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

It is currently 21 Feb 2019, 14:44

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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

A set of positive integers contains twice as many even integers as odd

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53063
A set of positive integers contains twice as many even integers as odd  [#permalink]

Show Tags

New post 31 Aug 2015, 09:31
1
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

21% (02:50) correct 79% (02:47) wrong based on 166 sessions

HideShow timer Statistics

Knewton Brutal Math Challenge



A set of positive integers contains twice as many even integers as odd integers. How many integers are in the set?

(1) If two integers are chosen at random from the set, the probability that their sum will be even is 26/75 less than the probability that their product will be even.
(2) The number of integers in the set has fewer than six factors, and one of these factors is 17.

Kudos for a correct solution.

_________________

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

Most Helpful Community Reply
Manager
Manager
User avatar
Joined: 14 Mar 2014
Posts: 146
GMAT 1: 710 Q50 V34
A set of positive integers contains twice as many even integers as odd  [#permalink]

Show Tags

New post 31 Aug 2015, 23:54
7
4
IMO: D

Question Stem:

No. of odd Integers = x
No. of Even Integers = 2x
Total no. of Integers in the set = 3x

St 1:If two integers are chosen at random from the set, the probability that their sum will be even is 26/75 less than the probability that their product will be even

probability that sum will be even = probability that their product will be even - 26/75 --(ii)

probability that sum will be even = prob of picking two even integers + prob of picking two odd integers
= \(\frac{(2xC2 + xC2 )}{3xC2}\) = \(\frac{(2x *(2x-1) + x *(x-1) )}{3x * (3x-1) )}\)
= \(\frac{( 5x^2 - 3x )}{9x^2 - 3x )}\)

probability that their product will be even = 1 - two numbers are odd
= 1 - \(\frac{(xC2 )}{3xC2}\)
= \(\frac{( 8x^2 - 2x )}{9x^2 - 3x )}\)

Sub in eq --(ii) we get
\(9x^2 - 153x = 0\)
9x(x-17)= 0
x = 0 or x = 17 .
Since x cannot be equal to 0. x = 17
Hence suff.

St 2: The number of integers in the set has fewer than six factors, and one of these factors is 17

The number of integers in the set = has less than 6 factors.
i.e The number of integers in the set = \(Prime ^ a\) where is a < 5
OR
The number of integers in the set = \((P_1)^a * (P_2)^b\) (where a =1 & b =1 )
17 is one of the factors
if 3x is the total number of factors then "3" is also one of the factors.

Hence 3,17 are among the factors of total number of integers in the set

Thus condition 2 must be the case, making total no. of integers = 3*17 = 51
Hence suff


Bunuel
It has taken me nearly 4-5 min to solve this question.
What do you advise if we come across such question in GMAT exam?
Solve it even if it takes 4 min and hope that I come across few easy questions to make up the time or not risk and take a guess?

_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯ :-)

General Discussion
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9879
Premium Member
Re: A set of positive integers contains twice as many even integers as odd  [#permalink]

Show Tags

New post 10 Oct 2018, 02:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: A set of positive integers contains twice as many even integers as odd   [#permalink] 10 Oct 2018, 02:09
Display posts from previous: Sort by

A set of positive integers contains twice as many even integers as odd

  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®.