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

Question

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

Archit3110 · Answer

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

yoannnesme · Answer

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?

EncounterGMAT · Answer

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

Therefore, answer is Option B

anshkool4u · Answer

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

sumit10 · Answer

Question says multiple of 2 AND 8 not OR so 1/8 is correct

Posted from my mobile device

Archit3110 · Answer

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

Archit3110 · Answer

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

Gladiator59 · Answer

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,
Gladi

NCRanjan · Answer

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

Archit3110 · Answer

Okay thanks I understood ..
I actually calculated both multiples of 2 & 8...

LeoN88 · Answer

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)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards