GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 26 May 2020, 22:44

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.

Close

Request Expert Reply

Confirm Cancel

If x2 - 100 < 300, how many integers x satisfy this condition?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
S
Joined: 26 Apr 2018
Posts: 38
If x2 - 100 < 300, how many integers x satisfy this condition?  [#permalink]

Show Tags

New post 01 Oct 2018, 07:18
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

49% (00:52) correct 51% (00:56) wrong based on 80 sessions

HideShow timer Statistics

If x^2 - 100 < 300, how many integers x satisfy this condition?

a) 42

b) 39

c) 38

e) 37

d) 19



source gmat tutor
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8590
Re: If x2 - 100 < 300, how many integers x satisfy this condition?  [#permalink]

Show Tags

New post 01 Oct 2018, 08:23
bettatantalo wrote:
If x^2 - 100 < 300, how many integers x satisfy this condition?

a) 42

b) 39

c) 38

e) 37

d) 19



source gmat tutor



\(x^2-100<300.....x^2<400....x<|20|.........-20<x<20\)
So x can take any value from -19 to 19..
Total 19 positive integers + 19 negative integers +0=19+19+1=39

B
_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4875
Location: Canada
GMAT 1: 770 Q49 V46
Re: If x2 - 100 < 300, how many integers x satisfy this condition?  [#permalink]

Show Tags

New post 01 Oct 2018, 08:24
Top Contributor
bettatantalo wrote:
If x² - 100 < 300, how many integers x satisfy this condition?

a) 42
b) 39
c) 38
e) 37
d) 19


Take: x² - 100 < 300
Add 100 to both sides to get: x² < 400

We know that 20² EQUALS 400, so x must be less than 20
For example, 19² < 400, so one possible solution is x = 19
Likewise, 18² < 400, so another possible solution is x = 18
Keep going to see that...
Another possible solution is x = 17
Another possible solution is x = 16
.
.
.
Another possible solution is x = 1
Another possible solution is x = 0

ARE WE DONE?
NO!

Negative values also work.
For example, (-1)² = 1, and 1 < 400. So another possible solution is x = -1
And (-2)² = 4, and 4 < 400. So another possible solution is x = -2
And (-3)² = 9, and 9 < 400. So another possible solution is x = -3
.
.
.
And (-19)² = 361, and 361 < 400. So another possible solution is x = -19
HOWEVER, (-20)² = 400, and 400 is NOT less than 400.

So, the integer solutions are: -19, -18, -17, . . . . 17, 18, 19
There are 39 such solutions.

Answer: B

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1238
If x2 - 100 < 300, how many integers x satisfy this condition?  [#permalink]

Show Tags

New post 01 Oct 2018, 10:01
bettatantalo wrote:
If x^2 - 100 < 300, how many integers x satisfy this condition?

a) 42

b) 39

c) 38

e) 37

d) 19



source gmat tutor



\(x^2 - 100 < 300\) (add 100 to both sides)

\(x^2 - 100+100 < 300+100\)

\(x^2 < 400\) square both sides

\(x<20\)

So x can be -19 or +19 , because \(\sqrt{x^2}=|x|\)

\(-19<x<19\)

\(19+19 +0 = 39\) (dont forget to count zero :) )


IMPORTANT PROPERTIES

1. \(|x|≥0\)

2. \(\sqrt{x^2}=|x|\)

3. \(|0|=0\)

4. \(|−x|=|x|\)

5. \(|x−y|=|y−x|\) . \(|x - y|\) represents the distance between \(x\) and \(y\), so naturally it equals to \(|y - x|\), which is the distance between \(y\) and \(x\).

6. \(|x|+|y|≥|x+y|\) Note that "=" sign holds for \(xy≥0\) (or simply when \(x\) and \(y\) have the same sign). So, the strict inequality (>) holds when \(xy<0\)

7. |x|−|y|≤|x−y| Note that "=" sign holds for \(xy>0\) (so when \(x\) and \(y\) have the same sign) and \(|x|≥|y|\) (simultaneously).
VP
VP
User avatar
D
Joined: 31 Oct 2013
Posts: 1489
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If x2 - 100 < 300, how many integers x satisfy this condition?  [#permalink]

Show Tags

New post 01 Oct 2018, 14:14
bettatantalo wrote:
If x^2 - 100 < 300, how many integers x satisfy this condition?

a) 42

b) 39

c) 38

e) 37

d) 19



source gmat tutor



\(x^2<300 +100\)

\(x^2 < 400.\)

Notes: 20^2 = 400. It means Highest value of x must be 19 and lowest value must be -19.

-19<x<19.

As we are dealing with \(x^2\) , negative value doesn't affect our calculation.


No. of x. : 19 - (-19) +1 = 39.

The best answer is B.
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10566
Location: United States (CA)
Re: If x2 - 100 < 300, how many integers x satisfy this condition?  [#permalink]

Show Tags

New post 03 Oct 2018, 16:34
bettatantalo wrote:
If x^2 - 100 < 300, how many integers x satisfy this condition?

a) 42

b) 39

c) 38

e) 37

d) 19


Simplifying, we have:

x^2 < 400

√(x^2) < √400

|x| < 20

Since all the integers from -19 to 19, inclusive, have an absolute value less than 20, there are 39 integers.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
202 Reviews

5-star rated online GMAT quant
self study course

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14982
Re: If x2 - 100 < 300, how many integers x satisfy this condition?  [#permalink]

Show Tags

New post 02 Apr 2020, 02:41
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.
_________________
GMAT Club Bot
Re: If x2 - 100 < 300, how many integers x satisfy this condition?   [#permalink] 02 Apr 2020, 02:41

If x2 - 100 < 300, how many integers x satisfy this condition?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne