GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Jun 2019, 18:46

### 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

# If one number is chosen at random from the first 1000 positive integer

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55758
If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 02:01
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:40) correct 35% (01:43) wrong based on 107 sessions

### HideShow timer Statistics

If one number is chosen at random from the first 1000 positive integers, then what is the probability that the number is a multiple of 2 and 8?

A. 1/16
B. 1/8
C. 1/4
D. 1/2
E. 2/3

_________________
CEO
Joined: 18 Aug 2017
Posts: 3920
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

Updated on: 04 Dec 2018, 09:45
Bunuel wrote:
If one number is chosen at random from the first 1000 positive integers, then what is the probability that the number is a multiple of 2 and 8?

A. 1/16
B. 1/8
C. 1/4
D. 1/2
E. 2/3

total multiple of 2 in 1-1000 : 1000/2= 500 and of 8 , 1000/8= 125

Multiples which are of both8 & 2 are to be found since multiplayer of 8 would be of 2 as well so:
125/1000= 1/8 IMO B
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 04 Dec 2018, 04:35.
Last edited by Archit3110 on 04 Dec 2018, 09:45, edited 1 time in total.
Intern
Joined: 17 May 2018
Posts: 49
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 07:32
1
Archit3110 wrote:
Bunuel wrote:
If one number is chosen at random from the first 1000 positive integers, then what is the probability that the number is a multiple of 2 and 8?

A. 1/16
B. 1/8
C. 1/4
D. 1/2
E. 2/3

total multiple of 2 in 1-1000 : 1000/2= 500 and of 8 , 1000/8= 125

500/1000 * 125/1000= 1/16 IMO A

Thing is, whatever number is a multiple of 8 is also a multiple of 2, so I would go and count only the multiples of 8 between 1 and 1000, or 125/1000 or 1/8.

Let's take a smaller range and test: between 1 and 20, there are 10 multiples of 2 and 2 multiples of 8. The answer should be 2/20 (or 1/10) and not 2/20 * 10/20, or 1/20.

Am I missing something?
_________________
¿Tienes que presentar el GMAT y no sabes por dónde empezar?
¡Visita GMAT para Principiantes y recibe el curso completo gratis!
Manager
Joined: 10 Oct 2018
Posts: 182
GPA: 4
If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 08:07
1
1. Multiple of 2 from 1-1000 is 1000/2=500 => P(A)= 500/1000=1/2
2. Any multiple of 8 is also a multiple of 2 so we need to find the multiples of 8 from 1 to 1000 the first one is 8 and the last one is 1000. Simple way is 1000/8=125
=> P(B)=125/1000=1/8

P(A and B) = P(A) x P(B)=1/2*1/8=1/16
Therefore, answer is Option A
_________________
Manager
Joined: 18 Oct 2018
Posts: 83
Location: India
Concentration: Finance, International Business
GPA: 4
WE: Business Development (Retail Banking)
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 08:19
1
Since the question says,the no.is a multiple of 2 and 8,this means we need to count the multiples of 8,as every multiple of 8 is also a multiple of 2.
As there are 125 no.s between 1-1000 which are multiple of 8,so answer should be 125/1000= 1/8.

Hence B

Posted from my mobile device
Intern
Joined: 23 May 2016
Posts: 1
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 08:22
Question says multiple of 2 AND 8 not OR so 1/8 is correct

Posted from my mobile device
CEO
Joined: 18 Aug 2017
Posts: 3920
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 08:57
yoannnesme wrote:
Archit3110 wrote:
Bunuel wrote:
If one number is chosen at random from the first 1000 positive integers, then what is the probability that the number is a multiple of 2 and 8?

A. 1/16
B. 1/8
C. 1/4
D. 1/2
E. 2/3

total multiple of 2 in 1-1000 : 1000/2= 500 and of 8 , 1000/8= 125

500/1000 * 125/1000= 1/16 IMO A

Thing is, whatever number is a multiple of 8 is also a multiple of 2, so I would go and count only the multiples of 8 between 1 and 1000, or 125/1000 or 1/8.

Let's take a smaller range and test: between 1 and 20, there are 10 multiples of 2 and 2 multiples of 8. The answer should be 2/20 (or 1/10) and not 2/20 * 10/20, or 1/20.

Am I missing something?

A number which would be multiple of 2 won't necessarily be a multiple of 8... But otherwise yes it would be correct to say that multiple of 8 would also be a multiple of 2.. so by doing 125/1000 you are only considering multiples of 8 only what about multiple of 2 i.e 4,6,12... which is why I calculated separate for 2 & 8 ...

Posted from my mobile device
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
CEO
Joined: 18 Aug 2017
Posts: 3920
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 08:58
sumit10 wrote:
Question says multiple of 2 AND 8 not OR so 1/8 is correct

Posted from my mobile device

Could you please reinstate what you mean by line "Question says multiple of 2 AND 8 not OR "??
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 751
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 09:17
Archit3110 wrote:
sumit10 wrote:
Question says multiple of 2 AND 8 not OR so 1/8 is correct

Posted from my mobile device

Could you please reinstate what you mean by line "Question says multiple of 2 AND 8 not OR "??

Draw a two-set Venn diagram: One set is all multiples of 2. The other set is all multiples of 8. And the intersection of the two sets is what we are interested in. Is so happens that the set "Multiples of 8"is completely inside the set multiple of 2 and 8. Hence we need to find only the multiples of 8 and it comes out to be one in every 8 numbers or 1/8.

Hope this makes sense.

Best,
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Intern
Joined: 10 Sep 2018
Posts: 44
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 09:37
multiple of 2 and 8 . All multiple of 8 will be multiple of 2 as well so we just need to find the multiples of 8 i.e 125
so 125/1000

should be 1/8
CEO
Joined: 18 Aug 2017
Posts: 3920
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

04 Dec 2018, 09:43
Archit3110 wrote:
sumit10 wrote:
Question says multiple of 2 AND 8 not OR so 1/8 is correct

Posted from my mobile device

Could you please reinstate what you mean by line "Question says multiple of 2 AND 8 not OR "??

Draw a two-set Venn diagram: One set is all multiples of 2. The other set is all multiples of 8. And the intersection of the two sets is what we are interested in. Is so happens that the set "Multiples of 8"is completely inside the set multiple of 2 and 8. Hence we need to find only the multiples of 8 and it comes out to be one in every 8 numbers or 1/8.

Hope this makes sense.

Best,

Okay thanks I understood ..
I actually calculated both multiples of 2 & 8...
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
ISB School Moderator
Joined: 08 Dec 2013
Posts: 452
Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Re: If one number is chosen at random from the first 1000 positive integer  [#permalink]

### Show Tags

24 May 2019, 08:06
Bunuel wrote:
If one number is chosen at random from the first 1000 positive integers, then what is the probability that the number is a multiple of 2 and 8?

A. 1/16
B. 1/8
C. 1/4
D. 1/2
E. 2/3

total number of numbers in the set: (1000 - 1) + 1= 1000

Now let's find the subset:-
All multiples of 8 are a multiple of 2 & 8.

Between 1 and 1000
there are 125 multiples of 8. Because 8*125=1000

Probability= 125/1000.
Option B (1/8)
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.

GMAT Math Book

-I never wanted what I gave up
I never gave up what I wanted-
Re: If one number is chosen at random from the first 1000 positive integer   [#permalink] 24 May 2019, 08:06
Display posts from previous: Sort by

# If one number is chosen at random from the first 1000 positive integer

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne