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# M22-08

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139549 [0], given: 12794

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16 Sep 2014, 00:16
Expert's post
11
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

33% (01:00) correct 67% (00:59) wrong based on 116 sessions

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What is the probability that one of the two integers randomly selected from range 20-29, inclusive, is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139549 [0], given: 12794

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139549 [0], given: 12794

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16 Sep 2014, 00:16
Expert's post
3
This post was
BOOKMARKED
Official Solution:

What is the probability that one of the two integers randomly selected from range 20-29, inclusive, is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20

Prime integers: 23 and 29. Multiples of 3: 21, 24, and 27.

The probability that the first number is prime while the second is a multiple of $$3 = \frac{2}{10} \frac{3}{10} = 0.06$$.

The probability that the first number is a multiple of 3 while the second is prime $$= \frac{3}{10} \frac{2}{10} = 0.06$$.

The probability that one of the two integers is prime and the other is a multiple of $$3 = 0.06 + 0.06 = 0.12$$.

_________________

Kudos [?]: 139549 [0], given: 12794

Intern
Joined: 27 Sep 2015
Posts: 16

Kudos [?]: 104 [0], given: 13

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03 Apr 2016, 05:15
Hi Bunuel

I was wondering why the order of the selection matters here ?

Thanks

Bunuel wrote:
Official Solution:

What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20

Prime integers: 23 and 29. Multiples of 3: 21, 24, and 27.

The probability that the first number is prime while the second is a multiple of $$3 = \frac{2}{10} \frac{3}{10} = 0.06$$.

The probability that the first number is a multiple of 3 while the second is prime $$= \frac{3}{10} \frac{2}{10} = 0.06$$.

The probability that one of the two integers is prime and the other is a multiple of $$3 = 0.06 + 0.06 = 0.12$$.

Kudos [?]: 104 [0], given: 13

Math Expert
Joined: 02 Aug 2009
Posts: 5534

Kudos [?]: 6439 [1], given: 122

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04 Apr 2016, 05:38
1
KUDOS
Expert's post
Michael KC Chen wrote:
Hi Bunuel

I was wondering why the order of the selection matters here ?

Thanks

Bunuel wrote:
Official Solution:

What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20

Prime integers: 23 and 29. Multiples of 3: 21, 24, and 27.

The probability that the first number is prime while the second is a multiple of $$3 = \frac{2}{10} \frac{3}{10} = 0.06$$.

The probability that the first number is a multiple of 3 while the second is prime $$= \frac{3}{10} \frac{2}{10} = 0.06$$.

The probability that one of the two integers is prime and the other is a multiple of $$3 = 0.06 + 0.06 = 0.12$$.

Hi,
more than often follow this rule if in doubt..
1) If you are picking two simultaneously/together, you do not have any order in place..
2) whenever you are picking two with/ without repetition, it can be picked as either A and B or B and A..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Kudos [?]: 6439 [1], given: 122

Manager
Joined: 03 Dec 2014
Posts: 120

Kudos [?]: 62 [0], given: 391

Location: India
GMAT 1: 620 Q48 V27
GPA: 1.9
WE: Engineering (Energy and Utilities)

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04 Apr 2016, 07:11
chetan2u wrote:
Michael KC Chen wrote:
Hi Bunuel

I was wondering why the order of the selection matters here ?

Thanks

Bunuel wrote:
Official Solution:

What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20

Prime integers: 23 and 29. Multiples of 3: 21, 24, and 27.

The probability that the first number is prime while the second is a multiple of $$3 = \frac{2}{10} \frac{3}{10} = 0.06$$.

The probability that the first number is a multiple of 3 while the second is prime $$= \frac{3}{10} \frac{2}{10} = 0.06$$.

The probability that one of the two integers is prime and the other is a multiple of $$3 = 0.06 + 0.06 = 0.12$$.

Hi,
more than often follow this rule if in doubt..
1) If you are picking two simultaneously/together, you do not have any order in place..
2) whenever you are picking two with/ without repetition, it can be picked as either A and B or B and A..

what is wrong when I do:
(2C1 x 3C1)/(10C2).

Kudos [?]: 62 [0], given: 391

Math Expert
Joined: 02 Aug 2009
Posts: 5534

Kudos [?]: 6439 [1], given: 122

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04 Apr 2016, 07:24
1
KUDOS
Expert's post
robu wrote:
chetan2u wrote:

what is wrong when I do:
(2C1 x 3C1)/(10C2).

Hi ,
two errors
1) 10C2 is wrong because it is given that the same number can be picked up again..
In other words it is with REPLACEMENT, that is number will remain 10 each time..
so total ways will be 10*10

2) 2C1 * 3C2..
there are two ways here
2C1*3C1 OR 3C1*2C1 so two ways
2C1*3C1*2
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Kudos [?]: 6439 [1], given: 122

Manager
Joined: 08 Jan 2015
Posts: 86

Kudos [?]: 10 [0], given: 53

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06 Sep 2016, 23:00
chetan2u wrote:
Michael KC Chen wrote:
Hi Bunuel

I was wondering why the order of the selection matters here ?

