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 sum of any two primes will be ____ - unless ______.
The middle number
3·3n = 3^{n+1}
The sum of any two primes will be even - unless one of the two primes is 2.
[(last - first) / increment] + 1

2. v225=
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER
15
Put the coefficient under the radical to get a better approximation

3. The PRODUCT of n consecutive integers is divisible by ____.
31 -37
23 -29
The PRODUCT of n consecutive integers is divisible by n!.
Prime

4. The formula for finding the number of consecutive multiples in a set is _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
25

5. If 2 cannot be one of the primes in the sum - the sum must be _____.
ODD
97
23 -29
If 2 cannot be one of the primes in the sum - the sum must be even.

6. If N is a divisor of x and y - then _______.
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
N is a divisor of x+y
[(last - first) / increment] + 1

7. v169=
13
25
15
The average of the set times the number of elements in the set

8. All perfect squares have a(n) _________ number of total factors.
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.
ODD
Prime factorization
53 -59

9. The prime factorization of a perfect square contains only ______ powers of primes.
31 -37
EVEN
[(last - first) / increment] + 1
The same sign as the base

10. Any integer with an EVEN number of total factors cannot be ______.
Never prime
A PERFECT SQUARE
Prime
Prime factorization

11. v625=
In an evenly spaced set - the average and the median are equal.
The PRODUCT of n consecutive integers is divisible by n!.
Never prime
25

12. 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

13. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE
41 -43 -47
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.

14. Positive integers with only two factors must be ___.
Prime
1.4
The middle number
25

15. Prime Numbers:5x
1.7
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
53 -59

16. Prime Numbers:2x
If 2 cannot be one of the primes in the sum - the sum must be even.
1. The smallest or largest element 2. The increment 3. The number of items in the set
71 -73 -79
23 -29

17. v5˜
2.5
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of the set times the number of elements in the set

18. The prime factorization of __________ contains only EVEN powers of primes.
ONLY the nonnegative root of the numberUNLIKE
The average of the set times the number of elements in the set
97
A PERFECT SQUARE

19. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The PRODUCT of n consecutive integers is divisible by n!.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of the set times the number of elements in the set
The average of an ODD number of consecutive integers will ALWAYS be an integer.

20. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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.
[(last - first) / increment] + 1
13

21. The average of an ODD number of consecutive integers will ________ be an integer.
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.
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.

22. In an evenly spaced set - the ____ and the ____ are equal.
NEVER CONTRADICT ONE ANOTHER
In an evenly spaced set - the average and the median are equal.
Never prime
83 -89

23. Prime Numbers:9x
53 -59
97
A PERFECT SQUARE
FACTOR

24. Prime Numbers:1x
41 -43 -47
1.4
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

25. Prime Numbers:7x
71 -73 -79
FACTOR
3·3n = 3^{n+1}
N is a divisor of x+y

26. v256=
83 -89
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.
EVEN
16

27. Positive integers with more than two factors are ____.
Never prime
15
61 -67
ODD

28. Let N be an integer. If you add two non-multiples of N - the result could be _______.
23 -29
Either a multiple of N or a non-multiple of N
The middle number
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

29. In an evenly spaced set - the sum of the terms is equal to ____.
97
15
The average of the set times the number of elements in the set
N is a divisor of x+y

30. 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.
11 -13 -17 -19
FACTOR
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

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

32. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The middle number
EVEN
A non-multiple of N.
ODD

33. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
15
EVEN
N is a divisor of x+y

34. The average of an EVEN number of consecutive integers will ________ be an integer.
14
The average of an EVEN number of consecutive integers will NEVER be an integer.
83 -89
Put the coefficient under the radical to get a better approximation

35. 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.
The PRODUCT of n consecutive integers is divisible by n!.
Prime factorization
A MULTIPLE

36. Prime Numbers:0x
Either a multiple of N or a non-multiple of N
1.4
The middle number
2 -3 -5 -7

37. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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.
13

38. 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.
97
N is a divisor of x+y
13

39. v3˜
1.7
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
14

40. 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?
71 -73 -79
11 -13 -17 -19
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.
ONLY the nonnegative root of the numberUNLIKE

41. Prime Numbers:8x
The average of an EVEN number of consecutive integers will NEVER be an integer.
ODD
31 -37
83 -89

42. v2˜
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime
1.4
2 -3 -5 -7

43. Prime Numbers:4x
1.7
1. The smallest or largest element 2. The increment 3. The number of items in the set
41 -43 -47
31 -37

44. Prime Numbers:6x
83 -89
16
1.7
61 -67

45. In an evenly spaced set - the average can be found by finding ________.
1.7
The middle number
EVEN
16

46. ³v216 =
The same sign as the base
97
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
In an evenly spaced set - the average and the median are equal.

47. 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
25
The average of an EVEN number of consecutive integers will NEVER be an integer.
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
31 -37

48. v196=
11 -13 -17 -19
14
61 -67
2.5

49. Prime Numbers:3x
3·3n = 3^{n+1}
Never prime
A non-multiple of N.
31 -37

50. N! is _____ of all integers from 1 to N.
1. The smallest or largest element 2. The increment 3. The number of items in the set
A MULTIPLE
FACTOR
Prime