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

It is currently 13 Nov 2018, 12:22

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Essential GMAT Time-Management Hacks

     November 14, 2018

     November 14, 2018

     07:00 PM PST

     08:00 PM PST

    Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST
  • $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)

If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?

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

Hide Tags

Manager
Manager
avatar
G
Joined: 28 Jun 2018
Posts: 146
Location: India
Concentration: Finance, Marketing
GMAT 1: 650 Q49 V30
GPA: 4
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?  [#permalink]

Show Tags

New post Updated on: 11 Sep 2018, 22:37
1
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

41% (01:24) correct 59% (01:50) wrong based on 22 sessions

HideShow timer Statistics

If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?


(1) Both roots are prime number
(2) 2 is one of root of the equation

_________________

What to do if you are new to GMAT:
https://gmatclub.com/forum/what-to-do-if-you-are-new-272708.html#p2108758

GMAC official guides : https://gmatclub.com/forum/gmac-official-guides-the-master-directory-links-240610.html#p1854935

Give me kudos if you like it , it's totally harmless :)


Originally posted by GMATbuster92 on 11 Sep 2018, 22:36.
Last edited by Bunuel on 11 Sep 2018, 22:37, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50572
If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?  [#permalink]

Show Tags

New post 11 Sep 2018, 22:43
If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?


Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).



(1) Both roots are prime number.

According to the theorem: \(x_1+x_2=\frac{-b}{a}=7\). 7 can be expressed as the sum of two primes only in one way 2 + 5 = 7. Knowing the roots we can find the value of k. Sufficient.


(2) 2 is one of root of the equation. Plug x = 2: 2^2 − 7*2 + k = 0. We can find k. Sufficient.


Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 08 Oct 2015
Posts: 241
Re: If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?  [#permalink]

Show Tags

New post 11 Sep 2018, 23:32
Bunuel wrote:
If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?


Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).



(1) Both roots are prime number.

According to the theorem: \(x_1+x_2=\frac{-b}{a}=7\). 7 can be expressed as the sum of two primes only in one way 2 + 5 = 7. Knowing the roots we can find the value of k. Sufficient.


(2) 2 is one of root of the equation. Plug x = 2: 2^2 − 7*2 + k = 0. We can find k. Sufficient.


Answer: D.

Hope it's clear.


can you explain why the sum has been taken as 7 and not 5? (3+2)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50572
Re: If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?  [#permalink]

Show Tags

New post 11 Sep 2018, 23:35
rahulkashyap wrote:
Bunuel wrote:
If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?


Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\)AND \(x_1*x_2=\frac{c}{a}\).



(1) Both roots are prime number.

According to the theorem: \(x_1+x_2=\frac{-b}{a}=7\).7 can be expressed as the sum of two primes only in one way 2 + 5 = 7. Knowing the roots we can find the value of k. Sufficient.


(2) 2 is one of root of the equation. Plug x = 2: 2^2 − 7*2 + k = 0. We can find k. Sufficient.


Answer: D.

Hope it's clear.


can you explain why the sum has been taken as 7 and not 5? (3+2)


Please re-read the highlighted parts.

\(x_1+x_2=\frac{-b}{a}=\frac{-(-7)}{1}=7\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: If integer k > 0 and x^2 − 7x + k = 0, what is the value of k? &nbs [#permalink] 11 Sep 2018, 23:35
Display posts from previous: Sort by

If integer k > 0 and x^2 − 7x + k = 0, what is the value of k?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.