Test your basic knowledge |

GMAT Number Properties

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. The prime factorization of __________ contains only EVEN powers of primes.
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
A PERFECT SQUARE
11 -13 -17 -19
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

2. Prime Numbers:0x
EVEN
NEVER CONTRADICT ONE ANOTHER
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
2 -3 -5 -7

3. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
Prime factorization
In an evenly spaced set - the average and the median are equal.
41 -43 -47

4. v2˜
1.4
25
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A MULTIPLE

5. How to solve: For any positive integer n - the sum of the 1st n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301? (A) 10 -100 (B) 20 -200 (C) 22 -650 (D) 40 -200 (E) 45 -150
ODD
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.4

6. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
In an evenly spaced set - the average and the median are equal.
NEVER CONTRADICT ONE ANOTHER
41 -43 -47
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

7. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE
Prime factorization

8. In an evenly spaced set - the sum of the terms is equal to ____.
The average of the set times the number of elements in the set
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Either a multiple of N or a non-multiple of N
EVEN

9. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
2.5
FACTOR
53 -59
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the

10. v5˜
1.4
23 -29
2.5
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.

11. Prime Numbers:3x
Either a multiple of N or a non-multiple of N
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
11 -13 -17 -19
31 -37

12. In an evenly spaced set - the ____ and the ____ are equal.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
The same sign as the base
1.4

13. If estimating a root with a coefficient - _____ .
1.4
Put the coefficient under the radical to get a better approximation
97
Look at the numbers from 1 to 30 - inclusive - that have at least one factor of 3 and count up how many each has: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.

14. Positive integers with more than two factors are ____.
Express as 2k + 3m = t. 1. If k is a multiple of 3 - then so is t and we have a yes. => S 2. If m is a multiple of 3 - we don't know. => I A/1 Alone.
Never prime
The sum of EVEN INTEGERS between 99 and 301 is the sum of EVEN INTEGERS between 100 and 300 - or the sum of the 50th EVEN INTEGER through the 150th EVEN INTEGER.To get this sum: -Find the sum of the FIRST 150 even integers (ie 2 times the sum of the
2 -3 -5 -7

15. v169=
The average of the set times the number of elements in the set
1.7
13
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

16. v3˜
1.7
In an evenly spaced set - the average and the median are equal.
31 -37
A MULTIPLE

17. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
Prime factorization
71 -73 -79
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE

18. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE
EVEN

19. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
PERFECT CUBES
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an ODD number of consecutive integers will ALWAYS be an integer.
25

20. How to test for sufficiency: If p is an integer - is p/n an integer? (1) k1p/n is an integer(2) k2p/n is an integer
1. The smallest or largest element 2. The increment 3. The number of items in the set
13
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD

21. Prime Numbers:9x
1.7
The sum of any two primes will be even - unless one of the two primes is 2.
97
A non-multiple of N.

22. For ODD ROOTS - the root has ______.
53 -59
The same sign as the base
14
83 -89

23. N! is _____ of all integers from 1 to N.
ODD
If 2 cannot be one of the primes in the sum - the sum must be even.
A MULTIPLE
13

24. All perfect squares have a(n) _________ number of total factors.
ODD
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE

25. How to find the sum of consecutive integers:
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
11 -13 -17 -19
13
61 -67

26. The formula for finding the number of consecutive multiples in a set is _______.
A PERFECT SQUARE
13
[(last - first) / increment] + 1
83 -89

27. Any integer with an EVEN number of total factors cannot be ______.
1.4
13
A PERFECT SQUARE
11 -13 -17 -19

28. The prime factorization of a perfect square contains only ______ powers of primes.
NEVER CONTRADICT ONE ANOTHER
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN
In an evenly spaced set - the average and the median are equal.

29. Prime Numbers:2x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The middle number
23 -29
PERFECT CUBES

30. The average of an EVEN number of consecutive integers will ________ be an integer.
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
23 -29
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The average of an EVEN number of consecutive integers will NEVER be an integer.

31. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
83 -89
1.7
A non-multiple of N.
Put the coefficient under the radical to get a better approximation

32. Prime Numbers:6x
61 -67
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
The PRODUCT of n consecutive integers is divisible by n!.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

33. In an evenly spaced set - the mean and median are equal to the _____ of _________.
The PRODUCT of n consecutive integers is divisible by n!.
2 -3 -5 -7
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

34. Prime Numbers:8x
61 -67
If 2 cannot be one of the primes in the sum - the sum must be even.
83 -89
41 -43 -47

35. Positive integers with only two factors must be ___.
Either a multiple of N or a non-multiple of N
Prime
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

36. v256=
16
Express as 2k + 3m = t. 1. If k is a multiple of 3 - then so is t and we have a yes. => S 2. If m is a multiple of 3 - we don't know. => I A/1 Alone.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the average and the median are equal.

