BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

is y greater than y^2? tricky concept Q for instructors

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 171
Joined: Fri Apr 16, 2010 1:02 am
Thanked: 1 times

is y greater than y^2? tricky concept Q for instructors

by san2009 » Wed Aug 04, 2010 10:15 am
I am having trouble rephrasring this question ALGEBRAICALLY and solving
I understand, that Y will be greater than y^2 if y is a proper fraction i.e. 0<y<1
HOWEVER, I am UNABLE to simplify this ALGEBRAICALLY. Pls advise


Is y greater than y^2 ?

1) y is greater than -1.
2) y^2 is greater than 1.

Please tell me where I am going wrong with this

First rephrase the original inequality
y>y^2?

y^2 - y < 0 ?

Factoring out the common y

y(y-1)<0 ?

In order for this inequality to hold
either y<0 and y-1>0 or
(y-1) <0 and y > 0
this is b/c the two must have opposite signs

The first possibility simplified gives us
y<0 and y>1

The second possibility simplified gives us
y>0 and y<1


statement 1:
y > -1
this doesnt even tell us whether y>0 or y<0
insuff

statement 2
y^2>1
then, either y>1 or y<-1
OA is B
HOW DO YOU FIGURE OUT THE ANSWER TO THE REPHRASED QUESTION WITH THIS STATEMENT??
Top
Source: — Data Sufficiency |
Senior | Next Rank: 100 Posts
Posts: 97
Joined: Thu Jan 28, 2010 2:07 am
Thanked: 9 times

by aloneontheedge » Wed Aug 04, 2010 10:27 am
san2009 wrote:I am having trouble rephrasring this question ALGEBRAICALLY and solving
I understand, that Y will be greater than y^2 if y is a proper fraction i.e. 0<y<1
HOWEVER, I am UNABLE to simplify this ALGEBRAICALLY. Pls advise


Is y greater than y^2 ?

1) y is greater than -1.
2) y^2 is greater than 1.

Please tell me where I am going wrong with this

First rephrase the original inequality
y>y^2?

y^2 - y < 0 ?

Factoring out the common y

y(y-1)<0 ?

In order for this inequality to hold
either y<0 and y-1>0 or
(y-1) <0 and y > 0
this is b/c the two must have opposite signs

The first possibility simplified gives us
y<0 and y>1

The second possibility simplified gives us
y>0 and y<1


statement 1:
y > -1
this doesnt even tell us whether y>0 or y<0
insuff

statement 2
y^2>1
then, either y>1 or y<-1
OA is B
HOW DO YOU FIGURE OUT THE ANSWER TO THE REPHRASED QUESTION WITH THIS STATEMENT??
What is the source?
y can be greater than y^2 only when 0<y<1
Top
Master | Next Rank: 500 Posts
Posts: 171
Joined: Fri Apr 16, 2010 1:02 am
Thanked: 1 times

by san2009 » Wed Aug 04, 2010 10:29 am
knewton
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Wed Aug 04, 2010 2:08 pm
san2009 wrote:I am having trouble rephrasring this question ALGEBRAICALLY and solving
I understand, that Y will be greater than y^2 if y is a proper fraction i.e. 0<y<1
HOWEVER, I am UNABLE to simplify this ALGEBRAICALLY. Pls advise


Is y greater than y^2 ?

1) y is greater than -1.
2) y^2 is greater than 1.

Please tell me where I am going wrong with this

First rephrase the original inequality
y>y^2?

y^2 - y < 0 ?

Factoring out the common y

y(y-1)<0 ?

In order for this inequality to hold
either y<0 and y-1>0 or
(y-1) <0 and y > 0
this is b/c the two must have opposite signs

The first possibility simplified gives us
y<0 and y>1

The second possibility simplified gives us
y>0 and y<1


statement 1:
y > -1
this doesnt even tell us whether y>0 or y<0
insuff

statement 2
y^2>1
then, either y>1 or y<-1
OA is B
HOW DO YOU FIGURE OUT THE ANSWER TO THE REPHRASED QUESTION WITH THIS STATEMENT??
Your method looks fine, if a bit long; it's just incomplete. First, when you analyze the question, you came up with two scenarios in which the answer to the question would be 'yes'. I've highlighted one of those two scenarios in red above. You should rewrite the inequalities you arrive at, if possible, as simple inequalities about y, so the statements will be easier to evaluate. In the first case, the one I highlighted in red, you discovered that y < 0 *and* y > 1 must *both* be true. That's impossible, so this case can never happen, and we should ignore it. In the other case, the one I did not highlight, you found that y > 0 and y < 1 must *both* be true. In other words, we can be sure the answer to the question is 'yes' if we know that 0 < y < 1. Conversely, we can be sure the answer to the question is 'no' if we know that y is *not* between 0 and 1.

