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:

hi, apply definition absolute value obtain two possibilites: A. if x≥0 then 0<|x|-4x<5 go 0<x-4x<5 go 0<-3x<5, go 0>x>-5/3. The intersection is empty B. if x<0 then 0<|x|-4x<5 go 0<-x-4x<5 go 0<-5x<5 go 0>x>-1. the intersection is -1<x<0

Got to the correct answer but took too much time...E

If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

0<|x|-4x<5 = ?

A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer. _________________

Got to the correct answer but took too much time...E

If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

0<|x|-4x<5 = ?

A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer.

I believe the choice of -4/5 to execlude D is wrong -4/5 is not in the range of -3/5<x<0 ????? accordingly i think both D and E could solve as the right range in my opinion is -5/3 < x < 0??? am i right or wrong plz advise!

Got to the correct answer but took too much time...E

If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

0<|x|-4x<5 = ?

A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer.

I believe the choice of -4/5 to execlude D is wrong -4/5 is not in the range of -3/5<x<0 ????? accordingly i think both D and E could solve as the right range in my opinion is -5/3 < x < 0??? am i right or wrong plz advise!

Focus on "and if there is even one value outside the given range that does satisfy the inequality, it is not the answer." given above.

-4/5 is a value which satisfies 0 < |x|-4x < 5 since |-4/5|-4(-4/5) = 4. Since -4/5 does not lie in the range -3/5<x<0 so (D) cannot be the answer. The correct range needs to cover all possible values of x. _________________

There are two options here - plugging in values given to us in the answer choices or simplifying the inequality.

0<|x|-4x<5

x>0: 0<x-4x<5 0<-3x<5 0<x<-5/3 -5/3<x<0 INVALID as x does not fall within the range of x>0 OR x<0: 0<(-x)-4x<5 0<-5x<5 0<x<-1 -1<x<0 VALID as x falls within the range of x<0

Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]
29 Jan 2014, 20:03

Expert's post

jlgdr wrote:

Would be happy to hear some comments on whether this approach is correct

|x|-4x>0

So we have two cases

If x>0 then x-4x>0 -3x>0 x<0, this contradicts and hence is not a valid solution

If x<0 then -5x>0 x<0, this solution is valid

So we get that -1<x<0 replacing in the original inequality

E

Knowing only x < 0, how do you choose between (A), (D) and (E)? You need to consider |x| - 4x < 5 too When x < 0, -x -4x < 5 -5x < 5 x > -1 That's how you get -1 < x < 0

Or work on the whole inequality in one go 0 < |x| - 4x < 5 When x < 0, 0< -x - 4x < 5 0 < -5x < 5 0 < -x < 1 0 > x > -1

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. _________________

Hey, So I had a doubt. For the equaltiy: 0<|x|-4x<5 if I try and solve it algebraically, i first take x<0 In that case won't this equality be: 0<-x-4(-x)<5. I can't just substitute mod x with -x and leave the other x be can I? Please help! Thanks!

Hey, So I had a doubt. For the equaltiy: 0<|x|-4x<5 if I try and solve it algebraically, i first take x<0 In that case won't this equality be: 0<-x-4(-x)<5. I can't just substitute mod x with -x and leave the other x be can I? Please help! Thanks!

Say you have an inequality: 4x < 5 and you know that x must be negative. How will you solve the inequality? Will you say that the inequality becomes -4x < 5? No. You are given that 4x < 5. Without changing the inequality, you can write this as x < 5/4. x needs to be negative. All negative values will be less than 5/4.

Why do you substitute -x in place of |x|? You cannot solve an equation/inequality with |x| in it. You need to remove the absolute value sign.

You know that |x| = x if x is positive and |x| = -x if x is negative.

Since you know that x is negative, you can write -x in place of |x| without changing the inequality. If you change the simple x to -x in the inequality, the inequality changes.

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

Every student has a predefined notion about a MBA degree:- hefty packages, good job opportunities, improvement in position and salaries but how many really know the journey of becoming...