ISEE upper Level Quantitative assist » Numbers and Operations » factors / Multiples » element Numbers » how to uncover out if a number is element

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Explanation:

Every number other than 1 has at least two determinants - 1 and itself. So us are trying to find a number with no other factors - that is, a prime.

You are watching: All the prime numbers between 10 and 20

3 is a aspect of both 33 and also 39, and also 5 is a factor of 35, so us can eliminate those choices. Us cannot remove 37, since it is a prime, having only 1 and also 37 together factors.


Which is the greater quantity?

(a) The number of prime numbers in between 70 and 110

(b) The number of prime number between 80 and 120


Explanation:

The primes between 80 and 110 are had in both sets, so all we should do is to to compare the variety of primes between 70 and 80 and the number of primes between 110 and 120.

(a) The primes in between 70 and 80 room 71, 73, and 79 - 3 primes

(b) The only prime in between 110 and 120 is 113.

(a) is the higher quantity


Which is the higher quantity?

(a) The number of prime numbers between 1 and 20 inclusive

(b) The variety of composite numbers in between 21 and also 30 inclusive


Explanation:

(a) The prime numbers between 1 and 20 inclusive room 2, 3, 5, 7, 11, 13, 17, 19 - eight total.

(b) The prime numbers in between 21 and also 30 inclusive room 23 and also 29 - 2 prime numbers out of ten integers. This pipeline eight composite numbers.

(a) and (b) are therefore equal.


Which is the better quantity?

(a) The number of prime numbers in between 1 and also 20 inclusive

(b) The number of composite numbers between 1 and 20 inclusive


Explanation:

The prime numbers between 1 and also 20 inclusive space 2, 3, 5, 7, 11, 13, 17, 19 - eight total. Because 1 is neither prime nor composite, this pipeline 11 composite numbers. (b) is the greater quantity.


Which is the better quantity?

(a) The amount of the prime numbers in between 11 and 19 inclusive

(b) The sum of the composite numbers between 11 and 19 inclusive


Explanation:

(a) The element numbers in the 11-19 selection are 11, 13, 17, and also 19. Their sum: 

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(b) The composite numbers in the 11-19 range are 12, 14, 15, 16, and 18. Their sum: 

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(b) is greater.


Which quantity is greater?

(a) The number of composite numbers between 1 and also 1,000 inclusive.

(b) The number of even integers between 1 and 1,000 inclusive.


Explanation:

It is not vital to count every one of the composite numbers in the 1-1,000 range. Except for 2, every even number is composite, and there are an ext than one strange composite numbers (15, 25) to consist of for 2. This makes (a) greater.


Which is the better quantity?

(a) The number of primes in between 20 and also 50

(b) The variety of primes in between 10 and also 40


Explanation:

The primes between 20 and 40 are consisted of in both sets, so every we must do is to compare the variety of primes in between 40 and 50 v the variety of primes between 10 and 20.

(a) The primes in between 40 and 50 are 41, 43, and also 47 - three.

(b) The primes in between 10 and also 20 room 11, 13, 17, and 19 - four.

Since the number of primes in between 10 and 20 outnumbers those in between 40 and 50, the number of primes in between 10 and 40 outnumber those between 20 and 50. Therefore, (b) is the greater.


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