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

It is currently 16 Oct 2019, 23:40

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

If 2 numbers are selected from the first 8 prime numbers, what is the

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

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82
If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

Show Tags

New post 10 Oct 2018, 01:01
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

80% (01:45) correct 20% (02:39) wrong based on 84 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

If 2 numbers are selected from the first 8 prime numbers, what is the probability that the sum of the 2 numbers selected is an even number?

\(A. \frac{1}{2}\)
\(B. \frac{1}{3}\)
\(C. \frac{2}{3}\)
\(D. \frac{1}{4}\)
\(E. \frac{3}{4}\)

_________________
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 $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Intern
avatar
B
Joined: 01 Feb 2018
Posts: 30
Re: If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

Show Tags

New post 10 Oct 2018, 01:43
E is the answer
As
We have 1st 8 prime no.s as
2,3,5,7,11,13,17 and 19

Now, we know that
Odd plus odd is even

So only 2 here is even which when added to any odd prime will give even sum

Hence we will select 2 primes out of 7 odd primes not considering 2

So

Total outcomes = 8C2 I.e 8*7

Favourable outcomes = 7C2 I.e 7*6

Hence ans is 6/8 or 3/4

Posted from my mobile device
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

Show Tags

New post 10 Oct 2018, 05:42
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If 2 DIFFERENT numbers are selected from the first 8 prime numbers, what is the probability that the sum of the 2 numbers selected is an even number?

\(A. \frac{1}{2}\)
\(B. \frac{1}{3}\)
\(C. \frac{2}{3}\)
\(D. \frac{1}{4}\)
\(E. \frac{3}{4}\)

\({\rm{first}}\,\,{\rm{8}}\,\,{\rm{primes}}\,\,\left\{ \matrix{
\,{\rm{first}} = 2 = {\rm{even}} \hfill \cr
\,{\rm{7}}\,{\rm{others}}\,\, = \,\,{\rm{odd}}\,\,\,\,\,\left( {{\rm{it}}\,\,{\rm{does}}\,\,{\rm{not}}\,\,{\rm{matter}}\,{\rm{who}}\,\,{\rm{they}}\,\,{\rm{are}}!} \right) \hfill \cr} \right.\,\,\,\,\,\,\)

\(? = P\left( {2\,\,{\text{different}}\,\,{\text{selected}}\,\,{\text{have}}\,{\text{sum}}\,\,{\text{even}}} \right) = P\left( {{\text{number}}\,\,{\text{2}}\,\,{\text{is}}\,\,{\text{not }}\,{\text{selected}}} \right)\)


\({\text{total}} = C\left( {8,2} \right)\,\,\,{\text{equiprobable}}\)

\({\text{favorable}}\,{\text{ = }}\,{\text{C}}\left( {7,2} \right)\,\,\,\,\,\,\left[ {{\text{number}}\,{\text{2}}\,\,{\text{is}}\,{\text{not}}\,{\text{an}}\,{\text{option}}} \right]\)


\(? = \frac{{C\left( {7,2} \right)}}{{C\left( {8,2} \right)}} = \frac{{7 \cdot 6}}{{8 \cdot 7}} = \frac{3}{4}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1230
Re: If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

Show Tags

New post 10 Oct 2018, 07:06
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If 2 numbers are selected from the first 8 prime numbers, what is the probability that the sum of the 2 numbers selected is an even number?

\(A. \frac{1}{2}\)
\(B. \frac{1}{3}\)
\(C. \frac{2}{3}\)
\(D. \frac{1}{4}\)
\(E. \frac{3}{4}\)



odd+odd = even

from total 8 prime numbers, 7 numbers are odd and one is even i.e. 2

\(C^7_2\) = 21 (choosing any two odd numbers from 7

\(C^8_2\) = 28 ( total number of outcomes)

\(\frac{21}{28}\) i.e. \(\frac{3}{4}\)
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

Show Tags

New post 12 Oct 2018, 08:35
=>

In order for the sum to be even, both primes selected must be odd. As 2 is the only even prime number, the number of selections with an even sum is equal to the number of ways to select 2 numbers from these 7 odd prime numbers, or 7C2.
The total number of selections of 2 prime numbers from the first 8 prime numbers is 8C2.
Therefore, the probability that the sum of the two numbers selected is even is
7C2 / 8C2 = \({\frac{(7*6)}{(1*2)}}/{\frac{(8*7)}{(1*2)}} = \frac{6}{8} = \frac{3}{4}.\)

Therefore, the answer is E.
Answer: 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 $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
User avatar
G
Joined: 06 Sep 2018
Posts: 173
Location: Pakistan
Concentration: Finance, Operations
GPA: 2.87
WE: Engineering (Other)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

Show Tags

New post 13 Oct 2018, 01:48
first 8 prime numbers are\(=2,3,5,7,11,13,17,19\)
sum of the two prime number will be even when 2 is not included in the pair.
So probability of 2 numbers with sum even\(=\frac{7C2}{8C2}=\frac{21}{28}=\frac{3}{4}\)
_________________
Hitting Kudos is the best way of appreciation. :)

Eric Thomas, "When you want to succeed as bad as you want to breathe, then you'll be successful."
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8085
Location: United States (CA)
Re: If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

Show Tags

New post 13 Oct 2018, 18:16
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If 2 numbers are selected from the first 8 prime numbers, what is the probability that the sum of the 2 numbers selected is an even number?

\(A. \frac{1}{2}\)
\(B. \frac{1}{3}\)
\(C. \frac{2}{3}\)
\(D. \frac{1}{4}\)
\(E. \frac{3}{4}\)


The first 8 prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19. We see that all of them are odd numbers except 2, and, in order for the sum of the 2 numbers selected to be even, the two numbers must be odd. Therefore, the probability is:

7/8 x 6/7 = 6/8 = 3/4

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: If 2 numbers are selected from the first 8 prime numbers, what is the   [#permalink] 13 Oct 2018, 18:16
Display posts from previous: Sort by

If 2 numbers are selected from the first 8 prime numbers, what is the

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne