ISEE Upper Level Quantitative Help » Numbers and Operations » Factors / Multiples » Prime Numbers » How to find out if a number is prime

Explanation:

Every number except 1 has at least two factors - 1 and itself. So we are looking for a number with no other factors - that is, a prime.

You are watching: Prime numbers between 20 and 40

3 is a factor of both 33 and 39, and 5 is a factor of 35, so we can eliminate those choices. We cannot eliminate 37, since it is a prime, having only 1 and 37 as factors.

Which is the greater quantity?

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

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

Explanation:

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

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

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

(a) is the greater quantity

Which is the greater quantity?

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

(b) The number of composite numbers between 21 and 30 inclusive

Explanation:

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

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

(a) and (b) are therefore equal.

Which is the greater quantity?

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

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

Explanation:

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

Which is the greater quantity?

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

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

Explanation:

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

(b) The composite 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 between 1 and 1,000 inclusive.

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

Explanation:

It is not necessary to count all of the composite numbers in the 1-1,000 range. Except for 2, every even number is composite, and there are more than one odd composite numbers (15, 25) to make up for 2. This makes (a) greater.

Which is the greater quantity?

(a) The number of primes between 20 and 50

(b) The number of primes between 10 and 40

Explanation:

The primes between 20 and 40 are included in both sets, so all we need to do is to compare the number of primes between 40 and 50 with the number of primes between 10 and 20.

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

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

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

See more: Change The Default View That Powerpoint Opens In Is Called ____ View.

Radford University, Bachelor of Science, Psychology. Catholic University of America, Master of Arts, Psychology.
Indian Institute of Technology, Engineering in Computer Science, Electrical Engineering. New York University, Masters in Busi...
Statistics Tutors in Washington DC, MCAT Tutors in Philadelphia, Spanish Tutors in Phoenix, Math Tutors in Dallas Fort Worth, ISEE Tutors in Dallas Fort Worth, Calculus Tutors in Philadelphia, SSAT Tutors in Philadelphia, ACT Tutors in Los Angeles, GMAT Tutors in Los Angeles, GMAT Tutors in New York City
LSAT Courses & Classes in New York City, GRE Courses & Classes in Miami, LSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Houston, SSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in New York City, MCAT Courses & Classes in Houston, SAT Courses & Classes in Boston, GRE Courses & Classes in Washington DC, ACT Courses & Classes in New York City
LSAT Test Prep in San Diego, GMAT Test Prep in Seattle, GRE Test Prep in Miami, GMAT Test Prep in Los Angeles, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in San Diego, GRE Test Prep in Denver, LSAT Test Prep in Los Angeles, ACT Test Prep in Houston, SSAT Test Prep in Atlanta
Report an issue with this question

If you"ve found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.