GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 May 2019, 15:44 ### 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. ### Request Expert Reply # Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5

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

### Hide Tags

Director  B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 532
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

2
Top Contributor
33 00:00

Difficulty:   35% (medium)

Question Stats: 69% (01:41) correct 31% (01:55) wrong based on 881 sessions

### HideShow timer Statistics

Is x<5 ?

(1) x^2 > 5

(2) x^2 + x < 5

_________________
Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges
##### Most Helpful Expert Reply
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6160
Location: United States (CA)
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

8
4
AbdurRakib wrote:
Is x<5 ?

(1) x^2 > 5

(2) x^2 + x < 5

We need to determine whether x < 5.

Statement One Alone:

x^2 > 5

If x = 3, then x is less than 5. However, if x = 6, then x is not less than 5. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x^2 + x < 5

Thus, we have x < 5 - x^2. Since x^2 is nonnegative, we have 5 - x^2 ≤ 5. Since x < 5 - x^2 and 5 - x^2 ≤ 5, we have x < 5.

Answer: B
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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.

##### Most Helpful Community Reply
Director  V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

12
5
AbdurRakib wrote:
Is x<5 ?

(1) $$x^2$$>5

(2) $$x^2$$+x<5

(1) $$x^2>5$$

If $$x = 6$$ or$$-6$$. $$x^2$$ will be greater than 5 in both cases.

However 6 is greater than 5 and -6 is less than 5.

(1) has multiple values. Hence I is Not Sufficient.

(2) $$x^2+x<5$$

$$x(x+1) < 5$$

$$x<5$$ or

$$x+1<5 = x < 4$$

(2) has x less than 5 or 4. Therefore x is less than 5. II is Sufficient. Answer (B)...
##### General Discussion
Manager  S
Joined: 05 Nov 2014
Posts: 106
Location: India
Concentration: Strategy, Operations
GMAT 1: 580 Q49 V21 GPA: 3.75
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

1
AbdurRakib wrote:
Is x<5 ?

(1) $$x^2$$>5

(2) $$x^2$$+x<5

Solution:

Statement 1: x can be 3,4,5 or 10. Insufficient.

Statement 2: The greatest positive value that satisfies the equation is 1. Therefore, x<5 . Sufficient.

Answer is Option B.
Retired Moderator P
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

2
1
Is x<5 ?

$$(1) x^2 > 5$$

This means x can have Positive and Negative values , lets check

$$x = 10 = x^2 = 100$$

$$x = - 10 = x^2 = 100$$

As we are getting answer as YES & NO

Eq. (1) =====> is NOT SUFFICIENT

$$(2) x^2 + x < 5$$

$$x^2 + x < 5$$

$$x(x + 1) < 5$$

$$x < 5$$ or

$$x < 4$$

As both these values are < 5

(2) =====> is SUFFICIENT

Hence, Answer is B
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7351
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

AbdurRakib wrote:
Is x<5 ?

(1) x^2 > 5

(2) x^2 + x < 5

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variables and 0 equations, D is most likely to be the answer and so we should consider each of conditions first.

Condition 1)
$$x = 10$$ : Yes
$$x = -10$$ : No
This is not sufficient.

Condition 2)
$$x^2 + x < 5$$
$$x < 5 - x^2 < 5$$
This is sufficient.

Therefore, the answer is B.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________
Intern  B
Joined: 15 Aug 2017
Posts: 5
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

ydmuley wrote:
Is x<5 ?

$$(2) x^2 + x < 5$$

$$x^2 + x < 5$$

$$x(x + 1) < 5$$

$$x < 5$$ or

$$x < 4$$

As both these values are < 5

(2) =====> is SUFFICIENT

Hence, Answer is B

can anyone please solve the second statement in detail ?
Manager  D
Joined: 17 May 2015
Posts: 249
Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

1
pranavpal ,

St(2): $$x^{2} + x < 5$$

There are a couple of ways, we can solve the second statement.

Method1: Use Quadratic equation root formula:

For a given Quadratic equation $$ax^{2} + bx + c = 0$$ (where $$a \neq 0$$), roots can be obtained using following frmula:

$$\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$$

Lets first solve the equality case of st(2) i.e. : $$x^{2} + x -5 = 0$$ . Here we have, a = 1, b = 1, c = -5. Put all the values in the above formula, we get:

Roots = $$\frac{-1 - \sqrt{21}}{2}, ~~~~ \frac{-1 + \sqrt{21}}{2}$$ => approximately roots are -3 and +2.

In order to solve the inequality, put the root's value on the number line and check whether the inequality gets satisfied or not in each section.

----------------Not satisfy ----------(-3) --------Satisfy--------(2)--------Not satisfy------------

It is very clear that the st(2) will satisfy only when -3 < x < 2. => x is definitely less than 5. Hence, Sufficient.

I hope this helps.

