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:

Concentration: General Management, Entrepreneurship

GPA: 3.54

WE: Project Management (Retail Banking)

Re: Which of the following inequalities specifies the shaded reg [#permalink]

Show Tags

22 Jun 2013, 02:03

9

This post received KUDOS

No need to plug here , from the shaded region we know that -1<x<4 so all you have to do is to check the answer choices whether they match with the given inequality

l 2x-3 l< 5 means that -5 < 2x - 3 < 5 --> -2 < 2x < 8 --> -1 < x < 4

Answer : B
_________________

KUDOS is the good manner to help the entire community.

"If you don't change your life, your life will change you"

Which of the following inequalities specifies the shaded region to the left?

From the diagram we know that \(-1<x<4\).

A. \(\sqrt{x^2+ 1}< 3\) --> square the inequality (we can do this since both sides are non-negative): \(x^2+1<9\) --> \(x^2<8\) --> \(-2\sqrt{2}<x<2\sqrt{2}\).

B. |2x - 3| < 5 --> \(-5<2x - 3<5\) --> add 3 to each part: \(-2<2x<8\) --> reduce by 2: \(-1<x<4\). BINGO!

C. |x + 1| > -1. No need to test this one. The absolute value is always more than or equal to zero, thus this inequality holds for any value of x.

D. x - 2 < 2 --> \(x<4\).

E. |x - 1| < 4 --> \(-4<x - 1<4\) --> add 1 to each part: \(-3<x<5\).

Re: Which of the following inequalities specifies the shaded reg [#permalink]

Show Tags

28 Jun 2013, 08:46

Bunuel wrote:

Which of the following inequalities specifies the shaded region to the left?

From the diagram we know that \(-1<x<4\).

A. \(\sqrt{x^2+ 1}< 3\) --> square the inequality (we can do this since both sides are non-negative): \(x^2+1<9\) --> \(x^2<8\) --> \(-2\sqrt{2}<x<2\sqrt{2}\).

B. |2x - 3| < 5 --> \(-5<2x - 3<5\) --> add 3 to each part: \(-2<2x<8\) --> reduce by 2: \(-1<x<4\). BINGO!

C. |x + 1| > -1. No need to test this one. The absolute value is always more than or equal to zero, thus this inequality holds for any value of x.

D. x - 2 < 2 --> \(x<4\).

E. |x - 1| < 4 --> \(-4<x - 1<4\) --> add 1 to each part: \(-3<x<5\).

Answer: B.

Does this make sense?

Hi Bunuel,

This does make sense. A lil doubt here I would like to understand the red colored bit above. How did you reach to the conclusion? I am sorry if the question sounds silly, but I am trying to learn the correct ways to handle such problems and I take it from the forum that you are the best goto guy for this. Thanks in advance, Vaibhav.
_________________

Which of the following inequalities specifies the shaded region to the left?

From the diagram we know that \(-1<x<4\).

A. \(\sqrt{x^2+ 1}< 3\) --> square the inequality (we can do this since both sides are non-negative): \(x^2+1<9\) --> \(x^2<8\) --> \(-2\sqrt{2}<x<2\sqrt{2}\).

B. |2x - 3| < 5 --> \(-5<2x - 3<5\) --> add 3 to each part: \(-2<2x<8\) --> reduce by 2: \(-1<x<4\). BINGO!

C. |x + 1| > -1. No need to test this one. The absolute value is always more than or equal to zero, thus this inequality holds for any value of x.

D. x - 2 < 2 --> \(x<4\).

E. |x - 1| < 4 --> \(-4<x - 1<4\) --> add 1 to each part: \(-3<x<5\).

Answer: B.

Does this make sense?

Hi Bunuel,

This does make sense. A lil doubt here I would like to understand the red colored bit above. How did you reach to the conclusion? I am sorry if the question sounds silly, but I am trying to learn the correct ways to handle such problems and I take it from the forum that you are the best goto guy for this. Thanks in advance, Vaibhav.

Not sure what to add...

|x + 1| is an absolute value --> absolute value is always more than or equal to zero \(|some \ expresseion|\geq{0}\), thus \(|x + 1|\geq{0}\) no matter the value of x --> \(|x + 1|\geq{0}>-1\).

Shouldn't the answer choice B be -1<=x<=4 instead of -1<x<4?

We have strict inequality in |2x - 3| < 5, so solution should be as written: -1 < x < 4. Substitute the endpoints of the range (-1 and 4) to see that for them |2x - 3| < 5 does not hold true.
_________________

Re: Which of the following inequalities specifies the shaded reg [#permalink]

Show Tags

16 Dec 2013, 14:48

1

This post received KUDOS

Bunuel wrote:

mylifeisoracle wrote:

Dear Team,

Shouldn't the answer choice B be -1<=x<=4 instead of -1<x<4?

