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

It is currently 21 Feb 2019, 03:58

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

If p and q are two distinct numbers chosen from the set ..............

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

Hide Tags

 
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2589
If p and q are two distinct numbers chosen from the set ..............  [#permalink]

Show Tags

New post 30 Jan 2019, 00:43
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

25% (01:16) correct 75% (02:42) wrong based on 28 sessions

HideShow timer Statistics

If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.

    A. \(\frac{1}{30}\)

    B. \(\frac{1}{15}\)

    C. \(\frac{1}{9}\)

    D. \(\frac{2}{15}\)

    E. \(\frac{2}{9}\)


Image

_________________








Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Weession:- Key strategy to score 760

Success Stories
Q38 to Q50 | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Question to reach Q51 | Question of the week | Tips From V40+ Scoreres | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
B
Joined: 17 Jan 2019
Posts: 6
GMAT ToolKit User
Re: If p and q are two distinct numbers chosen from the set ..............  [#permalink]

Show Tags

New post 30 Jan 2019, 01:07
1
prime factors in the set: -3, -2, 2, 3, 5
Each product with 1 or -1 is also prime.
5*2/10C2=10/45=2/9→(E)

Posted from my mobile device
SVP
SVP
User avatar
G
Joined: 18 Aug 2017
Posts: 1887
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
If p and q are two distinct numbers chosen from the set ..............  [#permalink]

Show Tags

New post Updated on: 01 Feb 2019, 08:21
prime no are +ve integer value (2,3,5)
2,3,5 can be formed ( -3,-1) ,( -2,-1), ( 1,2), ( 1,3),(1,5) ; total 5 pairs p*q can be 2 ways; 5*2 = 10

total pairs = 5 and p*q = 10c2
5/10c2 ; 5/45
=1/9
IMOC

EgmatQuantExpert wrote:
If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.

    A. \(\frac{1}{30}\)

    B. \(\frac{1}{15}\)

    C. \(\frac{1}{9}\)

    D. \(\frac{2}{15}\)

    E. \(\frac{2}{9}\)


Image

_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.


Originally posted by Archit3110 on 30 Jan 2019, 06:04.
Last edited by Archit3110 on 01 Feb 2019, 08:21, edited 1 time in total.
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2589
Re: If p and q are two distinct numbers chosen from the set ..............  [#permalink]

Show Tags

New post 01 Feb 2019, 00:57

Solution


Given:
    • A set of 10 integers, {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
    • p and q are two distinct integers chosen from the given set

To find:
    • The probability that p * q is a prime number

Approach and Working:
The total number of ways of choosing two distinct integers from a set of 10 elements = \(^{10}C_2 = 45\)

Now, for p * q to be prime, one of them must be ±1 and the other must be = ± a prime number.
    • Thus, the possible cases are {-1, -2}, {-1, -3}, {1, 2}, {1, 3}, {1, 5}

Therefore, probability = \(\frac{5}{45} = \frac{1}{9}\)

Hence the correct answer is Option C.

Answer: C

Image

_________________








Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Weession:- Key strategy to score 760

Success Stories
Q38 to Q50 | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Question to reach Q51 | Question of the week | Tips From V40+ Scoreres | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Bot
Re: If p and q are two distinct numbers chosen from the set ..............   [#permalink] 01 Feb 2019, 00:57
Display posts from previous: Sort by

If p and q are two distinct numbers chosen from the set ..............

  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®.