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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. Positive integers with more than two factors are ____.
Never prime
1.4
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of an EVEN number of consecutive integers will NEVER be an integer.

2. If N is a divisor of x and y - then _______.
2.5
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS be an integer.
15

3. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
14
The PRODUCT of n consecutive integers is divisible by n!.

4. Prime Numbers:0x
2.5
If 2 cannot be one of the primes in the sum - the sum must be even.
2 -3 -5 -7
15

5. 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.
97
Prime
Either a multiple of N or a non-multiple of N

6. Prime Numbers:4x
A PERFECT SQUARE
16
41 -43 -47
A non-multiple of N.

7. v5˜
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
1.7
2.5

8. Any integer with an EVEN number of total factors cannot be ______.
FACTOR
1.4
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

9. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
FACTOR
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
83 -89

10. 3n + 3n + 3n = _____ = ______
Never prime
3·3n = 3^{n+1}
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.
Prime

11. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
Prime factorization
13
23 -29

12. Prime Numbers:1x
11 -13 -17 -19
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

13. v256=
1.7
A MULTIPLE
53 -59
16

14. The average of an ODD number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

15. Prime Numbers:6x
61 -67
97
The sum of any two primes will be even - unless one of the two primes is 2.
41 -43 -47

16. Prime Numbers:5x
Prime
Put the coefficient under the radical to get a better approximation
53 -59
FACTOR

17. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
97
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
In an evenly spaced set - the average and the median are equal.

18. For ODD ROOTS - the root has ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Either a multiple of N or a non-multiple of N
The same sign as the base
53 -59

19. v2˜
31 -37
Prime
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.
1.4

20. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
[(last - first) / increment] + 1
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.4
FACTOR

21. If 2 cannot be one of the primes in the sum - the sum must be _____.
2.5
The middle number
If 2 cannot be one of the primes in the sum - the sum must be even.
A non-multiple of N.

22. The two statements in a data sufficiency problem will _______________.
31 -37
15
[(last - first) / increment] + 1
NEVER CONTRADICT ONE ANOTHER

23. In an evenly spaced set - the average can be found by finding ________.
The middle number
53 -59
Prime factorization
Never prime

24. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ONLY the nonnegative root of the numberUNLIKE
The same sign as the base

25. v169=
13
A non-multiple of N.
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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

26. The sum of any two primes will be ____ - unless ______.
Prime factorization
The average of the set times the number of elements in the set
The sum of any two primes will be even - unless one of the two primes is 2.
[(last - first) / increment] + 1

27. The prime factorization of a perfect square contains only ______ powers of primes.
25
EVEN
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.

28. v625=
NEVER CONTRADICT ONE ANOTHER
The sum of any two primes will be even - unless one of the two primes is 2.
25
In an evenly spaced set - the average and the median are equal.

29. Positive integers with only two factors must be ___.
The PRODUCT of n consecutive integers is divisible by n!.
1.4
13
Prime

30. ³v216 =
61 -67
[(last - first) / increment] + 1
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The same sign as the base

31. The formula for finding the number of consecutive multiples in a set is _______.
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The same sign as the base
[(last - first) / increment] + 1

32. 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
Prime
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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

33. N! is _____ of all integers from 1 to N.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ONLY the nonnegative root of the numberUNLIKE
A MULTIPLE
The same sign as the base

34. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
3·3n = 3^{n+1}
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.

35. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The average of the set times the number of elements in the set
Prime factorization
16
ONLY the nonnegative root of the numberUNLIKE

36. In an evenly spaced set - the sum of the terms is equal to ____.
N is a divisor of x+y
The same sign as the base
The average of the set times the number of elements in the set
14

37. 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.
Prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

38. Let N be an integer. If you add two non-multiples of N - the result could 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.
The same sign as the base
Either a multiple of N or a non-multiple of N
ODD

39. Prime Numbers:9x
97
2 -3 -5 -7
The same sign as the base
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.

40. v225=
PERFECT CUBES
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
15
A non-multiple of N.

41. 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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
25
In an evenly spaced set - the average and the median are equal.

42. Prime Numbers:2x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
23 -29
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
NEVER CONTRADICT ONE ANOTHER

43. Prime Numbers:7x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1. The smallest or largest element 2. The increment 3. The number of items in the set
71 -73 -79
Prime

44. 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 same sign as the base
PERFECT CUBES
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
97

45. How to find the sum of consecutive integers:
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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.
Put the coefficient under the radical to get a better approximation

46. Prime Numbers:8x
1.7
83 -89
EVEN
25

47. All perfect squares have a(n) _________ number of total factors.
Prime
53 -59
ODD
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

48. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE
41 -43 -47
1. The smallest or largest element 2. The increment 3. The number of items in the set

49. 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

50. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime factorization
Prime