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. v625=
53 -59
1.4
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
25

2. The two statements in a data sufficiency problem will _______________.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7
13

3. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
A MULTIPLE
[(last - first) / increment] + 1
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

4. The average of an EVEN number of consecutive integers will ________ be an integer.
The middle number
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.
ONLY the nonnegative root of the numberUNLIKE

5. 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.
Never prime
If 2 cannot be one of the primes in the sum - the sum must be even.
2.5

6. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
ONLY the nonnegative root of the numberUNLIKE
PERFECT CUBES
15

7. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
97
The same sign as the base

8. v169=
ODD
3·3n = 3^{n+1}
13
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

9. v5˜
Prime
83 -89
2 -3 -5 -7
2.5

10. N! is _____ of all integers from 1 to N.
25
14
A MULTIPLE
Never prime

11. In an evenly spaced set - the sum of the terms is equal to ____.
Prime factorization
The average of the set times the number of elements in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Put the coefficient under the radical to get a better approximation

12. Positive integers with more than two factors are ____.
The PRODUCT of n consecutive integers is divisible by n!.
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.
Never prime

13. v2˜
Prime factorization
16
1.4
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. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
15
Prime
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.7

15. 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
14
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.
A PERFECT SQUARE

16. 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.
14
13
EVEN

17. 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 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
Prime factorization
25
11 -13 -17 -19

18. Prime Numbers:0x
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.
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.

19. v256=
A PERFECT SQUARE
FACTOR
16
Never prime

20. In an evenly spaced set - the ____ and the ____ are equal.
2 -3 -5 -7
The same sign as the base
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

21. How to find the sum of consecutive integers:
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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 middle number
The same sign as the base

22. Prime factors of _____ must come in pairs of three.
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
PERFECT CUBES
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

23. Let N be an integer. If you add two non-multiples of N - the result could be _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
Either a multiple of N or a non-multiple of N
83 -89
1. The smallest or largest element 2. The increment 3. The number of items in the set

24. The prime factorization of a perfect square contains only ______ powers of primes.
In an evenly spaced set - the average and the median are equal.
2.5
EVEN
Prime

25. Positive integers with only two factors must be ___.
If 2 cannot be one of the primes in the sum - the sum must be even.
PERFECT CUBES
71 -73 -79
Prime

26. All perfect squares have a(n) _________ number of total factors.
61 -67
ODD
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

27. For ODD ROOTS - the root has ______.
A PERFECT SQUARE
11 -13 -17 -19
In an evenly spaced set - the average and the median are equal.
The same sign as the base

28. Any integer with an EVEN number of total factors cannot be ______.
N is a divisor of x+y
53 -59
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.

29. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
PERFECT CUBES
The sum of any two primes will be even - unless one of the two primes is 2.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

30. Prime Numbers:6x
16
61 -67
The middle number
53 -59

31. 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

32. The prime factorization of __________ contains only EVEN powers of primes.
25
A PERFECT SQUARE
ODD
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

33. Prime Numbers:5x
53 -59
The same sign as the base
The middle number
A PERFECT SQUARE

34. If estimating a root with a coefficient - _____ .
EVEN
FACTOR
ONLY the nonnegative root of the numberUNLIKE
Put the coefficient under the radical to get a better approximation

35. The sum of any two primes will be ____ - unless ______.
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
41 -43 -47
The sum of any two primes will be even - unless one of the two primes is 2.

36. Prime Numbers:9x
11 -13 -17 -19
31 -37
97
13

37. If the problem states/assumes that a number is an integer - check to see if you can use _______.
14
83 -89
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime factorization

38. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
53 -59
EVEN
Prime

39. v3˜
1.7
N is a divisor of x+y
61 -67
The sum of any two primes will be even - unless one of the two primes is 2.

40. 3n + 3n + 3n = _____ = ______
15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
3·3n = 3^{n+1}
83 -89

41. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
53 -59
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set

42. Prime Numbers:2x
23 -29
The average of the set times the number of elements in the set
3·3n = 3^{n+1}
15

43. If N is a divisor of x and y - then _______.
A PERFECT SQUARE
The average of an EVEN number of consecutive integers will NEVER be an integer.
ODD
N is a divisor of x+y

44. ³v216 =
PERFECT CUBES
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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

45. In an evenly spaced set - the average can be found by finding ________.
The middle number
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
ONLY the nonnegative root of the numberUNLIKE

46. The average of an ODD number of consecutive integers will ________ 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.
14
13
The average of an ODD number of consecutive integers will ALWAYS be an integer.

47. Prime Numbers:8x
A PERFECT SQUARE
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.
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

48. v225=
15
14
Prime
The sum of any two primes will be even - unless one of the two primes is 2.

49. Prime Numbers:3x
A MULTIPLE
97
31 -37
EVEN

50. Prime Numbers:7x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
71 -73 -79
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6