It is currently 19 Mar 2018, 13:31

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 June
Open Detailed Calendar

If two different numbers are randomly selected from set { 1,

Author Message
TAGS:

Hide Tags

Director
Joined: 07 Jun 2004
Posts: 607
Location: PA
If two different numbers are randomly selected from set { 1, [#permalink]

Show Tags

23 Jul 2010, 08:52
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

75% (00:47) correct 25% (03:54) wrong based on 21 sessions

HideShow timer Statistics

If two different numbers are randomly selected from set { 1, 2, 3, 4, 5} what is the probability that the sum of the two numbers is greater than 4?

OA ia
[Reveal] Spoiler:
4/5

[Reveal] Spoiler:
My approach was

total outcomes 5 C 2 = 20

outcomes where sum > 4 are

1,4 1,5 = 2
2,3 2,4 2,5 = 3
3,2, 3,3 3,4 3,5 = 4

4 any of the 5 = 5
5 any of the 5 = 5

total 19

so P(>4) = 19/20

why is this wrong

_________________

If the Q jogged your mind do Kudos me : )

Last edited by Bunuel on 13 Dec 2012, 02:07, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 06 Jul 2010
Posts: 97

Show Tags

23 Jul 2010, 09:15
1
KUDOS
rxs005,
First problem is 5C2 = 10 .. Not 20..

Point 2, you sum should be greater than 4, so these are the following possibilities you have
({1,4},{1,5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5}) which leads to 8 pairs

So the probability is 8 on 10 or 4/5..
Director
Joined: 07 Jun 2004
Posts: 607
Location: PA

Show Tags

23 Jul 2010, 09:46
you are right thanks!

the key is "different" numbers in the Q

i missed that
_________________

If the Q jogged your mind do Kudos me : )

Math Expert
Joined: 02 Sep 2009
Posts: 44321
If two different numbers are randomly selected from set { 1, [#permalink]

Show Tags

23 Jul 2010, 13:06
Expert's post
4
This post was
BOOKMARKED
rxs0005 wrote:
If two different numbers are randomly selected from set { 1, 2, 3, 4, 5} what is the probability that the sum of the two numbers is greater than 4?

OA ia 4/5

My approach was

total outcomes 5 C 2 = 20

outcomes where sum > 4 are

1,4 1,5 = 2
2,3 2,4 2,5 = 3
3,2, 3,3 3,4 3,5 = 4

4 any of the 5 = 5
5 any of the 5 = 5

total 19

so P(>4) = 19/20

why is this wrong

Another approach: $$P(of \ event \ X)=1-P(of \ opposite \ event \ X)$$. Opposite event would be if we choose 2 different numbers so that their sum will be less or equal to 4.

# of total outcomes is $$C^2_5=10$$ (total # of choosing 2 different numbers from the set of 5 different numbers);

# of outcomes when $$sum\leq{4}$$ is (1,2) and (1,3), so 2.

$$P=1-\frac{2}{10}=\frac{4}{5}$$.

Answer: $$\frac{4}{5}$$.

P. S. In the future pleas post the answer choices too.
_________________
Intern
Joined: 18 Mar 2012
Posts: 13

Show Tags

13 Dec 2012, 01:53
sridhar wrote:
rxs005,
First problem is 5C2 = 10 .. Not 20..

Point 2, you sum should be greater than 4, so these are the following possibilities you have
({1,4},{1,5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5}) which leads to 8 pairs

So the probability is 8 on 10 or 4/5..

How is the pare 1,4 GREATER than 4, I would say it is equal to four and therefore the answer should be 7/10.
Any argument ?
Intern
Joined: 18 Nov 2011
Posts: 36
Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98

Show Tags

10 Jan 2013, 21:54
arnijon90 wrote:
sridhar wrote:
rxs005,
First problem is 5C2 = 10 .. Not 20..

Point 2, you sum should be greater than 4, so these are the following possibilities you have
({1,4},{1,5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5}) which leads to 8 pairs

So the probability is 8 on 10 or 4/5..

How is the pare 1,4 GREATER than 4, I would say it is equal to four and therefore the answer should be 7/10.
Any argument ?

Because: 1+4 = 5 and 5>4
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2305
Location: United States (CA)
Re: If two different numbers are randomly selected from set { 1, [#permalink]

Show Tags

03 Dec 2017, 18:54
rxs0005 wrote:
If two different numbers are randomly selected from set { 1, 2, 3, 4, 5} what is the probability that the sum of the two numbers is greater than 4?

The number of ways to select 2 numbers from 5 is 5C2 = (5 x 4)/2! = 20/2 = 10.

To find the number of sums that are greater than 4, we can find the number of sums that ARE NOT greater than 4 and subtract that from 10.

1, 2

1, 3

So there are 10 - 2 = 8 sums that are greater than 4.

So the probability that the sum of the two numbers is greater than 4 is 8/10 = 4/5.
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: If two different numbers are randomly selected from set { 1,   [#permalink] 03 Dec 2017, 18:54
Display posts from previous: Sort by