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

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Approach 1: I tried to simplify this question as follows x^2 + 1 - xy > 0 x(y-x) < 1 But we can't be sure of the sign of the inequality as I have cross multiplied by x (whose sign I do now know). So in essence the question can be rephrased as: x(y-x) [greater than, equal to or less than] 1 --> This is what is actually being asked.

I want to know if i have made any fundamental mistake when doing this rephrasing. As I have already mentioned I know that the sign of the inequality should be reversed when multiplied by a negative number.

So going by this approach the answer is A

Approach 2:

I will consider both cases of x before cross multiplying.

Case 1: x is negative x^2+1 < xy x^2-xy + 1 < 0 x(x-y) + 1 <0

Case 2: x is positive x^2+1 > xy x^2-xy + 1 > 0 x(x-y) + 1 > 0

So based on these 2 equations we find that statement (1) alone is not sufficient because it gives different answers for Case 1 and 2 i.e. 1 < 0 and 1 > 0.

Statement 2 is also insufficient because it does not say anything about x.

Combining 1 and 2 - y > 0 x = y Therefore, x > 0 x(x-y) + 1 > 0

Therefore C is the answer.

The second approach looks more methodical but I want to understand why the first approach is INVALID (if it is so).

... So in essence the question can be rephrased as: x(y-x) [greater than, equal to or less than] 1 --> This is what is actually being asked.

You can't rephrase it in that way. First of all you need to drop "equal" and then add conditions: x(y-x) [greater than (for negative x) or less than (for positive x)] 1 It actually means your second approach.

I don't know what x!=0 means. There is no x for which x!=0
_________________

What will be the correct answer to this question? I am confused.

Approach 1: I tried to simplify this question as follows x^2 + 1 - xy > 0 x(y-x) < 1 But we can't be sure of the sign of the inequality as I have cross multiplied by x (whose sign I do now know). So in essence the question can be rephrased as: x(y-x) [greater than, equal to or less than] 1 --> This is what is actually being asked.

I want to know if i have made any fundamental mistake when doing this rephrasing. As I have already mentioned I know that the sign of the inequality should be reversed when multiplied by a negative number.

So going by this approach the answer is A

There is no problem in re-phrasing . But how do u get A? st.1 says X=Y from rephrase X(y-X)<1 X(X-X)<1 X*0<1 0<1........ not sufficient

Even here, statement (1) is sufficient to answer the question! how is it insufficient!?

You can't multiply both sides of an inequality by a variable unless the variable is positive. The inequality may be reversed e.g. 1>-4 Multiplying both sides by -1 we get- -1<4 & not -1>4

Another way to solve this is to just simplify the equation (x^2+1)/x>Y or x+1/x>y

Start with statement 2, to make the solution simpler. 2. y>0 we have no idea what the value of x is. x can be positive but lesser/greater than y or negative which would make the expression negative. Eliminate B & D

1. x=y We don't know what are x & y so it's hard to precisely determine whether the expression will be greater or lesser than y

1+2 y>0 & x=y Positive+Positive is Positive. x+1/x=y+1/y i.e. positive number + some fraction so y+1/y>y

Hence C
_________________

Hit kudos if my post helps you. You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Statement 1... If x = 2, 2^2+1 =5. 5/2 = 2.5, given x=y=2 Then 2.5>2 If x = -2, (-2^2+1) = 5, 5/-2 = -2.5. Then -2.5 > -2 ...not true... 1 insufficient.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...