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??

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'.

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'.

Is y greater than y^2 ?

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