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:

Can someone point a mistake in my method? (1) Taking one of the equations: (x - 1)^2 > 4 x^2 + 1 - 2x > 4 x^2 + 1 - 2x - 4 > 0 x^2 - 3x + 1x - 3 > 0 (x-3) (x+1) > 0 x > 3 and x > -1

while in the explanation given the ans is coming out to be x > 3 and x < -1

Can someone point a mistake in my method? (1) Taking one of the equations: (x - 1)^2 > 4 x^2 + 1 - 2x > 4 x^2 + 1 - 2x - 4 > 0 x^2 - 3x + 1x - 3 > 0 (x-3) (x+1) > 0 x > 3 and x > -1

while in the explanation given the ans is coming out to be x > 3 and x < -1

Please help ..

If x is positive, is x > 3 ?

(1) (x - 1)^2 > 4 --> \((x+1)(x-3)>0\) --> roots are -1 and 3. Now, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>3\). Since given that \(x\) is positive then only one range is valid: \(x>3\). Sufficient.

(2) (x - 2)^2 > 9 --> \((x+1)(x-5)>0\) --> roots are -1 and 5. Again, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>5\). Since given that \(x\) is positive then only one range is valid: \(x>5\). Sufficient.

(1) (x - 1)^2 > 4 --> since both sides of the inequality are non-negative then we can take square root from both parts: \(|x-1|>2\). \(|x-1|\) is just the distance between 1 and \(x\) on the number line. We are told that this distance is more than 2: --(-1)----1----3-- so, \(x<-1\) or \(x>3\). Since given that \(x\) is positive then only one range is valid: \(x>3\). Sufficient.

(2) (x - 2)^2 > 9 --> \(|x-2|>3\). The same here: \(|x-2|\) is just the distance between 2 and \(x\) on the number line. We are told that this distance is more than 3: --(-1)----2----5-- so, \(x<-1\) or \(x>5\). Since given that \(x\) is positive then only one range is valid: \(x>5\). Sufficient.

Just wanted to clarify in the alternative approach you mentioned "non-negative" so if the other side of the inequality has a negative number, the only way to proceed with the problem is by expansion? _________________

Just wanted to clarify in the alternative approach you mentioned "non-negative" so if the other side of the inequality has a negative number, the only way to proceed with the problem is by expansion?

If it were (x - 1)^2 > -4, it would simply mean that x can take any value.

As for general rules for inequalities: taking the square root, squaring, ...

ADDING/SUBTRACTING INEQUALITIES:

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\). Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

RAISING INEQUALITIES TO EVEN/ODD POWER:

A. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality). For example: \(2<4\) --> we can square both sides and write: \(2^2<4^2\); \(0\leq{x}<{y}\) --> we can square both sides and write: \(x^2<y^2\);

But if either of side is negative then raising to even power doesn't always work. For example: \(1>-2\) if we square we'll get \(1>4\) which is not right. So if given that \(x>y\) then we can not square both sides and write \(x^2>y^2\) if we are not certain that both \(x\) and \(y\) are non-negative.

B. We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality). For example: \(-2<-1\) --> we can raise both sides to third power and write: \(-2^3=-8<-1=-1^3\) or \(-5<1\) --> \(-5^2=-125<1=1^3\); \(x<y\) --> we can raise both sides to third power and write: \(x^3<y^3\).

Can someone point a mistake in my method? (1) Taking one of the equations: (x - 1)^2 > 4 x^2 + 1 - 2x > 4 x^2 + 1 - 2x - 4 > 0 x^2 - 3x + 1x - 3 > 0 (x-3) (x+1) > 0 x > 3 and x > -1

while in the explanation given the ans is coming out to be x > 3 and x < -1

Please help ..

If x is positive, is x > 3 ?

(1) (x - 1)^2 > 4 --> \((x+1)(x-3)>0\) --> roots are -1 and 3. Now, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>3\). Since given that \(x\) is positive then only one range is valid: \(x>3\). Sufficient.