We have strict inequality in |2x - 3| < 5, so solution should be as written: -1 < x < 4. Substitute the endpoints of the range (-1 and 4) to see that for them |2x - 3| < 5 does not hold true.

Exatly, since it doesn't hold true for the endpoints, how can (B) be correct? Even though the endpoints in the picture make it seems as if those integer values are included in the range, (B) omits them. This is not intuitive, if (B) tells us that its inequality does NOTnecessarily hold true for the endpoints, that doesn't implicity mean that (B) asumes the endpoints in fact are "= 5", right?

Shouldn't the answer choice B be -1<=x<=4 instead of -1<x<4?

We have strict inequality in |2x - 3| < 5, so solution should be as written: -1 < x < 4. Substitute the endpoints of the range (-1 and 4) to see that for them |2x - 3| < 5 does not hold true.

Exatly, since it doesn't hold true for the endpoints, how can (B) be correct? Even though the endpoints in the picture make it seems as if those integer values are included in the range, (B) omits them. This is not intuitive, if (B) tells us that its inequality does NOTnecessarily hold true for the endpoints, that doesn't implicity mean that (B) asumes the endpoints in fact are "= 5", right?

Not sure I understand what you mean. The shaded region gives \(-1<x<4\) and option B also gives \(-1<x<4\). Thus B is correct. No other option gives this range, no matter whether you include endpoints on the diagram in the inequality or not.
_________________

Re: Which of the following inequalities specifies the shaded reg [#permalink]

Show Tags

17 Dec 2013, 02:13

Bunuel wrote:

Not sure I understand what you mean. The shaded region gives \(-1<x<4\) and option B also gives \(-1<x<4\). Thus B is correct. No other option gives this range, no matter whether you include endpoints on the diagram in the inequality or not.

What Im trying to say is that I interpret the shaded region as saying \(-1<=x<=4\), since both -1 and 4 are "covered" by the shaded area (at least it seems so to me). Thus, x could be -1 or it could be 4. But \(-1<x<4\) means that x cannot be either -1 or 4, and this is what confuses me. Either I am misinterpreting the shaded area, or I lack a fundamental understanding of inequalities.

Re: Which of the following inequalities specifies the shaded reg [#permalink]

Show Tags

17 May 2015, 04:36

Hello from the GMAT Club BumpBot!

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.
_________________

Re: Which of the following inequalities specifies the shaded reg [#permalink]

Show Tags

14 Jan 2017, 16:40

Hello from the GMAT Club BumpBot!

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.
_________________

Re: Which of the following inequalities specifies the shaded reg [#permalink]

Show Tags

23 Sep 2017, 12:41

EMPOWERgmatRichC wrote:

Hi happyface101,

Your calculation includes values that are GREATER than 4 and LESS than -1, and those values fall outside the range of the drawing (which is -1 to +4).

Notice how you wrote (5 - 3/2)....

GMAT assassins aren't born, they're made, Rich

EMPOWERgmatRichC - Hi, Could you be a bit more specific on what mistake happyface101 did in his equation? It'd help a great deal if you actually showed me how to answer this question along the lines of what happyface101 did.

How to solve this question without plugging in values?

Using midpoint and distance, write an absolute value inequality in the form

|x - (midpoint)| < distance

1) Find the midpoint of the region, exactly halfway between -1 and 4, which is \(\frac{3}{2}\)

2) Find the distances of the endpoints from the midpoint

-1 is a distance of \(\frac{5}{2}\) from \(\frac{3}{2}\), and

4 is a distance of \(\frac{5}{2}\) from \(\frac{3}{2}\)

The distance cannot equal \(\frac{5}{2}\) because the endpoints aren't included. The distance can be anything up to, but less than, \(\frac{5}{2}\)

3. Set up the inequality

From above, the distance of x from the midpoint,* namely |x - \(\frac{3}{2}\)|, is < \(\frac{5}{2}\)

4. Write the inequality.

|x - (midpoint)| < distance

|x - \(\frac{3}{2}\)| < \(\frac{5}{2}\)

5. Find the answer that matches that inequality.

Eliminate C, which is always true (absolute value is always \(\geq0\), hence also always \(>-1\)), and D, which, without absolute value bars, does not cover two directions.

From the remaining choices: The answer must account for \(\frac{3}{2}\) somehow. There is only one answer with a 3 on LHS:

B) |2x - 3| < 5

That fits; just multiply all terms of the inequality derived from midpoint and distance by 2:

|x - \(\frac{3}{2}\)| < \(\frac{5}{2}\) (each term * 2)

|2x - 3| < 5

ANSWER B

*|x - (some number)| is the distance of x from (some number) |x - 4| is the distance of x from 4 |x + 4| is the distance of x from -4

Blackbox, I'm not sure whether or not how I solved the problem is what you seek. I think it might be.