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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:37) correct
41%
(01:48)
wrong
based on 482
sessions
History
Date
Time
Result
Not Attempted Yet
25 Sep 2012, 01:20
Kudos
Bookmarks
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:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#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.
\(yz\neq{0}\) 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:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#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.
12 Mar 2013, 06:37
Kudos
Bookmarks
To be honest, I'm a huge fan of DS 
so forgive me in advance for being too giddy ! :p
So let's get cracking !
Let's start by understanding the problem : We're told that y*z is not equal to zero. This should automatically give you the following information : neither y nor z are equal to 0 !!. Then we're asked to answer by yes or no (consider the question stem : "Is... ?") whether \(0<y<1\)
Put your answer choice grid up : (Something I've inherited from MGMAT prep)
AD (I chose to start with statement 1)
BCE
Statement 1 : \(y <\frac{1}{y}\)
Since y isn't equal to 0, the inequality is sound. However since we don't know the sign of y (whether y is positive or negative) we can't multiply each side of the inequality by y since there's the risk that the inequality is flipped. So statement 1 is insufficient.
The grid should look like this by now :
AD
BCE
Statement 2 : \(y = z^2\)
The only information we can gather from this statement is that y is positive. This will be particularily useful when we'll combine both statements. But up to this point, statement 2 is insufficient.
Our grid should look like this :
AD
BCE
Let's combine statements 1 and 2.
From statement 2, we know that y is positive. Therefore, we can multiply the inequality in statement 1 by y without risking to have the inequality flipped. From statement 1 we have, \(y^2<1\). Applying the square root to this inequality yields \(y<1\).
Therefore, we can clearly say that \(0<y<1\). So the final answer is C ! (Oh and don't forget to cross off the E in your grid as well
).
Hope that helped
so forgive me in advance for being too giddy ! :pSo let's get cracking !
Let's start by understanding the problem : We're told that y*z is not equal to zero. This should automatically give you the following information : neither y nor z are equal to 0 !!. Then we're asked to answer by yes or no (consider the question stem : "Is... ?") whether \(0<y<1\)
Put your answer choice grid up : (Something I've inherited from MGMAT prep)
AD (I chose to start with statement 1)
BCE
Statement 1 : \(y <\frac{1}{y}\)
Since y isn't equal to 0, the inequality is sound. However since we don't know the sign of y (whether y is positive or negative) we can't multiply each side of the inequality by y since there's the risk that the inequality is flipped. So statement 1 is insufficient.
The grid should look like this by now :
BCE
Statement 2 : \(y = z^2\)
The only information we can gather from this statement is that y is positive. This will be particularily useful when we'll combine both statements. But up to this point, statement 2 is insufficient.
Our grid should look like this :
Let's combine statements 1 and 2.
From statement 2, we know that y is positive. Therefore, we can multiply the inequality in statement 1 by y without risking to have the inequality flipped. From statement 1 we have, \(y^2<1\). Applying the square root to this inequality yields \(y<1\).
Therefore, we can clearly say that \(0<y<1\). So the final answer is C ! (Oh and don't forget to cross off the E in your grid as well
).Hope that helped
