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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. v2˜
ODD
[(last - first) / increment] + 1
1.4
13

2. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
PERFECT CUBES
N is a divisor of x+y

3. v3˜
A non-multiple of N.
1.7
Prime
N is a divisor of x+y

4. v5˜
23 -29
The PRODUCT of n consecutive integers is divisible by n!.
2.5
Put the coefficient under the radical to get a better approximation

5. 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
61 -67
In an evenly spaced set - the average and the median are equal.
97
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

6. Let N be an integer. If you add two non-multiples of N - the result could be _______.
97
The PRODUCT of n consecutive integers is divisible by n!.
2 -3 -5 -7
Either a multiple of N or a non-multiple of N

7. Prime Numbers:2x
Prime factorization
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A MULTIPLE
23 -29

8. In an evenly spaced set - the average can be found by finding ________.
Never prime
The middle number
The sum of any two primes will be even - unless one of the two primes is 2.
PERFECT CUBES

9. The sum of any two primes will be ____ - unless ______.
83 -89
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set

10. v625=
FACTOR
1. The smallest or largest element 2. The increment 3. The number of items in the set
3·3n = 3^{n+1}
25

11. In an evenly spaced set - the mean and median are equal to the _____ of _________.
N is a divisor of x+y
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ODD
3·3n = 3^{n+1}

12. Prime factors of _____ must come in pairs of three.
1.7
53 -59
PERFECT CUBES
11 -13 -17 -19

13. Prime Numbers:8x
83 -89
Never prime
Put the coefficient under the radical to get a better approximation
N is a divisor of x+y

14. The average of an EVEN number of consecutive integers will ________ be an integer.
61 -67
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.

15. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
61 -67
NEVER CONTRADICT ONE ANOTHER

16. v225=
The PRODUCT of n consecutive integers is divisible by n!.
15
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE

17. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

18. If 2 cannot be one of the primes in the sum - the sum must 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.
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
16

19. Prime Numbers:9x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97
1.7
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

20. Prime Numbers:5x
PERFECT CUBES
25
53 -59
13

21. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
25
A non-multiple of N.
Either a multiple of N or a non-multiple of N
The average of the set times the number of elements in the set

22. For ODD ROOTS - the root has ______.
The same sign as the base
14
25
[(last - first) / increment] + 1

23. Any integer with an ODD number of total factors must be _______.
Never prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
3·3n = 3^{n+1}
A PERFECT SQUARE

24. All perfect squares have a(n) _________ number of total factors.
97
Never prime
2 -3 -5 -7
ODD

25. 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.
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.
1.7
Prime factorization

26. In an evenly spaced set - the sum of the terms is equal to ____.
61 -67
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
A non-multiple of N.

27. How to find the sum of consecutive integers:
13
A non-multiple of N.
PERFECT CUBES
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.

28. v169=
13
83 -89
EVEN
15

29. If estimating a root with a coefficient - _____ .
Either a multiple of N or a non-multiple of N
ONLY the nonnegative root of the numberUNLIKE
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

30. Prime Numbers:3x
2 -3 -5 -7
25
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
31 -37

31. The average of an ODD number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
13
The average of an ODD number of consecutive integers will ALWAYS be an integer.

32. The formula for finding the number of consecutive multiples in a set is _______.
The same sign as the base
Never prime
[(last - first) / increment] + 1
2.5

33. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
EVEN
41 -43 -47
15

34. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
83 -89
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.
25
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

35. The two statements in a data sufficiency problem will _______________.
13
NEVER CONTRADICT ONE ANOTHER
41 -43 -47
2 -3 -5 -7

36. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
The PRODUCT of n consecutive integers is divisible by n!.
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

37. Prime Numbers:0x
A MULTIPLE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2 -3 -5 -7
11 -13 -17 -19

38. N! is _____ of all integers from 1 to N.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A MULTIPLE
A non-multiple of N.
1. The smallest or largest element 2. The increment 3. The number of items in the set

39. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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
83 -89
PERFECT CUBES

40. v256=
3·3n = 3^{n+1}
The middle number
16
The average of an ODD number of consecutive integers will ALWAYS be an integer.

41. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
[(last - first) / increment] + 1
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
2 -3 -5 -7

42. Positive integers with only two factors must be ___.
16
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
41 -43 -47
Prime

43. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

44. Prime Numbers:1x
Put the coefficient under the radical to get a better approximation
11 -13 -17 -19
The middle number
61 -67

45. Prime Numbers:6x
Either a multiple of N or a non-multiple of N
61 -67
The average of an EVEN number of consecutive integers will NEVER be an integer.
In an evenly spaced set - the average and the median are equal.

46. The prime factorization of __________ contains only EVEN powers of primes.
PERFECT CUBES
Either a multiple of N or a non-multiple of N
2 -3 -5 -7
A PERFECT SQUARE

47. If N is a divisor of x and y - then _______.
ONLY the nonnegative root of the numberUNLIKE
N is a divisor of x+y
1.7
Prime factorization

48. Positive integers with more than two factors are ____.
Never prime
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
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.
3·3n = 3^{n+1}

49. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set
13
53 -59

50. ³v216 =
15
Either a multiple of N or a non-multiple of N
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
3·3n = 3^{n+1}