Thanks.
Manager  B
Joined: 16 Jan 2018
Posts: 62
Concentration: Finance, Technology
GMAT 1: 600 Q40 V33 Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

3
Although most of the folks got it right, I want to mention something which most of the folks got wrong..

x(x+1)<5

DOES NOT MEAN - x < 5 or (x+1) < 5.

and you easily check it by substitution

See bunuel's post - https://gmatclub.com/forum/inequalities ... 06653.html
Senior Manager  P
Joined: 10 Apr 2018
Posts: 258
Location: United States (NC)
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

pranavpal wrote:
ydmuley wrote:
Is x<5 ?

$$(2) x^2 + x < 5$$

$$x^2 + x < 5$$

$$x(x + 1) < 5$$

$$x < 5$$ or

$$x < 4$$

As both these values are < 5

(2) =====> is SUFFICIENT

Hence, Answer is B

can anyone please solve the second statement in detail ?

Hi,

The second statemnt if we read it along we can understand if this would be sufficient.

We are told that square of a number added to the number itself is less than 5. that means at least x< 5 and also that at least $$x^2< 5$$

Probus
_________________
Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
Intern  B
Joined: 29 Oct 2017
Posts: 3
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

Hi all,

I understand that plugging in values is a very good approach for this question. Still, I am wondering how to solve Statement 1 algebraically.

My way:

(1) x^2 > 5
|x| > √5 (correct?)
x > √5 or x < -√5 --> Therefore x can be bigger than 5, insufficient

Thanks a lot!
Intern  B
Joined: 09 Aug 2018
Posts: 13
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

Can someone please show the exact steps from: "Since x < 5 - x^2 and 5 - x^2 ≤ 5, we have x < 5."
Why is x ≤ 5 not possible? Or how do I know which sign I should take when adding inequalities?

ScottTargetTestPrep Bunuel chetan2u

Thank you in advance!
Math Expert V
Joined: 02 Aug 2009
Posts: 7681
Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

1
lstsch wrote:
Can someone please show the exact steps from: "Since x < 5 - x^2 and 5 - x^2 ≤ 5, we have x < 5."
Why is x ≤ 5 not possible? Or how do I know which sign I should take when adding inequalities?

ScottTargetTestPrep Bunuel chetan2u

Thank you in advance!

$$x < 5 - x^2$$ and $$5 - x^2 ≤ 5$$
When we combine the two, we get $$x< 5 - x^2 ≤ 5$$... This, x< 5 - x^2 ≤ 5 gives us x<5
_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6160
Location: United States (CA)
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

2
First of all, we are NOT adding the two inequalities to arrive to the conclusion that x < 5. Let’s be clear on that. It’s a transitive property in inequalities.

For example, if a < b and b < c, then a < c. Another example is: if a ≤ b and b ≤ c, then a ≤ c. Of course, here we have if a < b and b ≤ c, then a < c. You can see that the premise actually can be combined into a double inequality, that is, for short, we can say: a < b < c implies that a < c; a ≤ b ≤ c implies that a ≤ c; and last but not least, a < b ≤ c implies a < c.

So your question is, if a double inequality have both < and ≤ signs, why we take the < sign, instead of the ≤ sign?

The reason is we always take the sign of the < (“strictly less than”) sign when a double inequality have both. That is because in a < b ≤ c, it says b is no more than c, so if a is strictly less than b, it will be also strictly less than c, hence the conclusion inequality a < c. The other way around is also true.

That is, a ≤ b < c also implies a < c. Here, it means a is no more than b, but if b is strictly less than c, so does a.
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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.

Intern  B
Joined: 01 Jan 2019
Posts: 29
Location: Canada
Concentration: Finance, Economics
GPA: 3.24
Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

Hi Bunuel VeritasKarishma,

I need ur expert opinion in this..

I got the answer correct but need to know whether my process is correct or no..

S2: x^2+x<5
X^2+x-5<0
(X+1)(x-5)<0

X<-1 or x<5

Posted from my mobile device
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9224
Location: Pune, India
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

Shef08 wrote:
Hi Bunuel VeritasKarishma,

I need ur expert opinion in this..

I got the answer correct but need to know whether my process is correct or no..

S2: x^2+x<5
X^2+x-5<0
(X+1)(x-5)<0

X<-1 or x<5

Posted from my mobile device

(x + 1)*(x - 5) is not the same as (x^2 + x - 5). It is same as (x^2 - 4x -5).

(x^2 + x - 5) does not have integer roots but we can guess the roots using the formula as done in this comment above: https://gmatclub.com/forum/is-x-5-1-x-2 ... l#p2042359

If the roots are approximately -3 and 2, then (x^2 + x - 5) = (x + 3)(x - 2) < 0
which gives us -3 < x < 2
So in any case, x is less than 5.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   [#permalink] 11 Apr 2019, 23:48
Display posts from previous: Sort by

# Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  