From Statement 1, we don't know whether y is between 0 and 1. From Statement 2, however, as you showed above, we know that either y < -1, or y > 1. That is, we can be absolutely certain that y is *not* between 0 and 1, and thus can be absolutely certain that the answer to the original question is 'no'. Since we can answer the question, the statement is sufficient - we don't care if the answer is 'yes' or 'no', of course.

I'd add that these kinds of yes/no DS questions, where one statement gives you enough information to be certain that the answer to the question is 'no', are *far* more common in prep company materials than they are on the real GMAT. There is, for example, only one yes/no DS question in the entire Official Guide (out of about 50 yes/no examples) where you have enough information to give a 'no' answer. It's the kind of trap that is overemphasized in some prep material; on most (with occasional exceptions) yes/no DS questions on the real GMAT, if you have enough information to answer the question, the answer will turn out to be 'yes'.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Senior | Next Rank: 100 Posts
Posts: 97
Joined: Thu Jan 28, 2010 2:07 am
Thanked: 9 times

by aloneontheedge » Wed Aug 04, 2010 7:50 pm
Ian Stewart wrote:
san2009 wrote:I am having trouble rephrasring this question ALGEBRAICALLY and solving
I understand, that Y will be greater than y^2 if y is a proper fraction i.e. 0<y<1
HOWEVER, I am UNABLE to simplify this ALGEBRAICALLY. Pls advise


Is y greater than y^2 ?

1) y is greater than -1.
2) y^2 is greater than 1.

Please tell me where I am going wrong with this

First rephrase the original inequality
y>y^2?

y^2 - y < 0 ?

Factoring out the common y

y(y-1)<0 ?

In order for this inequality to hold
either y<0 and y-1>0 or
(y-1) <0 and y > 0
this is b/c the two must have opposite signs

The first possibility simplified gives us
y<0 and y>1

The second possibility simplified gives us
y>0 and y<1


statement 1:
y > -1
this doesnt even tell us whether y>0 or y<0
insuff

statement 2
y^2>1
then, either y>1 or y<-1
OA is B
HOW DO YOU FIGURE OUT THE ANSWER TO THE REPHRASED QUESTION WITH THIS STATEMENT??
Your method looks fine, if a bit long; it's just incomplete. First, when you analyze the question, you came up with two scenarios in which the answer to the question would be 'yes'. I've highlighted one of those two scenarios in red above. You should rewrite the inequalities you arrive at, if possible, as simple inequalities about y, so the statements will be easier to evaluate. In the first case, the one I highlighted in red, you discovered that y < 0 *and* y > 1 must *both* be true. That's impossible, so this case can never happen, and we should ignore it. In the other case, the one I did not highlight, you found that y > 0 and y < 1 must *both* be true. In other words, we can be sure the answer to the question is 'yes' if we know that 0 < y < 1. Conversely, we can be sure the answer to the question is 'no' if we know that y is *not* between 0 and 1.

From Statement 1, we don't know whether y is between 0 and 1. From Statement 2, however, as you showed above, we know that either y < -1, or y > 1. That is, we can be absolutely certain that y is *not* between 0 and 1, and thus can be absolutely certain that the answer to the original question is 'no'. Since we can answer the question, the statement is sufficient - we don't care if the answer is 'yes' or 'no', of course.

