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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. If estimating a root with a coefficient - _____ .
11 -13 -17 -19
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Put the coefficient under the radical to get a better approximation
The middle number

2. Prime Numbers:3x
If 2 cannot be one of the primes in the sum - the sum must be even.
A MULTIPLE
31 -37
41 -43 -47

3. N! is _____ of all integers from 1 to N.
A MULTIPLE
NEVER CONTRADICT ONE ANOTHER
61 -67
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

4. Prime factors of _____ must come in pairs of three.
97
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
1. The smallest or largest element 2. The increment 3. The number of items in the set

5. The sum of any two primes will be ____ - unless ______.
Put the coefficient under the radical to get a better approximation
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 any two primes will be even - unless one of the two primes is 2.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

6. 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
EVEN
FACTOR

7. 3n + 3n + 3n = _____ = ______
The PRODUCT of n consecutive integers is divisible by n!.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A MULTIPLE
3·3n = 3^{n+1}

8. For ODD ROOTS - the root has ______.
41 -43 -47
The same sign as the base
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19

9. v256=
In an evenly spaced set - the average and the median are equal.
16
The average of the set times the number of elements in the set
The PRODUCT of n consecutive integers is divisible by n!.

10. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The PRODUCT of n consecutive integers is divisible by 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.
A non-multiple of N.

11. The formula for finding the number of consecutive multiples in a set is _______.
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.
[(last - first) / increment] + 1
Either a multiple of N or a non-multiple of N

12. Prime Numbers:1x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A MULTIPLE
Prime factorization
11 -13 -17 -19

13. 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
16
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
Either a multiple of N or a non-multiple of N

14. v5˜
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.
3·3n = 3^{n+1}
2.5

15. In an evenly spaced set - the sum of the terms is equal to ____.
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 average of an EVEN number of consecutive integers will NEVER be an integer.
The average of the set times the number of elements in the set
N is a divisor of x+y

16. v169=
11 -13 -17 -19
13
Put the coefficient under the radical to get a better approximation
61 -67

17. Positive integers with more than two factors are ____.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
Never prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

18. v225=
61 -67
The same sign as the base
Prime
15

19. The two statements in a data sufficiency problem will _______________.
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 factorization
25
NEVER CONTRADICT ONE ANOTHER

20. 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.
Either a multiple of N or a non-multiple of N
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

21. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
If 2 cannot be one of the primes in the sum - the sum must be even.
The same sign as the base
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Put the coefficient under the radical to get a better approximation

22. In an evenly spaced set - the ____ and the ____ are equal.
41 -43 -47
23 -29
The same sign as the base
In an evenly spaced set - the average and the median are equal.

23. The PRODUCT of n consecutive integers is divisible by ____.
NEVER CONTRADICT ONE ANOTHER
If 2 cannot be one of the primes in the sum - the sum must be even.
The PRODUCT of n consecutive integers is divisible by n!.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

24. If 2 cannot be one of the primes in the sum - the sum must be _____.
25
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.

25. The prime factorization of __________ contains only EVEN powers of primes.
Never prime
53 -59
A non-multiple of N.
A PERFECT SQUARE

26. The average of an ODD number of consecutive integers will ________ be an integer.
The average of the set times the number of elements in the set
61 -67
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

27. Positive integers with only two factors must be ___.
2.5
Prime factorization
Prime
53 -59

28. Prime Numbers:9x
97
A non-multiple of N.
N is a divisor of x+y
61 -67

29. Prime Numbers:5x
The average of an EVEN number of consecutive integers will NEVER be an integer.
53 -59
ONLY the nonnegative root of the numberUNLIKE
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.

30. 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.
25
15
11 -13 -17 -19

31. v625=
61 -67
25
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
97

32. v2˜
1.7
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.4
N is a divisor of x+y

33. All perfect squares have a(n) _________ number of total factors.
Prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A non-multiple of N.
ODD

34. v3˜
71 -73 -79
1.7
The sum of any two primes will be even - unless one of the two primes is 2.
1. The smallest or largest element 2. The increment 3. The number of items in the set

35. If the problem states/assumes that a number is an integer - check to see if you can use _______.
23 -29
A PERFECT SQUARE
16
Prime factorization

36. Any integer with an EVEN number of total factors cannot be ______.
14
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.
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation

37. The prime factorization of a perfect square contains only ______ powers of primes.
Put the coefficient under the radical to get a better approximation
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN
53 -59

38. Prime Numbers:7x
[(last - first) / increment] + 1
71 -73 -79
EVEN
NEVER CONTRADICT ONE ANOTHER

39. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
The same sign as the base

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

41. Prime Numbers:2x
Never prime
ONLY the nonnegative root of the numberUNLIKE
EVEN
23 -29

42. If N is a divisor of x and y - then _______.
A PERFECT SQUARE
A PERFECT SQUARE
97
N is a divisor of x+y

43. Let N be an integer. If you add two non-multiples of N - the result could be _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
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.

44. In an evenly spaced set - the average can be found by finding ________.
25
Put the coefficient under the radical to get a better approximation
The sum of any two primes will be even - unless one of the two primes is 2.
The middle number

45. Prime Numbers:0x
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.
97
2 -3 -5 -7
11 -13 -17 -19

46. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The same sign as the base
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
A PERFECT SQUARE

47. v196=
14
31 -37
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.

48. Prime Numbers:6x
97
1. The smallest or largest element 2. The increment 3. The number of items in the set
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

49. ³v216 =
14
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Never prime
3·3n = 3^{n+1}

50. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The middle number
Never prime
13
ONLY the nonnegative root of the numberUNLIKE