 It is currently 15 Jun 2019, 22:37 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

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  Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1889 , given: 397

How many integers are in the solution set of the inequality [#permalink]
Expert's post 00:00

Question Stats: 44% (00:39) correct 55% (00:47) wrong based on 34 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  Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1889 , given: 397

Re: How many integers are in the solution set of the inequality [#permalink]
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 Target Test Prep Representative Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4

Kudos [?]: 140  , given: 0

Re: How many integers are in the solution set of the inequality [#permalink]
4
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.

_________________

Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews Manager Joined: 23 Jan 2016
Posts: 134
Followers: 4

Kudos [?]: 118  , given: 15

Re: How many integers are in the solution set of the inequality [#permalink]
1
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 Joined: 10 Apr 2015
Posts: 1958
Followers: 60

Kudos [?]: 1790 , given: 9

Re: How many integers are in the solution set of the inequality [#permalink]
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  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 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®.