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 prime factorization of __________ contains only EVEN powers of primes.
1.4
The sum of any two primes will be even - unless one of the two primes is 2.
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

2. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
[(last - first) / increment] + 1
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.4

3. 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
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2.5
2 -3 -5 -7

4. The average of an EVEN number of consecutive integers will ________ be an integer.
[(last - first) / increment] + 1
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7
The average of an EVEN number of consecutive integers will NEVER be an integer.

5. 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
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
14

6. Prime Numbers:1x
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 any two primes will be even - unless one of the two primes is 2.
1.4
11 -13 -17 -19

7. Positive integers with more than two factors are ____.
The middle number
Either a multiple of N or a non-multiple of N
Never prime
1.7

8. v5˜
A PERFECT SQUARE
2.5
ODD
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

9. Prime Numbers:6x
53 -59
In an evenly spaced set - the average and the median are equal.
PERFECT CUBES
61 -67

10. 3n + 3n + 3n = _____ = ______
15
NEVER CONTRADICT ONE ANOTHER
3·3n = 3^{n+1}
The PRODUCT of n consecutive integers is divisible by n!.

11. Any integer with an EVEN number of total factors cannot be ______.
15
2.5
A PERFECT SQUARE
The same sign as the base

12. The two statements in a data sufficiency problem will _______________.
11 -13 -17 -19
FACTOR
NEVER CONTRADICT ONE ANOTHER
The same sign as the base

13. How to find the sum of consecutive integers:
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
The same sign as the base
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. The formula for finding the number of consecutive multiples in a set is _______.
11 -13 -17 -19
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
[(last - first) / increment] + 1

15. Positive integers with only two factors must be ___.
11 -13 -17 -19
The PRODUCT of n consecutive integers is divisible by n!.
ONLY the nonnegative root of the numberUNLIKE
Prime

16. v225=
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ONLY the nonnegative root of the numberUNLIKE
15
41 -43 -47

17. Prime Numbers:0x
PERFECT CUBES
A PERFECT SQUARE
EVEN
2 -3 -5 -7

18. If N is a divisor of x and y - then _______.
N is a divisor of x+y
ONLY the nonnegative root of the numberUNLIKE
The sum of any two primes will be even - unless one of the two primes is 2.
EVEN

19. 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.
3·3n = 3^{n+1}
97
83 -89

20. Prime Numbers:9x
97
13
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.
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.

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

22. Prime Numbers:8x
PERFECT CUBES
83 -89
Put the coefficient under the radical to get a better approximation
11 -13 -17 -19

23. 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

24. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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 mean and median are equal to the average of the first and the last number.
3·3n = 3^{n+1}

25. v3˜
N is a divisor of x+y
1.7
1.4
EVEN

26. Prime Numbers:3x
2.5
23 -29
1.7
31 -37

27. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
In an evenly spaced set - the average and the median are equal.
The same sign as the base
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

28. Prime Numbers:5x
53 -59
16
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
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

29. In an evenly spaced set - the average can be found by finding ________.
11 -13 -17 -19
1.4
The middle number
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

30. Prime factors of _____ must come in pairs of three.
1.7
PERFECT CUBES
N is a divisor of x+y
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.

31. If estimating a root with a coefficient - _____ .
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set
Put the coefficient under the radical to get a better approximation
A non-multiple of N.

32. All perfect squares have a(n) _________ number of total factors.
ODD
14
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1.7

33. The prime factorization of a perfect square contains only ______ powers of primes.
14
97
EVEN
61 -67

34. Prime Numbers:2x
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

35. Any integer with an ODD number of total factors must be _______.
1.7
2.5
13
A PERFECT SQUARE

36. The average of an ODD number of consecutive integers will ________ be an integer.
41 -43 -47
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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

37. N! is _____ of all integers from 1 to N.
PERFECT CUBES
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
A MULTIPLE

38. 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.
31 -37
FACTOR
23 -29

39. Prime Numbers:7x
The same sign as the base
71 -73 -79
41 -43 -47
13

40. v169=
23 -29
13
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE

41. v196=
2 -3 -5 -7
14
ODD
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.

42. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
97
FACTOR
Never prime
83 -89

43. Let N be an integer. If you add two non-multiples of N - the result could be _______.
16
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.
97
Either a multiple of N or a non-multiple of N

44. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
1.4
ONLY the nonnegative root of the numberUNLIKE
1.7
A PERFECT SQUARE

45. In an evenly spaced set - the sum of the terms is equal to ____.
Never prime
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
A non-multiple of N.

46. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD
16

47. In an evenly spaced set - the ____ and the ____ are equal.
The sum of any two primes will be even - unless one of the two primes is 2.
97
N is a divisor of x+y
In an evenly spaced set - the average and the median are equal.

48. The sum of any two primes will be ____ - unless ______.
NEVER CONTRADICT ONE ANOTHER
The sum of any two primes will be even - unless one of the two primes is 2.
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set

49. v2˜
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.4
[(last - first) / increment] + 1
16

50. The PRODUCT of n consecutive integers is divisible by ____.
Put the coefficient under the radical to get a better approximation
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!.
1. The smallest or largest element 2. The increment 3. The number of items in the set