It is currently 19 Sep 2019, 20:03
My Tests

Close

GMAT Club Daily Prep

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.

How many integers are in the solution set of the inequality

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GRE Prep Club Legend
GRE Prep Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 135

Kudos [?]: 2085 [0], given: 397

How many integers are in the solution set of the inequality [#permalink] New post 20 May 2016, 18:02
Expert's post
00:00

Question Stats:

48% (00:40) correct 51% (00:48) wrong based on 47 sessions
How many integers are in the solution set of the inequality \(x^2 - 10 < 0\)?

A. Two
B. Five
C. Six
D. Seven
E. Ten

Practice Questions
Question: 11
Page: 83
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GRE Prep Club Legend
GRE Prep Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 135

Kudos [?]: 2085 [0], given: 397

Re: How many integers are in the solution set of the inequality [#permalink] New post 20 May 2016, 18:05
Expert's post
Explanation

The inequality \(x^2 - 10 < 0\) is equivalent to \(x^2 < 10\). By inspection, the positive integers that satisfy this inequality are 1, 2, and 3. Note that 0 and the negative integers –1, –2, and –3 also satisfy the inequality, and there are no other integer solutions. So there are seven integers in the solution set: –3, –2, –1, 0, 1, 2, and 3.

Thus the correct answer is Choice D.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

4 KUDOS received
Target Test Prep Representative
User avatar
Status: Head GRE Instructor
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 6

Kudos [?]: 156 [4] , given: 0

Re: How many integers are in the solution set of the inequality [#permalink] New post 23 May 2016, 16:23
4
This post received
KUDOS
Expert's post
sandy wrote:
How many integers are in the solution set of the inequality \(x^2 - 10 < 0\)?

A. Two
B. Five
C. Six
D. Seven
E. Ten


We can simplify the inequality to:

x^2 < 10

√x^2 < √10

|x| < √10

We can rewrite the square root of 10 as 3.2 (the estimated value of √10)

|x| < 3.2

Finally, we can solve for when x is positive and negative.

When x is positive:

x < 3.2

When x is negative:

-x < 3.2

x > -3.2

Thus, -3.2 < x < 3.2

The integers that satisfy the inequality are -3, -2, -1, 0, 1, 2, and 3. So 7 integers satisfy the inequality.

Answer: D
_________________

Jeffrey Miller

Head of GRE Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
22 Reviews

5-star rated online GRE quant
self study course

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews

1 KUDOS received
Manager
Manager
Joined: 23 Jan 2016
Posts: 134
Followers: 4

Kudos [?]: 125 [1] , given: 15

Re: How many integers are in the solution set of the inequality [#permalink] New post 23 May 2016, 19:51
1
This post received
KUDOS
The x is between - square root of 10 and + square root of 10. As x is an integer, all integers from -3 to +3 are values of x, hence the answer is 7
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 2387
Followers: 78

Kudos [?]: 2358 [0], given: 33

CAT Tests
Re: How many integers are in the solution set of the inequality [#permalink] New post 12 Jun 2019, 09:15
Expert's post
sandy wrote:
How many integers are in the solution set of the inequality \(x^2 - 10 < 0\)?

A. Two
B. Five
C. Six
D. Seven
E. Ten

Practice Questions
Question: 11
Page: 83


Take: \(x^2 - 10 < 0\)
Add 10 to both sides: \(x^2 < 10\)

Let's test some POSITIVE values.
x = 2 satisfies the equation, since \(2^2 < 10\)
x = 3 satisfies the equation, since \(3^2 < 10\)
However, x = 4 does NOT satisfy the equation, since \(4^2 > 10\)
So, the biggest integer value of x is 3.

Let's test some NEGATIVE values.
x = -2 satisfies the equation, since \((-2)^2 < 10\)
x = -3 satisfies the equation, since \((-3)^2 < 10\)
However, x = -4 does NOT satisfy the equation, since \((-4)^2 > 10\)
So, the smallest integer value of x is -3.

When we combine the results, we can see that can be any integer value from -3 to 3 inclusive.
In other words, x can be -3, -2, -1, 0, 1, 2 or 3 (seven possible values)

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for my free GRE Question of the Day emails

Re: How many integers are in the solution set of the inequality   [#permalink] 12 Jun 2019, 09:15
Display posts from previous: Sort by

How many integers are in the solution set of the inequality

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.