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# A number is randomly chosen from the first 100 positive inte

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1612 [0], given: 375

A number is randomly chosen from the first 100 positive inte [#permalink]  30 Jul 2018, 10:40
Expert's post
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Question Stats:

83% (00:15) correct 16% (00:47) wrong based on 12 sessions
A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3??

A. $$\frac{32}{100}$$
B. $$\frac{33}{100}$$
C. $$\frac{1}{3}$$
D. $$\frac{34}{100}$$
E. $$\frac{2}{3}$$
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [1] , given: 375

Re: A number is randomly chosen from the first 100 positive inte [#permalink]  07 Aug 2018, 06:01
1
KUDOS
Expert's post
Explanation

The first 100 positive integers comprise the set of numbers containing the integers 1 to 100.

Of these numbers, the only ones that are divisible by 3 are {3, 6, 9, …, 96, 99}, which adds up to exactly 33 numbers. This can be determined in several ways. One option is to count the multiples of 3, but that’s a bit slow. Alternatively, compute $$\frac{99}{3}= 33$$ and realize that there are 33 multiples of 3 up to and including 99.

The number 100 is not divisible by 3, so the correct answer is $$\frac{33}{100}$$.

Alternatively, use the “add one before you’re done” trick, subtracting the first multiple of 3 from the last multiple of 3, dividing by 3 and then adding 1: $$\frac{99-3}{3}+ 1 = 33$$.

Then, since probability is determined by the number of desired options divided by the total number of options, the probability that the number chosen is a multiple of 3 is $$\frac{33}{100}$$.
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Sandy
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Joined: 06 Jun 2018
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Kudos [?]: 55 [1] , given: 0

Re: A number is randomly chosen from the first 100 positive inte [#permalink]  09 Aug 2018, 14:12
1
KUDOS
sandy wrote:
A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3??

A. $$\frac{32}{100}$$
B. $$\frac{33}{100}$$
C. $$\frac{1}{3}$$
D. $$\frac{34}{100}$$
E. $$\frac{2}{3}$$

Total numbers = 100

Total multiple of 3 = 33*3 = 99. It means there are 33 multiple of 3 up to 100.

Probability = 33 / 100.

Re: A number is randomly chosen from the first 100 positive inte   [#permalink] 09 Aug 2018, 14:12
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