ISEE upper Level Quantitative assist » Numbers and Operations » determinants / Multiples » prime Numbers » how to find out if a number is element

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Explanation:

Every number other than 1 has at least two components - 1 and also itself. So us are looking for a number v no other components - the is, a prime.

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3 is a factor of both 33 and also 39, and also 5 is a element of 35, so us can remove those choices. Us cannot get rid of 37, because it is a prime, having only 1 and 37 as factors.


Which is the better 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 every we have to do is to to compare the number of primes between 70 and also 80 and also the number of primes between 110 and also 120.

(a) The primes between 70 and also 80 space 71, 73, and also 79 - three primes

(b) The just prime 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 between 21 and also 30 inclusive


Explanation:

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

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

(a) and also (b) are therefore equal.


Which is the higher quantity?

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

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


Explanation:

The prime numbers in between 1 and 20 inclusive space 2, 3, 5, 7, 11, 13, 17, 19 - eight total. Because 1 is neither prime no one composite, this leaves 11 composite numbers. (b) is the higher quantity.


Which is the better quantity?

(a) The sum of the prime numbers between 11 and also 19 inclusive

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


Explanation:

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

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

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(b) is greater.


Which amount is greater?

(a) The variety of composite numbers in 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 all of the composite numbers in the 1-1,000 range. Except for 2, every also number is composite, and there are much more than one strange composite numbers (15, 25) to comprise for 2. This renders (a) greater.


Which is the better quantity?

(a) The variety of primes between 20 and also 50

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


Explanation:

The primes between 20 and also 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 in between 10 and also 20.

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

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

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

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