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. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
25
ONLY the nonnegative root of the numberUNLIKE
15
A PERFECT SQUARE

2. How to find the sum of consecutive integers:
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
Never prime
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.

3. Prime Numbers:0x
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
2 -3 -5 -7
61 -67

4. ³v216 =
Never prime
41 -43 -47
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
31 -37

5. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
97
A PERFECT SQUARE

6. The formula for finding the number of consecutive multiples in a set is _______.
25
[(last - first) / increment] + 1
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 MULTIPLE

7. v256=
16
The average of the set times the number of elements in the set
97
1.4

8. The two statements in a data sufficiency problem will _______________.
1.4
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
NEVER CONTRADICT ONE ANOTHER

9. Prime factors of _____ must come in pairs of three.
Either a multiple of N or a non-multiple of N
3·3n = 3^{n+1}
PERFECT CUBES
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

10. In an evenly spaced set - the sum of the terms is equal to ____.
71 -73 -79
Either a multiple of N or a non-multiple of N
Never prime
The average of the set times the number of elements in the set

11. 3n + 3n + 3n = _____ = ______
71 -73 -79
14
The middle number
3·3n = 3^{n+1}

12. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A non-multiple of N.
The sum of any two primes will be even - unless one of the two primes is 2.
1.7
31 -37

13. If N is a divisor of x and y - then _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
N is a divisor of x+y
NEVER CONTRADICT ONE ANOTHER
The average of an EVEN number of consecutive integers will NEVER be an integer.

14. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
[(last - first) / increment] + 1
1.4
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime factorization

15. 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

16. Any integer with an EVEN number of total factors cannot be ______.
61 -67
3·3n = 3^{n+1}
A PERFECT SQUARE
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.

17. All perfect squares have a(n) _________ number of total factors.
1.7
FACTOR
ODD
Prime

18. v196=
Put the coefficient under the radical to get a better approximation
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
11 -13 -17 -19
14

19. v625=
Put the coefficient under the radical to get a better approximation
53 -59
25
A non-multiple of N.

20. Prime Numbers:2x
NEVER CONTRADICT ONE ANOTHER
83 -89
PERFECT CUBES
23 -29

21. 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
The average of an ODD number of consecutive integers will ALWAYS 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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47

22. 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.
3·3n = 3^{n+1}
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.7

23. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
FACTOR
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.
Prime factorization

24. v2˜
14
The PRODUCT of n consecutive integers is divisible by n!.
1.4
In an evenly spaced set - the average and the median are equal.

25. 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.
97
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If 2 cannot be one of the primes in the sum - the sum must be even.

26. Prime Numbers:9x
53 -59
97
13
23 -29

27. If 2 cannot be one of the primes in the sum - the sum must be _____.
The middle number
23 -29
If 2 cannot be one of the primes in the sum - the sum must be even.
2 -3 -5 -7

28. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
14
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is 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
ODD

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

30. 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.
PERFECT CUBES
If 2 cannot be one of the primes in the sum - the sum must be even.
16

31. The prime factorization of __________ contains only EVEN powers of primes.
61 -67
The same sign as the base
The average of the set times the number of elements in the set
A PERFECT SQUARE

32. Prime Numbers:5x
61 -67
31 -37
53 -59
A PERFECT SQUARE

33. Prime Numbers:8x
83 -89
Either a multiple of N or a non-multiple of N
[(last - first) / increment] + 1
14

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

35. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
1. The smallest or largest element 2. The increment 3. The number of items in the set
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
A MULTIPLE

36. v5˜
[(last - first) / increment] + 1
11 -13 -17 -19
2.5
A non-multiple of N.

37. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Either a multiple of N or a non-multiple of N
16
Prime factorization
1.7

38. Prime Numbers:1x
1.7
25
11 -13 -17 -19
Prime

39. In an evenly spaced set - the ____ and the ____ are equal.
25
Never prime
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.
In an evenly spaced set - the average and the median are equal.

40. In an evenly spaced set - the average can be found by finding ________.
The sum of any two primes will be even - unless one of the two primes is 2.
N is a divisor of x+y
The average of an EVEN number of consecutive integers will NEVER be an integer.
The middle number

41. N! is _____ of all integers from 1 to N.
NEVER CONTRADICT ONE ANOTHER
PERFECT CUBES
The average of the set times the number of elements in the set
A MULTIPLE

42. v3˜
53 -59
ODD
EVEN
1.7

43. If estimating a root with a coefficient - _____ .
1.4
Put the coefficient under the radical to get a better approximation
13
EVEN

44. For ODD ROOTS - the root has ______.
The same sign as the base
The average of the set times the number of elements in the set
FACTOR
13

45. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
PERFECT CUBES
The same sign as the base

46. v169=
Prime
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
16
13

47. Prime Numbers:7x
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
Put the coefficient under the radical to get a better approximation
71 -73 -79
In an evenly spaced set - the average and the median are equal.

48. The prime factorization of a perfect square contains only ______ powers of primes.
The PRODUCT of n consecutive integers is divisible by n!.
1.4
EVEN
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

49. Positive integers with only two factors must be ___.
A non-multiple of N.
2 -3 -5 -7
3·3n = 3^{n+1}
Prime

50. The average of an EVEN number of consecutive integers will ________ be an integer.
Prime
The PRODUCT of n consecutive integers is divisible by n!.
61 -67
The average of an EVEN number of consecutive integers will NEVER be an integer.