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 2 cannot be one of the primes in the sum - the sum must be _____.
[(last - first) / increment] + 1
Either a multiple of N or a non-multiple of N
If 2 cannot be one of the primes in the sum - the sum must be even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

2. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
The middle number
PERFECT CUBES
61 -67

3. Prime Numbers:1x
11 -13 -17 -19
A MULTIPLE
2.5
23 -29

4. Prime Numbers:8x
ODD
83 -89
97
61 -67

5. Any integer with an ODD number of total factors must be _______.
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 PERFECT SQUARE
FACTOR
NEVER CONTRADICT ONE ANOTHER

6. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
14
A non-multiple of N.
Put the coefficient under the radical to get a better approximation
1. The smallest or largest element 2. The increment 3. The number of items in the set

7. Let N be an integer. If you add two non-multiples of N - the result could be _______.
2.5
Either a multiple of N or a non-multiple of N
1.7
A non-multiple of N.

8. 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
97
41 -43 -47
NEVER CONTRADICT ONE ANOTHER
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

9. The average of an EVEN number of consecutive integers will ________ be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of an EVEN number of consecutive integers will NEVER be an integer.
The PRODUCT of n consecutive integers is divisible by n!.

10. Positive integers with more than two factors are ____.
Never prime
31 -37
A PERFECT SQUARE
The same sign as the base

11. v256=
83 -89
Prime factorization
23 -29
16

12. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
16
1.4

13. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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
41 -43 -47
97

14. The sum of any two primes will be ____ - unless ______.
Put the coefficient under the radical to get a better approximation
15
The middle number
The sum of any two primes will be even - unless one of the two primes is 2.

15. Prime Numbers:6x
11 -13 -17 -19
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.
61 -67
1. The smallest or largest element 2. The increment 3. The number of items in the set

16. The two statements in a data sufficiency problem will _______________.
11 -13 -17 -19
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
13
NEVER CONTRADICT ONE ANOTHER

17. If estimating a root with a coefficient - _____ .
N is a divisor of x+y
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
Put the coefficient under the radical to get a better approximation

18. The formula for finding the number of consecutive multiples in a set is _______.
15
[(last - first) / increment] + 1
Either a multiple of N or a non-multiple of N
2.5

19. 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.
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.
The PRODUCT of n consecutive integers is divisible by n!.
11 -13 -17 -19

20. Prime Numbers:2x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29
The PRODUCT of n consecutive integers is divisible by n!.
Never prime

21. In an evenly spaced set - the sum of the terms is equal to ____.
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
1.7
The average of the set times the number of elements in the set
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.

22. Prime Numbers:4x
61 -67
11 -13 -17 -19
PERFECT CUBES
41 -43 -47

23. Prime factors of _____ must come in pairs of three.
11 -13 -17 -19
ONLY the nonnegative root of the numberUNLIKE
Prime
PERFECT CUBES

24. In an evenly spaced set - the ____ and the ____ are equal.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the average and the median are equal.

25. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
61 -67
Prime factorization
1. The smallest or largest element 2. The increment 3. The number of items in the set
23 -29

26. v5˜
The middle number
2.5
The average of the set times the number of elements in the set
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.

27. All perfect squares have a(n) _________ number of total factors.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
Prime factorization
2.5

28. How to find the sum of consecutive integers:
If 2 cannot be one of the primes in the sum - the sum must be 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.
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.
In an evenly spaced set - the average and the median are equal.

29. The average of an ODD number of consecutive integers will ________ be an integer.
A MULTIPLE
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 ODD number of consecutive integers will ALWAYS be an integer.
61 -67

30. ³v216 =
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.
ODD
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

31. Prime Numbers:7x
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.
71 -73 -79
41 -43 -47

32. Prime Numbers:9x
97
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.
2 -3 -5 -7
A PERFECT SQUARE

33. 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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

34. 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?
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.
N is a divisor of x+y
NEVER CONTRADICT ONE ANOTHER

35. Prime Numbers:0x
The middle number
[(last - first) / increment] + 1
2 -3 -5 -7
83 -89

36. In an evenly spaced set - the average can be found by finding ________.
The middle number
16
In an evenly spaced set - the average and the median are equal.
3·3n = 3^{n+1}

37. 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
The sum of any two primes will be even - unless one of the two primes is 2.
Prime factorization
61 -67

38. v169=
The average of an EVEN number of consecutive integers will NEVER be an integer.
The same sign as the base
13
In an evenly spaced set - the average and the median are equal.

39. If N is a divisor of x and y - then _______.
71 -73 -79
N is a divisor of x+y
If 2 cannot be one of the primes in the sum - the sum must be even.
Put the coefficient under the radical to get a better approximation

40. Prime Numbers:3x
31 -37
A PERFECT SQUARE
[(last - first) / increment] + 1
Never prime

41. v2˜
1.4
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.

42. v196=
The sum of any two primes will be even - unless one of the two primes is 2.
14
Prime factorization
31 -37

43. Positive integers with only two factors must be ___.
[(last - first) / increment] + 1
Prime
3·3n = 3^{n+1}
23 -29

44. For ODD ROOTS - the root has ______.
The same sign as the base
Never prime
53 -59
FACTOR

45. Any integer with an EVEN number of total factors cannot be ______.
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.
25
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

46. The PRODUCT of n consecutive integers is divisible by ____.
The average of an EVEN number of consecutive integers will NEVER be an integer.
N is a divisor of x+y
The PRODUCT of n consecutive integers is divisible by n!.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

47. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
15
The same sign as the base
ONLY the nonnegative root of the numberUNLIKE
The sum of any two primes will be even - unless one of the two primes is 2.

48. In an evenly spaced set - the mean and median are equal to the _____ of _________.
ODD
The average of an EVEN number of consecutive integers will NEVER be an integer.
71 -73 -79
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

49. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
3·3n = 3^{n+1}
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
N is a divisor of x+y
FACTOR

50. v225=
A non-multiple of N.
1.7
ODD
15