NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 22:41 It is currently 24 Apr 2024, 22:41
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Set S is the prime integers between 0 and 20. If three numbers are cho

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618850 [19]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink] New post   27 Oct 2021, 08:15
2
Kudos
16
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

71% (02:26) correct 29% (02:49) wrong based on 266 sessions
Hide Show timer Statistics
Set S is the prime integers between 0 and 20. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?

(A) 15/56
(B) 3/8
(C) 15/28
(D) 5/8
(E) 3/4
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29918 [2]
Given Kudos: 799
Location: Canada
Send PM
Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink] New post   27 Oct 2021, 11:00
2
Kudos
Expert Reply
Top Contributor
Bunuel wrote:
Set S is the prime integers between 0 and 20. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?

(A) 15/56
(B) 3/8
(C) 15/28
(D) 5/8
(E) 3/4


Set S = {2, 3, 5, 7, 11, 13, 17, 19}

Important: Notice that 7 of the values are ODD, and 1 value is EVEN.
Also recognize that the sum of any 3 odd integers will always be ODD.
Conversely, the sum of 2 odd integers and 1 even integer will always be EVEN.

So, P(sum is odd) = P(all 3 selected numbers are odd)
= P(1st selected number is odd AND 2nd selected number is odd AND 3rd selected number is odd)
= P(1st selected number is odd) x P(2nd selected number is odd) x P(3rd selected number is odd)
= 7/8 x 6/7 x 5/6
= 5/8

Answer: D

Aside: P(1st selected number is odd) = 7/8, since 7 of the 8 numbers in the set are odd.
P(2nd selected number is odd) = 6/7, because once we select an odd number in the first draw, there are 7 numbers remaining, and 6 of them are odd.
etc....
General Discussion
avatar
B
Legis
Intern
Intern
Joined: 08 Dec 2021
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 739
Send PM
Re: Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink] New post   12 Mar 2022, 10:40
BrentGMATPrepNow wrote:
Bunuel wrote:
Set S is the prime integers between 0 and 20. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?

(A) 15/56
(B) 3/8
(C) 15/28
(D) 5/8
(E) 3/4


Set S = {2, 3, 5, 7, 11, 13, 17, 19}

Important: Notice that 7 of the values are ODD, and 1 value is EVEN.
Also recognize that the sum of any 3 odd integers will always be ODD.
Conversely, the sum of 2 odd integers and 1 even integer will always be EVEN.

So, P(sum is odd) = P(all 3 selected numbers are odd)
= P(1st selected number is odd AND 2nd selected number is odd AND 3rd selected number is odd)
= P(1st selected number is odd) x P(2nd selected number is odd) x P(3rd selected number is odd)
= 7/8 x 6/7 x 5/6
= 5/8

Answer: D

Aside: P(1st selected number is odd) = 7/8, since 7 of the 8 numbers in the set are odd.
P(2nd selected number is odd) = 6/7, because once we select an odd number in the first draw, there are 7 numbers remaining, and 6 of them are odd.
etc....





When should we assume that the numbers are taken out? The problem does not state that the numbers cannot be repeated.

If they can be repeated, would we also include the sum of (ODD+EVEN+EVEN), since that yields an odd number?
User avatar
B
RastogiSarthak99
Manager
Manager
Joined: 20 Mar 2019
Posts: 147
Own Kudos [?]: 14 [0]
Given Kudos: 282
Location: India
Send PM
GMAT ToolKit User
Re: Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink] New post   10 Aug 2022, 03:29
If you've figured out that only odd + odd + odd = odd then the sum becomes more familiar.

total numbers in the set = 8
total odd numbers = 7 (3,5,7...19)
total even numbers = 1 (only 2)

Fav outcomes/Total outcomes

choosing all odd/ total number of outcomes

7c3/8c3 = 5/8

the expression above basically means you choose all 3 as odd from 7 available numbers and divide it by 8c3 which is all outcomes from all available numbers

Bunuel - I have a query, although it won't make different to the answer, is it more accurate to write (7c3 * 1c0)/8c3?
User avatar
S
GmatPoint
Senior Manager
Senior Manager
Joined: 02 Jan 2022
Posts: 266
Own Kudos [?]: 94 [0]
Given Kudos: 3
GMAT 1: 760 Q50 V42
Send PM
Re: Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink] New post   10 Aug 2022, 04:22
The prime numbers between 0 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19.
The only even prime number is 2.
If all the three numbers selected are odd, then the sum of the numbers will be odd. If one of the numbers is 2, the sum will be even.
Thus, we have to discard the cases where 2 have been selected.

If 2 is selected, the total ways to select the other two numbers will be 7C2 = 21

Total number of ways to select 3 numbers = 8C3 = 56


Total favourable cases = 56 - 21 = 35

Required probability = 35/56 = 5/8

Thus, the correct option is D.
User avatar
B
naveeng15
Manager
Manager
Joined: 08 Dec 2021
Posts: 65
Own Kudos [?]: 11 [0]
Given Kudos: 31
Location: India
Concentration: Operations, Leadership
WE:Design (Manufacturing)
Send PM
Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink] New post   10 Aug 2022, 06:41
number of even numbers between 0 to 20
2,3,5,7,11,13,17,19
total 8

total possible cases = 8*7*6 , since once the number is taken the remaining will be 7 and then 6

rules of number
odd + odd = even so
even + odd + odd = even

so 3+3+3 will be odd

so favourable outcomes are 7*6*5 (since we should not select a even number i.e., 2 ) even + odd + odd will be even (2+3+3 =8) , so there should be no 2 in selection

so 7/8 X 6/ 7 X 5/ 6 = 210/336 = 5/8
User avatar
S
Maria240895chile
Manager
Manager
Joined: 23 Apr 2021
Posts: 127
Own Kudos [?]: 41 [0]
Given Kudos: 115
Send PM
Re: Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink] New post   12 Aug 2022, 09:45
Bunuel wrote:
Set S is the prime integers between 0 and 20. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?

(A) 15/56
(B) 3/8
(C) 15/28
(D) 5/8
(E) 3/4


prime numbers between 0-20=2,3,5,7,11,13,17,19= 8 numbers

They are asking how many sums of 3 numbers are odd, so we can start calculating the total number of sums using 3C8=56
in order for a sum of three numbers to be odd, we need to select 3 odd numbers ( exclude 2) so we need to select 3 numbers out of 7 using 3C7=35

the final answer is 35 out of 56 \(\frac{35}{56}\), simplify that by 7 to get \(\frac{5}{8}\).

IMO (D)
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32658
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink] New post   12 Oct 2023, 03:06
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 Club Bot
gmatclubot
Re: Set S is the prime integers between 0 and 20. If three numbers are cho [#permalink]
12 Oct 2023, 03:06
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions