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# M23-22

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Math Expert
Joined: 02 Sep 2009
Posts: 50585

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16 Sep 2014, 00:19
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:03) correct 44% (01:10) wrong based on 181 sessions

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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?

A. $$\frac{3}{5}$$
B. $$\frac{7}{10}$$
C. $$\frac{4}{5}$$
D. $$\frac{9}{10}$$
E. $$\frac{19}{20}$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50585

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16 Sep 2014, 00:19
2
Official Solution:

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?

A. $$\frac{3}{5}$$
B. $$\frac{7}{10}$$
C. $$\frac{4}{5}$$
D. $$\frac{9}{10}$$
E. $$\frac{19}{20}$$

Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

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

The number of outcomes when $$sum\leq{4}$$ is 2: only (1,2) and (1,3);

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

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Location: Uruguay
Concentration: General Management
Schools: Goizueta '19 (A)
GMAT 1: 610 Q41 V32
GMAT 2: 620 Q45 V31
GMAT 3: 640 Q46 V32
GPA: 3.97

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11 Jun 2016, 09:52
Bunuel wrote:
Official Solution:

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?

A. $$\frac{3}{5}$$
B. $$\frac{7}{10}$$
C. $$\frac{4}{5}$$
D. $$\frac{9}{10}$$
E. $$\frac{19}{20}$$

Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

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

The number of outcomes when $$sum\leq{4}$$ is 2: only (1,2) and (1,3);

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

Thank you for this great questions, gmat club is really good!
This said,
why do I have only 2 possible outcomes? (1,2) and (1,3).. why doesn't (2,1) and (3,1) work? I can randomly select them in this order as well?

Intern
Joined: 22 Jul 2016
Posts: 1

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11 Aug 2016, 03:21
1
By definition a subset contains only different elements of the subset. So {1,2} and {2,1} is the same subset.
Intern
Joined: 14 Oct 2015
Posts: 6

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04 Jul 2017, 07:35
[/m]
Bunuel wrote:
Official Solution:

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?

A. $$\frac{3}{5}$$
B. $$\frac{7}{10}$$
C. $$\frac{4}{5}$$
D. $$\frac{9}{10}$$
E. $$\frac{19}{20}$$

Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

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

The number of outcomes when $$sum\leq{4}$$ is 2: only (1,2) and (1,3);

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

$$P=1-\frac{2}{10}=\frac{8}{5}$$. and not$$\frac{4}{5}$$
Math Expert
Joined: 02 Sep 2009
Posts: 50585

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04 Jul 2017, 07:37
pranab223 wrote:
[/m]
Bunuel wrote:
Official Solution:

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?

A. $$\frac{3}{5}$$
B. $$\frac{7}{10}$$
C. $$\frac{4}{5}$$
D. $$\frac{9}{10}$$
E. $$\frac{19}{20}$$

Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

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

The number of outcomes when $$sum\leq{4}$$ is 2: only (1,2) and (1,3);

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

$$P=1-\frac{2}{10}=\frac{8}{5}$$. and not$$\frac{4}{5}$$

_________________
Intern
Joined: 14 Oct 2015
Posts: 6

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04 Jul 2017, 08:07
Bunuel wrote:
pranab223 wrote:
[/m]
Bunuel wrote:
Official Solution:

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?

A. $$\frac{3}{5}$$
B. $$\frac{7}{10}$$
C. $$\frac{4}{5}$$
D. $$\frac{9}{10}$$
E. $$\frac{19}{20}$$

Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

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

The number of outcomes when $$sum\leq{4}$$ is 2: only (1,2) and (1,3);

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

$$P=1-\frac{2}{10}=\frac{8}{5}$$. and not$$\frac{4}{5}$$

You are right its $$\frac{4}{5}$$
Intern
Joined: 21 May 2017
Posts: 2

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15 Jul 2017, 23:42
How is it not B =7/10?

When you consider the case , how many pairs of numbers whose sum is greater than 4, you get

(1,4),(1,5).(2,4),(2,5),(2,3),(3,4),(3,5),(4,5) which is 7 outcomes out of total possible 10 outcomes.

Math Expert
Joined: 02 Sep 2009
Posts: 50585

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16 Jul 2017, 03:12
ajanpaul wrote:
How is it not B =7/10?

When you consider the case , how many pairs of numbers whose sum is greater than 4, you get

(1,4),(1,5).(2,4),(2,5),(2,3),(3,4),(3,5),(4,5) which is 7 outcomes out of total possible 10 outcomes.

It's not that hard to do the following:
1 - (1,4)
2 - (1,5)
3 - (2,4)
4 - (2,5)
5 - (2,3)
6 - (3,4)
7 - (3,5)
8 - (4,5)
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Senior Manager
Joined: 08 Jun 2015
Posts: 435
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33

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15 Mar 2018, 08:25
Only (1,2) and (1,3) are less than or equal to 4. The required probability is 1-(2/5C2). The answer is 4/5.
_________________

" The few , the fearless "

Intern
Joined: 08 Aug 2017
Posts: 22
GMAT 1: 690 Q49 V35
GMAT 2: 720 Q48 V40

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30 Jun 2018, 11:55
When you say 2 different numbers are randomly selected from set means it cannot be {1,1}, {2,2}, {3,3}, {4,4}, and {5,5}.
But it can be {1,2} or {2,1}.

The question should clearly indicate that subsets have to be different.

Thanks.
Intern
Joined: 18 Nov 2013
Posts: 4

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20 Oct 2018, 03:41
Hi Brunei
This is my first post in GMAT club
I would like to know if the order matters for these type of questions.
I have seen the approach to be ambiguous in similar type of problems

Dan
Re: M23-22 &nbs [#permalink] 20 Oct 2018, 03:41
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# M23-22

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