ISEE Upper Level Quantitative Assistance » Numbers and also Operations » Factors / Multiples » Prime Numbers » How to discover out if a number is prime     Explanation:

Eextremely number except 1 has at leastern two determinants - 1 and also itself. So we are in search of a number through no various other factors - that is, a prime.

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3 is a variable of both 33 and also 39, and also 5 is a variable of 35, so we deserve to remove those selections. We cannot remove 37, because it is a prime, having just 1 and also 37 as factors.

Which is the better quantity?

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

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

Explanation:

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

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

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

(a) is the higher quantity

Which is the better quantity?

(a) The number of prime numbers between 1 and also 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 are 2, 3, 5, 7, 11, 13, 17, 19 - eight complete.

(b) The prime numbers in between 21 and 30 inclusive are 23 and also 29 - two prime numbers out of ten integers. This leaves eight compowebsite numbers.

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

Which is the higher quantity?

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

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

Explanation:

The prime numbers between 1 and also 20 inclusive are 2, 3, 5, 7, 11, 13, 17, 19 - eight full. Due to the fact that 1 is neither prime nor compowebsite, this leaves 11 compowebsite numbers. (b) is the better amount.

Which is the higher quantity?

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

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

Explanation:

(a) The prime numbers in the 11-19 range are 11, 13, 17, and also 19. Their sum: (b) The compowebsite numbers in the 11-19 range are 12, 14, 15, 16, and 18. Their sum: (b) is greater.

Which quantity is greater?

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

(b) The variety of also integers in between 1 and also 1,000 inclusive.

Explanation:

It is not essential to count every one of the compowebsite numbers in the 1-1,000 selection. Except for 2, eexceptionally even number is compowebsite, and also there are even more than one odd composite numbers (15, 25) to consist of for 2. This renders (a) better.

Which is the better quantity?

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

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

Explanation:

The primes between 20 and also 40 are consisted of in both sets, so all we must execute is to compare the number of primes in between 40 and also 50 via the variety of primes in between 10 and also 20.

(a) The primes between 40 and also 50 are 41, 43, and also 47 - 3.

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

Due to the fact that the variety of primes in between 10 and also 20 outnumbers those in between 40 and also 50, the number of primes in between 10 and 40 outnumber those between 20 and 50. Therefore, (b) is the better.

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