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:

VeritasPrep blogpost: GMAT Data Sufficiency Powers and Roots [#permalink]

Show Tags

01 May 2013, 18:29

Hi,

An article was posted 2 days back on their blog and I can't seem to open it now. I have the post saved on my Android app "Pocket". Here's the post in its entirety:

Even if you know the basic rules for questions involving powers and roots, it’s still common to feel some intimidation towards harder-looking GMAT questions. The “ ” symbol is called the “radical” symbol. You may know the square root, but how comfortable are you with cube roots? For instance:

The “3″ in the above is the “index” of the radical; to simplify radicals, use your knowledge of factors:

64 = 2 x 2 x 2 x 2 x 2 x 2

There are six 2’s in 64. Since the index is 3, we know we need three of the same number to pull it out from underneath the radical. Exponents and radicals appear most frequently on the GMAT in data sufficiency questions dealing with number properties:

If z < 0, then what is

? If z is negative, then –z will be z. The absolute value of –z will be z. The square root of z*z = z. Since z is negative, the answer is –z. The number underneath a radical cannot be negative. It is imaginary.

When multiplying radicals, we can multiply the elements underneath the radicals: √3 x √2 = √6

When dividing radicals, we can divide the elements underneath the radicals: √6 / √2 = √3

When adding or subtracting similar radicals, treat the radicals like variables and combine like terms: 2√3 + 4√3 – √2 + 7√2 = 6√3 + 6√2

On the GMAT, you will never be required to know a decimal equivalent of a radical. If you see a complicated-looking radical, try to “ballpark” it. For example, it is enough to recognize that √110 is going to be slightly larger than 10, since √100 = 10. Let’s look at a question involving exponents:

Is x2 > x ?

(1) x2 > 4 (2) x > -2

Because you know your exponent rules, you know that whether x2 > x is true is dependent on what kind of number x is. Let’s quickly plug in:

If x = 1, then x2 > x = 1 > 1. Not true. If x = ½, then x2 > x = ¼ > ½. Not true. If x = 0, then x2 > x = 0 > 0. Not true. If x = -1/2, then x2 > x = ¼ > -1/2. True. If x = -1, then x2 > x = 1 > -1. True.

We can see that when x is negative, the answer will be YES. When x is positive, the answer will be NO. For Statement (1), x could be negative or positive, so insufficient. For (2), x could still be negative or positive. If we combine, x > 2 in order to satisfy both conditions.

The correct answer is (C).

The rules don’t change because powers and roots are combined with a secondary concept, such as inequalities here, so don’t let a combination of ideas throw you as you practice!

I'm having trouble understanding why the answer is C. For x^2 to be greater than x, x needs to have a 'value' greater than 1. For any x in -1 <= x <= 1, x^2 is not greater than x. (1) seems to indicate that x is at least 2+ in value, which is sufficient to conclude that x^2 > x.

either both are positive x-2>0 and x+2>0 that means x>2 and x>-2

or both are negative x-2<0 and x+2<0 that means x<-2 and x<2

After considering outermost intervals of both possibilities we can conclude that x is greater than 2 or less than -2, which is sufficient to answer the question.

Re: VeritasPrep blogpost: GMAT Data Sufficiency Powers and Roots [#permalink]

Show Tags

02 May 2013, 22:38

The explanation to this problem is incorrect.

Is x^2 > x ?

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

Statement 1: x^2>4 implies that either x>2 or x<-2, if x =3 then the answer to the question is Yes(9>3). In general, any number greater than 1 when squared is greater than the original number so the answer is Yes for all values of x greater than 2. If we consider the case of x<-2, here the square of x will always be positive and that will always exceed x, again the answer is Yes. Sufficient.

Statement 2: x > -2. If x = -1.5, then the answer is Yes, but if x = 1/2, then the answer is No. One can also use x = 0 or x = 1 to show No. Insufficient.

An article was posted 2 days back on their blog and I can't seem to open it now. I have the post saved on my Android app "Pocket". Here's the post in its entirety:

Even if you know the basic rules for questions involving powers and roots, it’s still common to feel some intimidation towards harder-looking GMAT questions. The “ ” symbol is called the “radical” symbol. You may know the square root, but how comfortable are you with cube roots? For instance:

The “3″ in the above is the “index” of the radical; to simplify radicals, use your knowledge of factors:

64 = 2 x 2 x 2 x 2 x 2 x 2

There are six 2’s in 64. Since the index is 3, we know we need three of the same number to pull it out from underneath the radical. Exponents and radicals appear most frequently on the GMAT in data sufficiency questions dealing with number properties:

If z < 0, then what is

? If z is negative, then –z will be z. The absolute value of –z will be z. The square root of z*z = z. Since z is negative, the answer is –z. The number underneath a radical cannot be negative. It is imaginary.

When multiplying radicals, we can multiply the elements underneath the radicals: √3 x √2 = √6

When dividing radicals, we can divide the elements underneath the radicals: √6 / √2 = √3

When adding or subtracting similar radicals, treat the radicals like variables and combine like terms: 2√3 + 4√3 – √2 + 7√2 = 6√3 + 6√2

On the GMAT, you will never be required to know a decimal equivalent of a radical. If you see a complicated-looking radical, try to “ballpark” it. For example, it is enough to recognize that √110 is going to be slightly larger than 10, since √100 = 10. Let’s look at a question involving exponents:

Is x2 > x ?

(1) x2 > 4 (2) x > -2

Because you know your exponent rules, you know that whether x2 > x is true is dependent on what kind of number x is. Let’s quickly plug in:

If x = 1, then x2 > x = 1 > 1. Not true. If x = ½, then x2 > x = ¼ > ½. Not true. If x = 0, then x2 > x = 0 > 0. Not true. If x = -1/2, then x2 > x = ¼ > -1/2. True. If x = -1, then x2 > x = 1 > -1. True.

We can see that when x is negative, the answer will be YES. When x is positive, the answer will be NO. For Statement (1), x could be negative or positive, so insufficient. For (2), x could still be negative or positive. If we combine, x > 2 in order to satisfy both conditions.

The correct answer is (C).

The rules don’t change because powers and roots are combined with a secondary concept, such as inequalities here, so don’t let a combination of ideas throw you as you practice!

I'm having trouble understanding why the answer is C. For x^2 to be greater than x, x needs to have a 'value' greater than 1. For any x in -1 <= x <= 1, x^2 is not greater than x. (1) seems to indicate that x is at least 2+ in value, which is sufficient to conclude that x^2 > x.

Please help me understand.

Thank you!

I would guess that the reason you cannot find that post anymore is that it has been put down because an error had crept into it. The answer to this question is (A).

(1) \(x^2 > 4\) tells you that x > 2 or x < -2 In that case, definitely, \(x^2 > x\) holds
_________________

Re: VeritasPrep blogpost: GMAT Data Sufficiency Powers and Roots [#permalink]

Show Tags

03 May 2013, 18:13

VeritasPrepKarishma wrote:

I would guess that the reason you cannot find that post anymore is that it has been put down because an error had crept into it. The answer to this question is (A).

(1) \(x^2 > 4\) tells you that x > 2 or x < -2 In that case, definitely, \(x^2 > x\) holds

Thank you, Karishma!

gmatclubot

Re: VeritasPrep blogpost: GMAT Data Sufficiency Powers and Roots
[#permalink]
03 May 2013, 18:13

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...