I'd add that these kinds of yes/no DS questions, where one statement gives you enough information to be certain that the answer to the question is 'no', are *far* more common in prep company materials than they are on the real GMAT. There is, for example, only one yes/no DS question in the entire Official Guide (out of about 50 yes/no examples) where you have enough information to give a 'no' answer. It's the kind of trap that is overemphasized in some prep material; on most (with occasional exceptions) yes/no DS questions on the real GMAT, if you have enough information to answer the question, the answer will turn out to be 'yes'.
Thanks Ian,
I just missed that point. Ur explanation was awesome
Top
Master | Next Rank: 500 Posts
Posts: 171
Joined: Fri Apr 16, 2010 1:02 am
Thanked: 1 times

by san2009 » Thu Aug 05, 2010 12:13 am
Ian Stewart wrote:
san2009 wrote:I am having trouble rephrasring this question ALGEBRAICALLY and solving
I understand, that Y will be greater than y^2 if y is a proper fraction i.e. 0<y<1
HOWEVER, I am UNABLE to simplify this ALGEBRAICALLY. Pls advise


Is y greater than y^2 ?

1) y is greater than -1.
2) y^2 is greater than 1.

Please tell me where I am going wrong with this

First rephrase the original inequality
y>y^2?

y^2 - y < 0 ?

Factoring out the common y

y(y-1)<0 ?

In order for this inequality to hold
either y<0 and y-1>0 or
(y-1) <0 and y > 0
this is b/c the two must have opposite signs

The first possibility simplified gives us
y<0 and y>1

The second possibility simplified gives us
y>0 and y<1


statement 1:
y > -1
this doesnt even tell us whether y>0 or y<0
insuff

statement 2
y^2>1
then, either y>1 or y<-1
OA is B
HOW DO YOU FIGURE OUT THE ANSWER TO THE REPHRASED QUESTION WITH THIS STATEMENT??
Your method looks fine, if a bit long; it's just incomplete. First, when you analyze the question, you came up with two scenarios in which the answer to the question would be 'yes'. I've highlighted one of those two scenarios in red above. You should rewrite the inequalities you arrive at, if possible, as simple inequalities about y, so the statements will be easier to evaluate. In the first case, the one I highlighted in red, you discovered that y < 0 *and* y > 1 must *both* be true. That's impossible, so this case can never happen, and we should ignore it. In the other case, the one I did not highlight, you found that y > 0 and y < 1 must *both* be true. In other words, we can be sure the answer to the question is 'yes' if we know that 0 < y < 1. Conversely, we can be sure the answer to the question is 'no' if we know that y is *not* between 0 and 1.

From Statement 1, we don't know whether y is between 0 and 1. From Statement 2, however, as you showed above, we know that either y < -1, or y > 1. That is, we can be absolutely certain that y is *not* between 0 and 1, and thus can be absolutely certain that the answer to the original question is 'no'. Since we can answer the question, the statement is sufficient - we don't care if the answer is 'yes' or 'no', of course.

I'd add that these kinds of yes/no DS questions, where one statement gives you enough information to be certain that the answer to the question is 'no', are *far* more common in prep company materials than they are on the real GMAT. There is, for example, only one yes/no DS question in the entire Official Guide (out of about 50 yes/no examples) where you have enough information to give a 'no' answer. It's the kind of trap that is overemphasized in some prep material; on most (with occasional exceptions) yes/no DS questions on the real GMAT, if you have enough information to answer the question, the answer will turn out to be 'yes'.
Thanks Ian. DS Inequality questions are tricky to say the least. I see your point about getting a definitive "no" to the original rephrased Q. In fact, it seems that when you do get a definitive "no" the information you get matches very closely to the rephrased Q and very rarely requires little interpretation as did statement 2 -- which can be difficult under timing constraints. Thanks again!
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 233
Joined: Mon Jun 09, 2008 1:30 am
Thanked: 5 times

by blaster » Thu Aug 05, 2010 1:17 am
Is y greater than y^2 ?

1) y is greater than -1.
2) y^2 is greater than 1.
first we must think about in which situation it can happen? it only happens when 0<y<1 .
1) doesn't give us something. y can be 0.5 and also 1. that's why INSUF
2) here we see that y is not 0<y<1 ,that's why sufficient.
Top
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Wed Apr 21, 2010 11:56 am

by mahen_gupta » Thu Aug 05, 2010 3:45 pm
This is my First Post

Statement 1:

y > -1 So Y can be -1/2, 0 and 1. If you use these 3 values, you get different results for statement is y > y^2?
So Insuff.

Statement 2:

y^2 > 1 means (y^2 - 1) > 0 means either y > 1 or y < -1, again pick 2 values such as -3 and 3, you will see that

y is never greater than y^2 so Suff.

Answer - B
Top
Post new topic Post Reply
• Page 1 of 1