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ISEE Upper Level Math : How to find out if a number is prime

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Example Questions

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Example Question #1 : How To Find Out If A Number Is Prime

Add all of the prime numbers between 50 and 70.

Possible Answers:

240

181

309

238

187

Correct answer:

240

Explanation:

The prime numbers between 50 and 70 are 53, 59, 61, and 67. Their sum is

53 + 59 + 61 + 67 = 240 .

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Example Question #2 : How To Find Out If A Number Is Prime

Add all of the prime numbers between 20 and 40.

Possible Answers:

147

159

120

Correct answer:

120

Explanation:

The prime numbers between 20 and 40 are 23, 29, 31, and 37.

Their sum is 23 + 29 + 31 + 37 = 120 .

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Example Question #31 : Factors / Multiples

Which of these numbers is prime?

Possible Answers:

Correct answer:

Explanation:

A prime number has exactly two factors, 1 and itself. We can eliminate four choices by finding other factors:

$49 = 7 \times 7$

$50 = 2 \times 25$

$51 = 3 \times 17$

$52 = 2 \times 26$

53 has only 1 and 53 as factors, so it is the only prime among the choices.

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Example Question #3 : How To Find Out If A Number Is Prime

How many composite numbers are between 61 and 80 inclusive?

Possible Answers:

Correct answer:

Explanation:

There are twenty integers from 61 to 80 inclusive. Counting composite numbers can be made easier by weeding out the primes - 61, 67, 71, 73, 79. Removal of these five primes leave fifteen composite numbers.

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Example Question #1 : How To Find Out If A Number Is Prime

Which of the following numbers is prime?

123, 147, 163, 177

Possible Answers:

147

123

163

177

Correct answer:

163

Explanation:

The correct answer is 163 , and this can be determined in the following manner.

First, find the approximate square root of the number:

$\sqrt{163}\approx12.75\approx13$

We know this because:

$\sqrt{169}=13$

Therefore, we only need to consider prime numbers through $13\: (2, 3, 5, 7, 11, 13).$

Is 163 evenly divisible by any of these numbers? In this case, the answer is no, therefore 163 is prime. Consider the case where the answer is not prime: 147 .

$\sqrt{147}\approx12$

We know this because:

$\sqrt{144}=12$

Therefore, we need to consider the followig prime numbers: 2, 3, 5, 7, 11

Is 147 divisible by any of these numbers? In this case, the answer is yes. 147 is divisible by .

$\frac{147}{3}=49$

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Example Question #4 : How To Find Out If A Number Is Prime

How many composite numbers are between and inclusive?

Possible Answers:

Correct answer:

Explanation:

There are twenty integers from to inclusive. Counting composite numbers can be made easier by weeding out the primes - 31, 37, 41, 43, 47 . Removal of these five primes leaves composite numbers.

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Example Question #1 : How To Find Out If A Number Is Prime

Which of the following numbers is prime?

Possible Answers:

437

367

759

611

Correct answer:

367

Explanation:

The correct answer to this question is 367 . To determine if a number is prime, first find the approximate square root of the number:

$\sqrt{367}\approx19$

Next, determine if the number is divisible by any prime numbers up to and including the square root. In this instance consider the numbers:

2,3,5,7,9,11,13,17,19

367 is not divisible by any of the above numbers; therefore, it is prime.

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Example Question #3 : How To Find Out If A Number Is Prime

How many composite numbers are between and 100 inclusive?

Possible Answers:

Correct answer:

Explanation:

There are thirty integers from to 100 . Counting composite numbers can be made easier by weeding out the primes - 71, 73, 79, 83, 89, 97 . There are six primes in this range, so this leaves twenty-four composite numbers.

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Example Question #32 : Factors / Multiples

Reduce the fraction:

$\frac{\sqrt{52}}{2}$

Possible Answers:

$\frac{\sqrt{13}}{2}$

$\sqrt{26}$

$\sqrt{13}$

Correct answer:

$\sqrt{13}$

Explanation:

$\frac{\sqrt{52}}{2}$

First, given that 13 times 4 is 52, the numerator can be simplified by taking the square root of 4 and multiplying it by the square root of 13.

$\frac{\sqrt{4}\cdot \sqrt{13}}{2}$

$\frac{2\cdot \sqrt{13}}{2}$

$\sqrt{13}$

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Example Question #1 : How To Find Out If A Number Is Prime

How many prime numbers are there between 1 and 20?

Possible Answers:

Correct answer:

Explanation:

A prime number is one in which only itself and 1 can go into it. Therefore, 2, 3, 5, 7, 11, 13, 17, and 19 are the only prime numbers in that set.

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ISEE Upper Level Math : How to find out if a number is prime

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find Out If A Number Is Prime

Example Question #2 : How To Find Out If A Number Is Prime

Example Question #31 : Factors / Multiples

Example Question #3 : How To Find Out If A Number Is Prime

Example Question #1 : How To Find Out If A Number Is Prime

Example Question #4 : How To Find Out If A Number Is Prime

Example Question #1 : How To Find Out If A Number Is Prime

Example Question #3 : How To Find Out If A Number Is Prime

Example Question #32 : Factors / Multiples

Example Question #1 : How To Find Out If A Number Is Prime

All ISEE Upper Level Math Resources

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