|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
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 484
sessions
History
Date
Time
Result
Not Attempted Yet
If yz not equal to zero is 0 < y < 1?
(1) y < 1/y
(2) y = z^2
(1) y < 1/y
(2) y = z^2
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
25 Sep 2012, 00:19
Kudos
Bookmarks
harikris
Statement 1 is true for values between 0 and 1, but is also true for any negative number less than -1 (you can plug in, say, -2 to confirm). So Statement 1 is not sufficient. Statement 2 is clearly not sufficient since we have no information about z besides the fact that it's nonzero.
Taking the Statements together, from Statement 2, y must be positive, since it is equal to a nonzero square. So looking at Statement 1, we can multiply both sides by y, since y is positive, without worrying about whether to reverse the inequality. We then find that y^2 < 1, and if y is positive, that means 0 < y < 1. So the two statements together are sufficient and the answer is C.
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.
so forgive me in advance for being too giddy ! :p
).
