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. If N is a divisor of x and y - then _______.
The middle number
N is a divisor of x+y
The sum of any two primes will be even - unless one of the two primes is 2.
The same sign as the base

2. The average of an ODD number of consecutive integers will ________ be an integer.
Prime factorization
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.4

3. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
ODD
A non-multiple of N.
83 -89
71 -73 -79

4. Prime Numbers:4x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
41 -43 -47
FACTOR
1.4

5. Prime Numbers:8x
41 -43 -47
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
83 -89

6. The sum of any two primes will be ____ - unless ______.
NEVER CONTRADICT ONE ANOTHER
The middle number
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.

7. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
Put the coefficient under the radical to get a better approximation
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime factorization

8. Positive integers with more than two factors are ____.
The sum of any two primes will be even - unless one of the two primes is 2.
Prime factorization
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Never prime

9. The prime factorization of a perfect square contains only ______ powers of primes.
Prime
14
EVEN
Either a multiple of N or a non-multiple of N

10. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
A MULTIPLE
15
The middle number
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

11. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
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.
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

12. In an evenly spaced set - the average can be found by finding ________.
The middle number
Prime
The sum of any two primes will be even - unless one of the two primes is 2.
11 -13 -17 -19

13. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime
In an evenly spaced set - the average and the median are equal.

14. v3˜
The same sign as the base
NEVER CONTRADICT ONE ANOTHER
A MULTIPLE
1.7

15. All perfect squares have a(n) _________ number of total factors.
ODD
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
16
83 -89

16. If estimating a root with a coefficient - _____ .
Prime factorization
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.
3·3n = 3^{n+1}
Put the coefficient under the radical to get a better approximation

17. 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?
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.
83 -89
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation

18. For ODD ROOTS - the root has ______.
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
Prime
The same sign as the base

19. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
71 -73 -79
14
ONLY the nonnegative root of the numberUNLIKE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

20. N! is _____ of all integers from 1 to N.
23 -29
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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.
A MULTIPLE

21. v5˜
13
97
The average of the set times the number of elements in the set
2.5

22. Prime Numbers:2x
The middle number
23 -29
In an evenly spaced set - the average and the median are equal.
61 -67

23. v2˜
The middle number
PERFECT CUBES
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.
1.4

24. Prime Numbers:5x
1.7
53 -59
EVEN
PERFECT CUBES

25. v256=
The middle number
16
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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

26. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Either a multiple of N or a non-multiple of N
EVEN
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.7

27. Prime Numbers:9x
97
N is a divisor of x+y
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

28. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25
A PERFECT SQUARE
The middle number

29. 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
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
EVEN
83 -89

30. Positive integers with only two factors must be ___.
Prime
83 -89
ODD
61 -67

31. Prime Numbers:3x
41 -43 -47
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
31 -37

32. ³v216 =
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
25
Either a multiple of N or a non-multiple of N

33. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Either a multiple of N or a non-multiple of N
The same sign as the base

34. Prime Numbers:7x
1. The smallest or largest element 2. The increment 3. The number of items in the set
23 -29
71 -73 -79
A PERFECT SQUARE

35. v225=
3·3n = 3^{n+1}
2 -3 -5 -7
15
Prime factorization

36. The two statements in a data sufficiency problem will _______________.
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.
N is a divisor of x+y
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.

37. v196=
14
A non-multiple of N.
ONLY the nonnegative root of the numberUNLIKE
The PRODUCT of n consecutive integers is divisible by n!.

38. The PRODUCT of n consecutive integers is divisible by ____.
3·3n = 3^{n+1}
31 -37
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.

39. The average of an EVEN number of consecutive integers will ________ be an integer.
2 -3 -5 -7
Prime factorization
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
The average of an EVEN number of consecutive integers will NEVER be an integer.

40. How to find the sum of consecutive integers:
In an evenly spaced set - the average and the median are equal.
ONLY the nonnegative root of the numberUNLIKE
The average of an EVEN number of consecutive integers will NEVER 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.

41. Any integer with an ODD number of total factors must be _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
EVEN
A PERFECT SQUARE

42. Prime Numbers:1x
FACTOR
11 -13 -17 -19
N is a divisor of x+y
The average of an EVEN number of consecutive integers will NEVER be an integer.

43. Prime Numbers:6x
Either a multiple of N or a non-multiple of N
1.4
61 -67
A MULTIPLE

44. In an evenly spaced set - the ____ and the ____ are equal.
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the average and the median are equal.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.4

45. Prime Numbers:0x
1.4
53 -59
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

46. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
Prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A non-multiple of N.

47. Prime factors of _____ must come in pairs of three.
EVEN
A MULTIPLE
The average of the set times the number of elements in the set
PERFECT CUBES

48. How to solve: If k - m - and t are positive integers and k/6 + m/4 = t/12 - do t and 12 have a common factor greater than 1? 1. k is a multiple of 3 2. m is a multiple of 3

49. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
31 -37
1.4
The PRODUCT of n consecutive integers is divisible by n!.

50. Any integer with an EVEN number of total factors cannot be ______.
61 -67
A PERFECT SQUARE
1.7
16