37. If N is a divisor of x and y - then _______.
A non-multiple of N.
2 -3 -5 -7
N is a divisor of x+y
The middle number

38. Prime factors of _____ must come in pairs of three.
1.7
1. The smallest or largest element 2. The increment 3. The number of items in the set
3·3n = 3^{n+1}
PERFECT CUBES

39. Prime Numbers:1x
1. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
A non-multiple of N.
11 -13 -17 -19
Express as 2k + 3m = t. 1. If k is a multiple of 3 - then so is t and we have a yes. => S 2. If m is a multiple of 3 - we don't know. => I A/1 Alone.

40. v196=
A non-multiple of N.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
14
61 -67

41. Prime Numbers:4x
2.5
41 -43 -47
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The middle number

42. The average of an ODD number of consecutive integers will ________ be an integer.
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.
3·3n = 3^{n+1}
1.7

43. v225=
[(last - first) / increment] + 1
15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
11 -13 -17 -19

44. 3n + 3n + 3n = _____ = ______
Put the coefficient under the radical to get a better approximation
3·3n = 3^{n+1}
[(last - first) / increment] + 1
EVEN

45. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
Either a multiple of N or a non-multiple of N

46. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
NEVER CONTRADICT ONE ANOTHER
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.4

47. Prime Numbers:7x
Never prime
The average of the set times the number of elements in the set
71 -73 -79
23 -29

48. v625=
ODD
71 -73 -79
25
The same sign as the base

49. How to solve: If p is the product of the integers from 1 to 30 - inclusive - what is the greatest integer n for which 3n is a factor of p?
83 -89
The sum of any two primes will be even - unless one of the two primes is 2.
Look at the numbers from 1 to 30 - inclusive - that have at least one factor of 3 and count up how many each has: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

50. In an evenly spaced set - the average can be found by finding ________.
31 -37
The middle number
Express as 2k + 3m = t. 1. If k is a multiple of 3 - then so is t and we have a yes. => S 2. If m is a multiple of 3 - we don't know. => I A/1 Alone.
Never prime

Sorry!:) No result found.

Can you answer 50 questions in 15 minutes?

Major Subjects
Tests & Exams AP CLEP DSST GRE SAT GMAT	Certifications CISSP go to https://www.isc2.org/ PMP ITIL RHCE MCTS More...	IT Skills Android Programming Data Modeling Objective C Programming Basic Python Programming Adobe Illustrator More...	Business Skills Advertising Techniques Business Accounting Basics Business Strategy Human Resource Management Marketing Basics More...
Soft Skills Body Language People Skills Public Speaking Persuasion Job Hunting And Resumes More...	Vocabulary GRE Vocab SAT Vocab TOEFL Essential Vocab Basic English Words For All Global Words You Should Know Business English More...	Languages AP German Vocab AP Latin Vocab SAT Subject Test: French Italian Survival Norwegian Survival More...	Engineering Audio Engineering Computer Science Engineering Aerospace Engineering Chemical Engineering Structural Engineering More...
Health Sciences Basic Nursing Skills Health Science Language Fundamentals Veterinary Technology Medical Language Cardiology Clinical Surgery More...	English Grammar Fundamentals Literary And Rhetorical Vocab Elements Of Style Vocab Introduction To English Major Complete Advanced Sentences Literature Homonyms More...	Math Algebra Formulas Basic Arithmetic: Measurements Metric Conversions Geometric Properties Important Math Facts Number Sense Vocab Business Math More...	Other Major Subjects Science Economics History Law Performing-arts Cooking Logic & Reasoning Trivia

Test your basic knowledge |

GMAT Number Properties

Sorry!:) No result found.

Can you answer 50 questions in 15 minutes?

Let me suggest you:

Browse all subjects

Browse all tests

Most popular tests

Major Subjects

Tests & Exams

Certifications

IT Skills

Business Skills

Soft Skills

Vocabulary

Languages

Engineering

Health Sciences

English

Math

Other Major Subjects

Browse all subjects

Browse all tests

Most popular tests