Thanks

Bunuel wrote:
Official Solution:

What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20

Prime integers: 23 and 29. Multiples of 3: 21, 24, and 27.

The probability that the first number is prime while the second is a multiple of $$3 = \frac{2}{10} \frac{3}{10} = 0.06$$.

The probability that the first number is a multiple of 3 while the second is prime $$= \frac{3}{10} \frac{2}{10} = 0.06$$.

The probability that one of the two integers is prime and the other is a multiple of $$3 = 0.06 + 0.06 = 0.12$$.

Hi,
more than often follow this rule if in doubt..
1) If you are picking two simultaneously/together, you do not have any order in place..
2) whenever you are picking two with/ without repetition, it can be picked as either A and B or B and A..

It's not actually like that. Check this thread (probability-of-simultaneous-events-veritas-vs-mgat-105994-20.html)
Picking simultaneously is the same as picking one by one without replacement. In any case you need to multiply by the possible number of combinations.
The only case, when you don't need to multiply is when the order is strictly set - for instance, what's the probability that the FIRST number will be prime and the second will be a multiple of 3.

Kudos [?]: 10 [0], given: 53

Intern
Joined: 09 Jul 2016
Posts: 17

Kudos [?]: [0], given: 12

GMAT 1: 730 Q50 V39

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27 May 2017, 06:36
Can we get a confirmation that whether 0.06 is the answer or 0.12?

I am not sure whether we have to count the probability twice - i.e. for each case.

@Bunnel - can you please confirm.

Kudos [?]: [0], given: 12

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139549 [0], given: 12794

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27 May 2017, 07:49
Vikram_Katti wrote:
Can we get a confirmation that whether 0.06 is the answer or 0.12?

I am not sure whether we have to count the probability twice - i.e. for each case.

@Bunnel - can you please confirm.

The correct answer is B - 0.12
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Kudos [?]: 139549 [0], given: 12794

Intern
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10 Jul 2017, 07:37
I don't agree with the answer - if order is matter then it matter for both number of desirable events and for total number of events. SO total number of events is not 10x10 but 10x10x2 and desirable events are 3x4x2 also ! Then the answer is 0.06

The reply should be wrong here

Kudos [?]: [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139549 [0], given: 12794

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10 Jul 2017, 10:50
alexxko wrote:
I don't agree with the answer - if order is matter then it matter for both number of desirable events and for total number of events. SO total number of events is not 10x10 but 10x10x2 and desirable events are 3x4x2 also ! Then the answer is 0.06

The reply should be wrong here

This is not right. The order does matter - (prime, multiple of 3) and (multiple of 3, prime) are tow different cases. The reasoning as to why it should be 10*10*2 is not correct and not clear. For both cases we are choosing from 10 numbers, that's why it is 2/10*3/10 + 3/10*2/10.
_________________

Kudos [?]: 139549 [0], given: 12794

VP
Joined: 26 Mar 2013
Posts: 1370

Kudos [?]: 323 [1], given: 170

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10 Jul 2017, 23:44
1
KUDOS
Bunuel wrote:
What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20

Dear Bunuel,

I rarely post about phrasing your question but if you add word 'inclusive' after range 20-29, it would be clear.

Thanks

Kudos [?]: 323 [1], given: 170

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139549 [0], given: 12794

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11 Jul 2017, 01:29
Mo2men wrote:
Bunuel wrote:
What is the probability that one of the two integers randomly selected from range 20-29 is prime and the other is a multiple of 3?

(The numbers are selected independently of each other, i.e. they can be equal)

A. 0.06
B. 0.12
C. 0.15
D. 0.18
E. 0.20

Dear Bunuel,

I rarely post about phrasing your question but if you add word 'inclusive' after range 20-29, it would be clear.

Thanks

Edited as suggested. Thank you.
_________________

Kudos [?]: 139549 [0], given: 12794

Senior Manager
Joined: 08 Jun 2015
Posts: 365

Kudos [?]: 27 [0], given: 106

Location: India
GMAT 1: 640 Q48 V29

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03 Jan 2018, 07:58
chetan2u wrote:
robu wrote:
chetan2u wrote:

what is wrong when I do:
(2C1 x 3C1)/(10C2).

Hi ,
two errors
1) 10C2 is wrong because it is given that the same number can be picked up again..
In other words it is with REPLACEMENT, that is number will remain 10 each time..
so total ways will be 10*10

2) 2C1 * 3C2..
there are two ways here
2C1*3C1 OR 3C1*2C1 so two ways
2C1*3C1*2

Thanks for the explanation !!!
_________________

" The few , the fearless "

Kudos [?]: 27 [0], given: 106

Intern
Joined: 27 Jul 2017
Posts: 26

Kudos [?]: 2 [0], given: 65

Location: Spain
Schools: IMD '21
GMAT 1: 570 Q42 V27
GPA: 2.9

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04 Jan 2018, 02:55
What must change in the question stem, in order the result to be 0.06?
This is, no need to sum both probabilities.
Thanks

Kudos [?]: 2 [0], given: 65

Re: M22-08   [#permalink] 04 Jan 2018, 02:55
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# M22-08

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