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.

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:

If x is positive, is x > 3 [#permalink]
16 Apr 2012, 08:42

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

51% (01:43) correct
49% (00:52) wrong based on 144 sessions

If x is positive, is x > 3 ?

(1) (x - 1)^2 > 4 (2) (x - 2)^2 > 9

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

Re: If x is positive, is x > 3 [#permalink]
16 Apr 2012, 10:58

3

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

rohitgoel15 wrote:

If x is positive, is x > 3 ?

(1) (x - 1)^2 > 4 (2) (x - 2)^2 > 9

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.

Re: If x is positive, is x > 3 [#permalink]
20 Jul 2013, 05:57

Hi bunuel,

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? _________________

Re: If x is positive, is x > 3 [#permalink]
20 Jul 2013, 06:32

Expert's post

fozzzy wrote:

Hi bunuel,

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.

Re: If x is positive, is x > 3 [#permalink]
05 Sep 2013, 02:47

Bunuel wrote:

rohitgoel15 wrote:

If x is positive, is x > 3 ?

(1) (x - 1)^2 > 4 (2) (x - 2)^2 > 9

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..

Re: If x is positive, is x > 3 [#permalink]
05 Sep 2013, 02:52

Expert's post

SUNGMAT710 wrote:

Bunuel wrote:

rohitgoel15 wrote:

If x is positive, is x > 3 ?

(1) (x - 1)^2 > 4 (2) (x - 2)^2 > 9

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.

Re: If x is positive, is x > 3 [#permalink]
27 Oct 2013, 21:43

Bunuel wrote:

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.

Answer: D.

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

Re: If x is positive, is x > 3 [#permalink]
27 Oct 2013, 21:57

Expert's post

fozzzy wrote:

Bunuel wrote:

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.

Answer: D.

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

Hey everyone, today’s post focuses on the interview process. As I get ready for interviews at Kellogg and Tuck (and TheEngineerMBA ramps up for his HBS... ...

I got invited to interview at Sloan! The date is October 31st. So, with my Kellogg interview scheduled for this Wednesday morning, and my MIT Sloan interview scheduled...