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Math Expert V
Joined: 02 Sep 2009
Posts: 56306

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12 00:00

Difficulty:   95% (hard)

Question Stats: 30% (02:04) correct 70% (01:54) wrong based on 131 sessions

### HideShow timer Statistics 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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56306

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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 $$3 = 0.06 + 0.06 = 0.12$$.

_________________
Intern  Joined: 27 Sep 2015
Posts: 15

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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 $$3 = 0.06 + 0.06 = 0.12$$.

Math Expert V
Joined: 02 Aug 2009
Posts: 7763

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1
3
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..
_________________
Manager  B
Joined: 03 Dec 2014
Posts: 99
Location: India
GMAT 1: 620 Q48 V27 GPA: 1.9
WE: Engineering (Energy and Utilities)

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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).
Math Expert V
Joined: 02 Aug 2009
Posts: 7763

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1
1
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
_________________
Current Student B
Joined: 08 Jan 2015
Posts: 75

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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.
Intern  B
Joined: 09 Jul 2016
Posts: 17
GMAT 1: 730 Q50 V39 ### Show Tags

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56306

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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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Intern  B
Joined: 01 Mar 2016
Posts: 1

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 56306

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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.
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SVP  V
Joined: 26 Mar 2013
Posts: 2284

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1
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
Math Expert V
Joined: 02 Sep 2009
Posts: 56306

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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.
_________________
Senior Manager  S
Joined: 08 Jun 2015
Posts: 421
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33

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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 "
Intern  B
Joined: 27 Jul 2017
Posts: 19
Location: Spain
Schools: IMD '20
GMAT 1: 570 Q42 V27 GPA: 2.9

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What must change in the question stem, in order the result to be 0.06?
This is, no need to sum both probabilities.
Thanks
Intern  B
Joined: 19 Nov 2012
Posts: 27

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Hello Bunuel:
Bunuel wrote:
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.

Can you please explain why does order matter here? In other words, how is 23, 27 different from 27, 23 as in both cases it's the same prime number and the same multiple of 3 that's being counted.

Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 56306

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sanjay1810 wrote:
Hello Bunuel:
Bunuel wrote:
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.

Can you please explain why does order matter here? In other words, how is 23, 27 different from 27, 23 as in both cases it's the same prime number and the same multiple of 3 that's being counted.

Thanks!

The point is that those are two different events. Imagine that there are 10 balls with integer values from 20 through 29 on them. We are picking two balls with replacement. The case when the first ball has a prime number on it and the second ball has a multiple of 3 on it is a different event from a case when the first ball has a multiple of 3 on it and the second ball has a prime number on it.
_________________
Senior Manager  G
Joined: 13 Feb 2018
Posts: 421
GMAT 1: 640 Q48 V28 ### Show Tags

I arrived at

($$\frac{2}{10}$$*$$\frac{3}{10}$$)*2
and everything seemed so easy with this 95% hard question ... BUT

The Ozone layer became thinner, The moon showed the dark side and my brain decided that 2/10=1/2

Ended up - Wrong

I coursed math
-**** this sh@t - I shouted throwing papers away ...
Several seconds later:
-I have to pass - gathering my goddamn papers again

Peace of mind, Peace of mind, Peace of mind Re: M22-08   [#permalink] 25 Mar 2019, 12:26
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# M22-08

Moderators: chetan2u, Bunuel  