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

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Manager
Joined: 25 Dec 2010
Posts: 65
If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y =  [#permalink]

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Updated on: 04 Oct 2011, 10:52
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:44) correct 45% (01:39) wrong based on 47 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

Originally posted by shashankp27 on 02 Oct 2011, 13:59.
Last edited by shashankp27 on 04 Oct 2011, 10:52, edited 1 time in total.
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Joined: 11 May 2011
Posts: 320
Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y =  [#permalink]

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

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

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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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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Joined: 09 Sep 2011
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Location: United States
Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y =  [#permalink]

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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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02 Oct 2011, 22:49
1
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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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.
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Joined: 02 Sep 2009
Posts: 52431
Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y =  [#permalink]

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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.

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-yz-not-eq ... 39571.html
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Re: If yz not equal to 0, is 0<y<1 ? (1) y< 1/y (2) y = &nbs [#permalink] 26 Nov 2017, 22:34
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