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# Probability | AMC-10A, 2003 | Problem 8

Try this beautiful problem from Probability: positive factors AMC-10A, 2003. You may use sequential hints to solve the problem

Try this beautiful problem from Probability based on Positive factors

## Probability – AMC-10A, 2003- Problem 8

What is the probability that a randomly drawn positive factor of $$60$$ is less than $$7$$?

• $$\frac{1}{3}$$
• $$\frac{1}{2}$$
• $$\frac{3}{4}$$

### Key Concepts

Probability

Factors

combinatorics

But try the problem first…

Answer: $$\frac{1}{2}$$

Source

AMC-10A (2003) Problem 8

Pre College Mathematics

## Try with Hints

First hint

Now at first we find out the positive factors of $$60$$ are $$1,2,3,4,5,6,10,12,15,20,30,60$$.but the positive factors which are less than $$7$$ are $$1,2,3,4,5,6$$

Can you now finish the problem ……….

Second Hint

so we may say that any For a positive number $$n$$ which is not a perfect square, exactly half of the positive factors will be less than $$\sqrt{n}$$.here $$60$$ is not a perfect square and $$\sqrt 60 \approx 7.746$$.Therefore half of the positive factors will be less than $$7$$

can you finish the problem……..

Final Step

Therefore the required probability=$$\frac{1}{2}$$

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