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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the probability that an integer in the set {1, 2, 3, ..., 100}

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Math Expert V
Joined: 02 Sep 2009
Posts: 59587
What is the probability that an integer in the set {1, 2, 3, ..., 100}  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 64% (01:54) correct 36% (02:02) wrong based on 86 sessions

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What is the probability that an integer in the set {1, 2, 3, ..., 100} is divisible by 2 and not divisible by 3 ?

(A) 1/6
(B) 33/100
(C) 17/50
(D) 1/2
(E) 18/25

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Manager  S
Joined: 05 Oct 2017
Posts: 102
Location: India
Schools: ISB '21, IIMA , IIMB
GPA: 4
WE: Analyst (Energy and Utilities)
Re: What is the probability that an integer in the set {1, 2, 3, ..., 100}  [#permalink]

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Bunuel wrote:
What is the probability that an integer in the set {1, 2, 3, ..., 100} is divisible by 2 and not divisible by 3 ?

(A) 1/6
(B) 33/100
(C) 17/50
(D) 1/2
(E) 18/25

Integers in the set {1,2,3,...,100} divisible by 2 = (last term-first term)/difference + 1 = (100-2)/2+1 = 50

We have to find the number of integers which is divisible by 2 but not by 3.

So we have to exclude numbers which are divisible by 2 and 3 i.e 6

No of integers in the set divisible by 6 = (96-6)/6 +1 = 16

Required number of integers = 50 -16 =34

Therefore probability = 34/100 = 17/50 (C)
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: What is the probability that an integer in the set {1, 2, 3, ..., 100}  [#permalink]

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Top Contributor
Bunuel wrote:
What is the probability that an integer in the set {1, 2, 3, ..., 100} is divisible by 2 and not divisible by 3 ?

(A) 1/6
(B) 33/100
(C) 17/50
(D) 1/2
(E) 18/25

I'd typically use the same approach that shuvodip04 used.
However, if you're not 100% sure about that approach, it doesn't take long to list and count all of integers (from 1 to 100) that are divisible by 2 and not divisible by 3

They are: 2, 4, 8, 10, 14, 16, 20, 22, 26, 28, 32, 34, 38, 40, 44, 46, 50, 52, 56, 58, 62, 64, 68, 70, 74, 76, 80, 82, 86, 88, 92, 94, 98, 100

There are 34 such integers
And there are 100 integers to choose from.

So, P(selected number is divisible by 2 and not divisible by 3) = 34/100 = 17/50

Cheers,
Brent
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Concentration: Sustainability, Marketing
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Re: What is the probability that an integer in the set {1, 2, 3, ..., 100}  [#permalink]

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Bunuel wrote:
What is the probability that an integer in the set {1, 2, 3, ..., 100} is divisible by 2 and not divisible by 3 ?

(A) 1/6
(B) 33/100
(C) 17/50
(D) 1/2
(E) 18/25

integers divisible by 2 in set (1,..100) = 50
out of which overlap integers which wont be divisible by 3 but by 2 ; LCM 6 ; 16
so 50-16 = 34
34/100; 17/50
IMO C
Manager  S
Joined: 01 Oct 2018
Posts: 112
Re: What is the probability that an integer in the set {1, 2, 3, ..., 100}  [#permalink]

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Bunuel wrote:
What is the probability that an integer in the set {1, 2, 3, ..., 100} is divisible by 2 and not divisible by 3 ?

(A) 1/6
(B) 33/100
(C) 17/50
(D) 1/2
(E) 18/25

Let's simple the task. Take not (1,2,3...100), but only (1,2,3).
Apparently, according to the condition probability is 1/3. Coz 2 is only appropriate variant.

Now, such pattern (1,2,3) multiply on 33 = 99 variants.
So, if we have in task 99 variants the probability would be 33/99 (same as 1/3)
But we have else one variant - "100".

That mean we need to add this possible outcome : (33+1)/(99+1) = 34/100 or 17/50 Re: What is the probability that an integer in the set {1, 2, 3, ..., 100}   [#permalink] 22 May 2019, 18:17
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