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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. In an evenly spaced set - the average can be found by finding ________.
Prime factorization
Never prime
The PRODUCT of n consecutive integers is divisible by n!.
The middle number

2. The prime factorization of a perfect square contains only ______ powers of primes.
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.
53 -59
EVEN
83 -89

3. v625=
53 -59
25
1.7
PERFECT CUBES

4. Prime Numbers:2x
The PRODUCT of n consecutive integers is divisible by n!.
23 -29
2 -3 -5 -7
ODD

5. If N is a divisor of x and y - then _______.
N is a divisor of x+y
Either a multiple of N or 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.
1.7

6. If estimating a root with a coefficient - _____ .
3·3n = 3^{n+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.
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.

7. Prime Numbers:5x
53 -59
The same sign as the base
61 -67
PERFECT CUBES

8. 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.
23 -29
13
N is a divisor of x+y

9. The formula for finding the number of consecutive multiples in a set is _______.
A PERFECT SQUARE
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
53 -59

10. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
23 -29
Prime factorization
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

11. If the problem states/assumes that a number is an integer - check to see if you can use _______.
1.7
15
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

12. Any integer with an EVEN number of total factors cannot be ______.
A MULTIPLE
15
A PERFECT SQUARE
The middle number

13. v256=
41 -43 -47
16
A PERFECT SQUARE
14

14. For ODD ROOTS - the root has ______.
15
PERFECT CUBES
The same sign as the base
EVEN

15. The prime factorization of __________ contains only EVEN powers of primes.
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.
2.5
A PERFECT SQUARE
FACTOR

16. 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
The PRODUCT of n consecutive integers is divisible by n!.
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

17. Prime Numbers:9x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
16
A PERFECT SQUARE
97

18. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
2.5
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
EVEN
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.

19. v196=
Never prime
14
1.4
The PRODUCT of n consecutive integers is divisible by n!.

20. Prime factors of _____ must come in pairs of three.
1.4
Never prime
A PERFECT SQUARE
PERFECT CUBES

21. 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.
EVEN
53 -59
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:7x
53 -59
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER
71 -73 -79

23. Prime Numbers:4x
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.
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.
71 -73 -79
41 -43 -47

24. Prime Numbers:3x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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
31 -37

25. How to find the sum of consecutive integers:
EVEN
N is a divisor of x+y
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.
2.5

26. ³v216 =
16
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.
NEVER CONTRADICT ONE ANOTHER

27. In an evenly spaced set - the ____ and the ____ are equal.
71 -73 -79
83 -89
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

28. 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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.7
PERFECT CUBES

29. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
ONLY the nonnegative root of the numberUNLIKE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.7

30. N! is _____ of all integers from 1 to N.
A MULTIPLE
The same sign as the base
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.

31. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
N is a divisor of x+y
2 -3 -5 -7
A MULTIPLE
ONLY the nonnegative root of the numberUNLIKE

32. v2˜
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.
1.4
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

33. 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?
83 -89
PERFECT CUBES
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.
N is a divisor of x+y

34. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set
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

35. In an evenly spaced set - the sum of the terms is equal to ____.
Either a multiple of N or a non-multiple of N
The average of the set times the number of elements in the set
14
53 -59

36. The sum of any two primes will be ____ - unless ______.
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
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.

37. v225=
A non-multiple of N.
15
11 -13 -17 -19
[(last - first) / increment] + 1

38. Any integer with an ODD number of total factors must be _______.
Prime
71 -73 -79
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

39. The PRODUCT of n consecutive integers is divisible by ____.
71 -73 -79
PERFECT CUBES
61 -67
The PRODUCT of n consecutive integers is divisible by n!.

40. The two statements in a data sufficiency problem will _______________.
A PERFECT SQUARE
83 -89
NEVER CONTRADICT ONE ANOTHER
31 -37

41. Prime Numbers:8x
PERFECT CUBES
1.4
83 -89
2 -3 -5 -7

42. All perfect squares have a(n) _________ number of total factors.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
EVEN
ODD
The average of an ODD number of consecutive integers will ALWAYS be an integer.

43. 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.
41 -43 -47
Either a multiple of N or a non-multiple of N
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

44. Positive integers with only two factors must be ___.
The average of an EVEN number of consecutive integers will NEVER be an integer.
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime

45. The average of an EVEN number of consecutive integers will ________ be an integer.
PERFECT CUBES
[(last - first) / increment] + 1
The average of an EVEN number of consecutive integers will NEVER be an integer.
83 -89

46. v169=
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
13
23 -29
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.

47. Positive integers with more than two factors are ____.
16
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
Never prime

48. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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
A non-multiple of N.
2 -3 -5 -7

49. Prime Numbers:0x
2 -3 -5 -7
83 -89
PERFECT CUBES
97

50. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
FACTOR
The average of an ODD number of consecutive integers will ALWAYS be an integer.