frac{y^2-1}{y}<0\) --> \(\frac{(y+1)(y-1)}{y}<0\) --> roots are -1, 0, and 1 --> this gives us 4 ranges: \(y<-1\), \(-1<y<0\), \(0<y<1\), and \(y>1\). Now, test some extreme value: for example if \(y\) is very large number then the whole expression is positive. Here comes the trick: since in the fourth range, when \(y>1\), the expression is positive, then in third range it'll be negative, in the second positive, and in the first range it'l be negative again: -+-+. Thus, the ranges when the expression is negative are: \(y<-1\) and \(0<y<1\). Not sufficient.

Solving inequalities:
http://gmatclub.com/forum/x2-4x-94661.html#p731476
http://gmatclub.com/forum/inequalities-trick-91482.html
http://gmatclub.com/forum/everything-is ... me#p868863
http://gmatclub.com/forum/xy-plane-7149 ... ic#p841486

(2) y = z^2. Since, we know that \(z\neq{0}\), then \(z^2>0\), hence \(y=z^2>0\) Clearly insufficient.

(1)+(2) Since from (2) \(y>0\), then only one range remains from (1): \(0<y<1\). Sufficient.

Answer: C.

Hope it helps.

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Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y =   [#permalink] 26 Nov 2017, 22:34
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