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

 It is currently 17 Feb 2019, 19:09

### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6955
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

10 Oct 2018, 00:01
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:46) correct 19% (02:31) wrong based on 80 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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 01 Feb 2018 Posts: 30 Re: If 2 numbers are selected from the first 8 prime numbers, what is the [#permalink] ### Show Tags 10 Oct 2018, 00:43 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 Status: GMATH founder Joined: 12 Oct 2010 Posts: 730 Re: If 2 numbers are selected from the first 8 prime numbers, what is the [#permalink] ### Show Tags 10 Oct 2018, 04:42 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 Joined: 09 Mar 2016 Posts: 1286 Re: If 2 numbers are selected from the first 8 prime numbers, what is the [#permalink] ### Show Tags 10 Oct 2018, 06:06 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 Joined: 16 Aug 2015 Posts: 6955 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 12 Oct 2018, 07:35 => 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$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Joined: 06 Sep 2018
Posts: 175
Location: Pakistan
Concentration: Finance, Operations
GPA: 2.87
WE: Engineering (Other)
Re: If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

### Show Tags

13 Oct 2018, 00:48
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
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4920
Location: United States (CA)
Re: If 2 numbers are selected from the first 8 prime numbers, what is the  [#permalink]

### Show Tags

13 Oct 2018, 17:16
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

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If 2 numbers are selected from the first 8 prime numbers, what is the   [#permalink] 13 Oct 2018, 17:16
Display posts from previous: Sort by