(2) (x - 2)^2 > 9 --> \((x+1)(x-5)>0\) --> roots are -1 and 5. Again, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>5\). Since given that \(x\) is positive then only one range is valid: \(x>5\). Sufficient.

(1) (x - 1)^2 > 4 --> since both sides of the inequality are non-negative then we can take square root from both parts: \(|x-1|>2\). \(|x-1|\) is just the distance between 1 and \(x\) on the number line. We are told that this distance is more than 2: --(-1)----1----3-- so, \(x<-1\) or \(x>3\). Since given that \(x\) is positive then only one range is valid: \(x>3\). Sufficient.

(2) (x - 2)^2 > 9 --> \(|x-2|>3\). The same here: \(|x-2|\) is just the distance between 2 and \(x\) on the number line. We are told that this distance is more than 3: --(-1)----2----5-- so, \(x<-1\) or \(x>5\). Since given that \(x\) is positive then only one range is valid: \(x>5\). Sufficient.

Answer: D.

I used x= +6 and -6 ..Which is true in both the cases..it shud be E..

Can someone point a mistake in my method? (1) Taking one of the equations: (x - 1)^2 > 4 x^2 + 1 - 2x > 4 x^2 + 1 - 2x - 4 > 0 x^2 - 3x + 1x - 3 > 0 (x-3) (x+1) > 0 x > 3 and x > -1

while in the explanation given the ans is coming out to be x > 3 and x < -1

Please help ..

If x is positive, is x > 3 ?

(1) (x - 1)^2 > 4 --> \((x+1)(x-3)>0\) --> roots are -1 and 3. Now, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>3\). Since given that \(x\) is positive then only one range is valid: \(x>3\). Sufficient.

(2) (x - 2)^2 > 9 --> \((x+1)(x-5)>0\) --> roots are -1 and 5. Again, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>5\). Since given that \(x\) is positive then only one range is valid: \(x>5\). Sufficient.

(1) (x - 1)^2 > 4 --> since both sides of the inequality are non-negative then we can take square root from both parts: \(|x-1|>2\). \(|x-1|\) is just the distance between 1 and \(x\) on the number line. We are told that this distance is more than 2: --(-1)----1----3-- so, \(x<-1\) or \(x>3\). Since given that \(x\) is positive then only one range is valid: \(x>3\). Sufficient.

(2) (x - 2)^2 > 9 --> \(|x-2|>3\). The same here: \(|x-2|\) is just the distance between 2 and \(x\) on the number line. We are told that this distance is more than 3: --(-1)----2----5-- so, \(x<-1\) or \(x>5\). Since given that \(x\) is positive then only one range is valid: \(x>5\). Sufficient.

Answer: D.

I used x= +6 and -6 ..Which is true in both the cases..it shud be E..

Stem says that x is a positive number, thus x cannot be -6.

(1) (x - 1)^2 > 4 --> \((x+1)(x-3)>0\) --> roots are -1 and 3.Now, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>3\). Since given that \(x\) is positive then only one range is valid: \(x>3\). Sufficient.

(2) (x - 2)^2 > 9 --> \((x+1)(x-5)>0\) --> roots are -1 and 5. Again, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>5\). Since given that \(x\) is positive then only one range is valid: \(x>5\). Sufficient.

Answer: D.

I have a question if the sign was "<" instead of ">" what would the solution be? (x+1)(x-3) < 0 _________________

(1) (x - 1)^2 > 4 --> \((x+1)(x-3)>0\) --> roots are -1 and 3.Now, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>3\). Since given that \(x\) is positive then only one range is valid: \(x>3\). Sufficient.

(2) (x - 2)^2 > 9 --> \((x+1)(x-5)>0\) --> roots are -1 and 5. Again, ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: \(x<-1\) or \(x>5\). Since given that \(x\) is positive then only one range is valid: \(x>5\). Sufficient.

Answer: D.

I have a question if the sign was "<" instead of ">" what would the solution be? (x+1)(x-3) < 0

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. _________________

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

Cal Newport is a computer science professor at GeorgeTown University, author, blogger and is obsessed with productivity. He writes on this topic in his popular Study Hacks blog. I was...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...