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

 It is currently 21 Aug 2018, 16:57

### 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

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

Author Message
TAGS:

### Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 551
GPA: 2.81
Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

24 Jun 2017, 03:15
Top Contributor
9
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:15) correct 30% (01:35) wrong based on 556 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

Director
Joined: 04 Dec 2015
Posts: 700
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

24 Jun 2017, 03:37
1
2
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)...
Manager
Joined: 05 Nov 2014
Posts: 114
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

24 Jun 2017, 03:44
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.

Retired Moderator
Joined: 19 Mar 2014
Posts: 969
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

26 Jun 2017, 14:55
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

_________________

"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

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3188
Location: United States (CA)
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

17 Nov 2017, 12:38
2
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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6045
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

18 Nov 2017, 16:39
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.

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 15 Aug 2017
Posts: 5
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

06 Apr 2018, 21:34
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

can anyone please solve the second statement in detail ?
Manager
Joined: 17 May 2015
Posts: 237
Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

06 Apr 2018, 23:27
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
Joined: 16 Jan 2018
Posts: 58
Concentration: Finance, Technology
GMAT 1: 600 Q40 V33
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

### Show Tags

07 Apr 2018, 17:40
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
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 &nbs [#permalink] 07 Apr 2018, 17:40
Display posts from previous: Sort by

# Events & Promotions

 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®.