A jar contains slips of paper numbered from 1… | GMAT Sprint

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PS · Problem Solving

705-805

Probability

A jar contains slips of paper numbered from 1 through 100, inclusive. If a single slip is drawn randomly, what is the approximate probability that the number written on it is not divisible by 2 or 3? $\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Answer Choices

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\frac{67}{100}

\frac{57}{100}

\frac{45}{100}

\frac{33}{100}

Correct

\frac{23}{100}

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Explanation

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Official Explanation

Official

To solve the problem of finding the probability that a randomly drawn slip from a jar containing numbers 1 through 100 is not divisible by 2 or 3, follow these steps:

Step 1: Find the Total Number of Outcomes

The jar contains slips numbered from 1 to 100, so the total number of possible outcomes is:

\text{Total number of outcomes} = 100

Step 2: Find the Number of Multiples of 2 (Even Numbers)

Numbers divisible by 2 (even numbers) between 1 and 100 can be calculated as:

\text{Number of multiples of 2} = \frac{100}{2} = 50

Step 3: Find the Number of Multiples of 3

Numbers divisible by 3 between 1 and 100 can be calculated as:

\text{Number of multiples of 3} = \left\lfloor \frac{100}{3} \right\rfloor = 33

Step 4: Find the Number of Multiples of Both 2 and 3 (i.e., Multiples of 6)

Numbers divisible by both 2 and 3 (i.e., multiples of 6) between 1 and 100 can be calculated as:

\text{Number of multiples of 6} = \left\lfloor \frac{100}{6} \right\rfloor = 16

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What this question tests

What it tests

Your ability to compute probabilities of single and compound events, including 'at least one' questions.

Common trap

Forgetting to use the complement for 'at least one', or treating dependent events as independent.