• Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • examPAL
    Most awarded test prep in the world
    Now free for 30 days

    Available with Beat the GMAT members only code

    MORE DETAILS
    examPAL

Is x < 5?

This topic has 4 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
Joined
24 Jul 2017
Posted:
83 messages

Is x < 5?

Post Thu Aug 03, 2017 12:07 pm
Is x < 5?
(1) x^2 > 5
(2) x^2 + x < 5

Official Guide question
Answer: B

  • +1 Upvote Post
  • Quote
  • Flag
Post Fri Nov 17, 2017 12:09 pm
jjjinapinch 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

  • +1 Upvote Post
  • Quote
  • Flag
Post Fri Aug 25, 2017 1:00 am
jjjinapinch wrote:
Is x < 5?
(1) x^2 > 5
(2) x^2 + x < 5

Official Guide question
Answer: B
Nice solutions by Brent and Rich. Here's one with brute force.

S1: x^2 > 5

    Plug-in a value of x > 5, say x = 6 such that x^2 > 5. We see that (6^2 = 36) > 5. The answer is No.

    Plug-in a value of x < 5, say x = -6 such that x^2 > 5. We see that (-6)^2 > 5 => 36 > 5. The answer is Yes.

No unique answer!

S2: x^2 + x < 5

    Plug-in a value of x > 5, say x = 6 such that x^2 + x > 5. We see that (6^2 + 6 = 42) < 5. It's not a valid value. Let's try with a smaller value.

    Say x = 2 such that x^2 + x > 5. We see that (2^2 + 2 = 6) < 5. It's not a valid value. Let's try with another smaller value.

    Say x = 1 such that x^2 + x > 5. We see that (1^2 + 1 = 6) > 5. It's a valid value. The answer is Yes.

There is no need to test further as we now know that x < 2, this means that x < 5. Sufficient.

The correct answer: B

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Barcelona | Manila | Melbourne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Thu Aug 03, 2017 1:03 pm
jjjinapinch wrote:
Is x < 5?
(1) x² > 5
(2) x² + x < 5

Official Guide question
Answer: B
Target question: Is x < 5?

Statement 1: x² > 5
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 3 is a possible value since 3² > 5. In this case, x < 5
Case b: x = 6 is a possible value since 6² > 5. In this case, x > 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

Statement 2: x² + x < 5
IMPORTANT: x² is greater than or equal to 0 for ALL values of x.
So, let's let 0+ represent the value of x². This notation reminds us that x² equals some value that's greater than or equal to 0
Our inequality becomes: (0+) + x < 5
In order for the left side to be less than 5, x CANNOT be greater than or equal to 5
In other words, it MUST be the case that x < 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources



Last edited by Brent@GMATPrepNow on Sat Aug 26, 2017 11:47 am; edited 1 time in total

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Post Thu Aug 03, 2017 9:03 pm
Hi jjjinapinch,

We're asked if X is less than 5. This is a YES/NO question. We can answer this question by TESTing VALUES and paying careful attention to the question that is asked. To start, we know that ANY negative value for X and X=0 will lead to a YES answer (as well as any values of X that are less than 5). Answers that are 5 or greater will lead to a NO answer.

1) X² > 5

With this inequality, there are clearly multiple values for X (positive and negative).
IF... X = 5, then the answer to the question is NO.
IF... X = -5, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) X² + X < 5

With this inequality, we know that there are negative solutions and that X=0 is a solution, so there are clearly "NO" answers to this question. However, we now have to think about how big X could get. Thankfully, there's a way to avoid doing that exact math and use a bit of 'brute force' to help us to stop working...

IF.... X=1, then (X^2 + X) = 1^2 + 1 = 2... which is less than 5
IF.... X=2, then (X^2 + X) = 2^2 + 2 = 6... which is GREATER than 5
As X increases, the sum of (X^2 + X) will also increase. Since we're already greater than 5 when X=2, there's no reason to check any larger values. Given this inequality, X MUST be less than 2, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 lheiannie07 108 topics
2 ardz24 67 topics
3 Roland2rule 63 topics
4 LUANDATO 52 topics
5 Vincen 51 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

150 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

114 posts
3 image description Rich.C@EMPOWERgma...

EMPOWERgmat

105 posts
4 image description Scott@TargetTestPrep

Target Test Prep

101 posts
5 image description Max@Math Revolution

Math Revolution

85 posts
See More Top Beat The GMAT Experts