• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Reach higher with Artificial Intelligence. Guaranteed
Now free for 30 days

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

## Manhattan Advanced Quant pg 84 #8

tagged by: ceilidh.erickson

This topic has 3 expert replies and 3 member replies
bpolley00 Master | Next Rank: 500 Posts
Joined
11 Jul 2012
Posted:
192 messages
Followed by:
5 members
20
Test Date:
3/29/2013
Target GMAT Score:
800
GMAT Score:
650

#### Manhattan Advanced Quant pg 84 #8

Mon Jan 28, 2013 7:26 pm
If yx cannot equal 0, is 0
1)y< 1/y
2) y=z^2

Can someone please explain why 1 is not sufficient? The Manhattan Explanation has two explanations; however, it says the same thing and says YES and NO. It starts If y<0 If y<0 and then gets yes and No. Can an expert please explain why 1 isn't sufficient here? I completely understand #2 but cannot wrap my mind around #1. Thank you.

-BP

hemanthkumarmn Junior | Next Rank: 30 Posts
Joined
31 Dec 2012
Posted:
14 messages
1
Tue Jan 29, 2013 11:21 pm
ceilidh.erickson : Thanks for your valuable advice.. And it's indeed true that one got to be very precise while reasoning a GMAT question, not only for the sake of others but also for self.. Point taken.. Thanks again..

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
14030 messages
Followed by:
1812 members
13060
GMAT Score:
790
Wed Jan 30, 2013 3:34 am
Quote:
If yz does not equal zero. Is 0 (1)y<1/y
(2)y=zÂ²
The solution below offers a slightly different way to reason through statement 1.

Statement 1: y < 1/y.
The CRITICAL POINTS are where y = 1/y or where the inequality is undefined.
y = 1/y when y=1 or y=-1.
y < 1/y is undefined when y=0.
When y is ANY OTHER VALUE, y < 1/y or y > 1/y.
Thus, there are 4 ranges to consider: y < -1, -11.

To determine the range of y, test one value to the left and right of each critical point.
If y = -2, then the inequality becomes -2 < -1/2.
This works. Thus, y<-1 is part of the range.

If y = -1/2, then the inequality becomes -1/2 < -2.
Doesn't work. Thus, -1
If y = 1/2, then the inequality becomes 1/2 < 2.
This works. Thus, 0
If y = 2, then the inequality becomes 2 < 1/2.
Doesn't work. Thus, y>1 is not part of the range.

Thus, it's possible that y<-1 or that 0 INSUFFICIENT.

Statement 2: y=zÂ².
Since the square of a number cannot be negative, and it is given that yzâ‰ 0, we know that y>0.
Thus, it's possible that y=1/2 (in which case 01).
INSUFFICIENT.

Statements 1 and 2 combined:
The only range that satisfies both statements is 0 SUFFICIENT.

An algebraic way to determine the CRITICAL POINTS of y<1/y is to multiply each side by yÂ².
We can safely multiply by yÂ² for the following reasons:
yâ‰ 0, since 1/y is undefined when y=0.
yÂ² cannot be negative, since the square of a value cannot be negative.
Thus, yÂ²>0.
The result is that we can safely multiply each side by yÂ², knowing that the direction of the inequality will not change:

yÂ²(y) < yÂ²(1/y)
yÂ³ < y
yÂ³ - y < 0
y(yÂ² - 1) < 0
y(y+1)(y-1) < 0.

The CRITICAL POINTS are where y(y+1)((y-1) = 0:
y=-1, y=0 and y=1.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
hemanthkumarmn Junior | Next Rank: 30 Posts
Joined
31 Dec 2012
Posted:
14 messages
1
Tue Jan 29, 2013 4:30 am
If yx cannot equal 0, is 0
y< 1/y

Sub Y=0.5

0.5<1/0.5 - true

Here we can conclude that Y lies between 0 and 1.

Similarly Sub Y= -2

-2< -1/2 - which is again true.

Here we can conclude that Y doesn't lie between 0 and 1.

Hence the statement contradicts each other.

So it isn't sufficient.

bpolley00 Master | Next Rank: 500 Posts
Joined
11 Jul 2012
Posted:
192 messages
Followed by:
5 members
20
Test Date:
3/29/2013
Target GMAT Score:
800
GMAT Score:
650
Tue Jan 29, 2013 5:38 am
Wow, that was really relatively simple. Not quite sure what I was thinking last night. I could have just substituted -2 -1 -.5 0 .5 1 2 in and figured it out. Thank you for the response sir.

-BP

### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
Joined
04 Dec 2012
Posted:
1778 messages
Followed by:
228 members
1443
Tue Jan 29, 2013 12:28 pm
Here's a good rule of thumb with DS questions - try to prove INSUFFICIENCY! That is, try to come up with an example that fits the statement and gives you a "yes" answer to the question, then try to come up with one that fits the statement but gives you a "no" answer. Hemanth came up with two good examples that prove this point.

If you're trying to prove insufficiency with inequalities, there are several things you need to keep in mind: positives v. negatives, integers v. fractions, and 0, 1, and -1 (these are values that can sometimes make things equal, although 0 was ruled out in this particular problem). If you only tested integers v. fractions, you were forgetting about positives v. negatives.

Statement 2 tells us that y must be positive, because it's a non-zero square. If it's positive, then it must be a positive fraction. The answer is C.

_________________

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education

Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
Joined
04 Dec 2012
Posted:
1778 messages
Followed by:
228 members
1443
Tue Jan 29, 2013 12:35 pm
hemanthkumarmn wrote:
If yx cannot equal 0, is 0
y< 1/y

Sub Y=0.5

0.5<1/0.5 - true

Here we can conclude that Y lies between 0 and 1.

Similarly Sub Y= -2

-2< -1/2 - which is again true.

Here we can conclude that Y doesn't lie between 0 and 1.

Hence the statement contradicts each other.

So it isn't sufficient.
Your number testing strategy worked perfectly here! Just a couple of notes...

Generally speaking, it's easier to deal with fractions than with decimals on the GMAT. They're much easier to manipulate when you don't have a calculator. I'd especially avoid mixing decimals and fractions together, like 1/0.5. In this case it didn't matter much, but on more complicated questions it could lead to confusion. (Again, this is not a rule, just a pro-tip).

Another thing - I knew exactly what you meant, but be careful of saying "the statements contradict each other." That's not exactly true. The issue here was that we could take the same statement (which we know must be true), and come up with contradicting answers to the question. Basically, this gives us a "maybe" answer to the question. But it's not the statement itself that is contradictory! Statements are always true. Just wanted to clarify that for the sake of anyone else reading.

_________________

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education

Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

### Best Conversation Starters

1 lheiannie07 80 topics
2 LUANDATO 59 topics
3 ardz24 52 topics
4 AAPL 45 topics
5 Roland2rule 43 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Rich.C@EMPOWERgma...

EMPOWERgmat

133 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

131 posts
3 GMATGuruNY

The Princeton Review Teacher

130 posts
4 Scott@TargetTestPrep

Target Test Prep

118 posts
5 Jeff@TargetTestPrep

Target Test Prep

114 posts
See More Top Beat The GMAT Experts