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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # 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 Status: I don't stop when I'm Tired,I stop when I'm done Joined: 11 May 2014 Posts: 542 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 24 Jun 2017, 02:15 2 Top Contributor 17 00:00 Difficulty: 35% (medium) Question Stats: 70% (01:15) correct 30% (01:31) wrong based on 766 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 Community Reply Director Joined: 04 Dec 2015 Posts: 715 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, 02:37 3 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)... ##### General Discussion Manager Joined: 05 Nov 2014 Posts: 107 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, 02:44 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. Answer is Option B. Retired Moderator Joined: 19 Mar 2014 Posts: 945 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, 13:55 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 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 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4171 Location: United States (CA) Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] ### Show Tags 17 Nov 2017, 11:38 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 GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6500 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, 15:39 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. 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. _________________ 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"
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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, 20:34
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: 245
Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

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06 Apr 2018, 22:27
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: 57
Concentration: Finance, Technology
GMAT 1: 600 Q40 V33
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

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07 Apr 2018, 16:40
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
Manager
Joined: 10 Apr 2018
Posts: 181
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

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14 Sep 2018, 21:22
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

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
Intern
Joined: 29 Oct 2017
Posts: 3
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5  [#permalink]

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16 Oct 2018, 04:55
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!
Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 &nbs [#permalink] 16 Oct 2018, 04:55
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