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. Prime Numbers:2x
3·3n = 3^{n+1}
PERFECT CUBES
23 -29
71 -73 -79

2. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The sum of any two primes will be even - unless one of the two primes is 2.
ONLY the nonnegative root of the numberUNLIKE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

3. Prime Numbers:6x
The average of an EVEN number of consecutive integers will NEVER be an integer.
61 -67
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set

4. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
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.
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.
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
FACTOR

5. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Prime
31 -37

6. v256=
The PRODUCT of n consecutive integers is divisible by n!.
The middle number
53 -59
16

7. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
25
Either a multiple of N or a non-multiple of N
53 -59

8. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
If 2 cannot be one of the primes in the sum - the sum must be even.
The sum of any two primes will be even - unless one of the two primes is 2.
1.4
1. The smallest or largest element 2. The increment 3. The number of items in the set

9. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.4
A PERFECT SQUARE

10. 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

11. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
If 2 cannot be one of the primes in the sum - the sum must be even.

12. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
Either a multiple of N or a non-multiple of N
FACTOR
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

13. Prime Numbers:3x
31 -37
The same sign as the base
The sum of any two primes will be even - unless one of the two primes is 2.
1.7

14. Prime Numbers:4x
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
83 -89
41 -43 -47

15. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
25
15
N is a divisor of x+y

16. v5˜
14
PERFECT CUBES
15
2.5

17. For ODD ROOTS - the root has ______.
A non-multiple of N.
The same sign as the base
1.7
23 -29

18. All perfect squares have a(n) _________ number of total factors.
The same sign as the base
ODD
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}

19. If 2 cannot be one of the primes in the sum - the sum must be _____.
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.
The average of the set times the number of elements in the set
A PERFECT SQUARE

20. 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.
If 2 cannot be one of the primes in the sum - the sum must be even.
3·3n = 3^{n+1}
61 -67

21. v2˜
If 2 cannot be one of the primes in the sum - the sum must be even.
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
1.4
A non-multiple of N.

22. The average of an ODD number of consecutive integers will ________ be an integer.
N is a divisor of x+y
14
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The average of an ODD number of consecutive integers will ALWAYS be an integer.

23. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Prime factorization
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.4
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

24. If N is a divisor of x and y - then _______.
31 -37
NEVER CONTRADICT ONE ANOTHER
N is a divisor of x+y
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

25. v196=
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.
3·3n = 3^{n+1}
14
15

26. Any integer with an EVEN number of total factors cannot be ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
71 -73 -79
A PERFECT SQUARE

27. If the problem states/assumes that a number is an integer - check to see if you can use _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set

28. ³v216 =
97
The average of an EVEN number of consecutive integers will NEVER be an integer.
[(last - first) / increment] + 1
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

29. Positive integers with more than two factors are ____.
Prime
EVEN
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime

30. Prime Numbers:7x
PERFECT CUBES
71 -73 -79
Put the coefficient under the radical to get a better approximation
1.7

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

32. In an evenly spaced set - the sum of the terms is equal to ____.
A non-multiple of N.
Never prime
2 -3 -5 -7
The average of the set times the number of elements in the set

33. Prime Numbers:1x
97
3·3n = 3^{n+1}
11 -13 -17 -19
1. The smallest or largest element 2. The increment 3. The number of items in the set

34. If estimating a root with a coefficient - _____ .
[(last - first) / increment] + 1
14
1.7
Put the coefficient under the radical to get a better approximation

35. Prime Numbers:0x
3·3n = 3^{n+1}
2 -3 -5 -7
Prime
53 -59

36. v625=
25
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.
NEVER CONTRADICT ONE ANOTHER

37. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
16
14
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

38. Prime Numbers:8x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER
83 -89
PERFECT CUBES

39. Prime Numbers:9x
The average of an EVEN number of consecutive integers will NEVER be an integer.
1.4
97
1.7

40. The prime factorization of __________ contains only EVEN powers of primes.
11 -13 -17 -19
A PERFECT SQUARE
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

41. Positive integers with only two factors must be ___.
Prime
14
16
Prime factorization

42. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A MULTIPLE
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 non-multiple of N.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

43. v225=
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.
15
The PRODUCT of n consecutive integers is divisible by n!.
The sum of any two primes will be even - unless one of the two primes is 2.

44. The formula for finding the number of consecutive multiples in a set is _______.
PERFECT CUBES
N is a divisor of x+y
1.7
[(last - first) / increment] + 1

45. N! is _____ of all integers from 1 to N.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13
A MULTIPLE
[(last - first) / increment] + 1

46. Prime factors of _____ must come in pairs of three.
A MULTIPLE
N is a divisor of x+y
[(last - first) / increment] + 1
PERFECT CUBES

47. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER
EVEN
61 -67

48. In an evenly spaced set - the average can be found by finding ________.
13
[(last - first) / increment] + 1
Never prime
The middle number

49. 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.
[(last - first) / increment] + 1
NEVER CONTRADICT ONE ANOTHER
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

50. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
23 -29
Either a multiple of N or a non-multiple of N
The average of the set times the number of elements in the set