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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. Prime Numbers:7x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
97
A PERFECT SQUARE
71 -73 -79

2. How to find the sum of consecutive integers:
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.
A PERFECT SQUARE
41 -43 -47

3. v3˜
2 -3 -5 -7
1.7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
23 -29

4. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
23 -29
Either a multiple of N or a non-multiple of N
ONLY the nonnegative root of the numberUNLIKE

5. In an evenly spaced set - the average can be found by finding ________.
A non-multiple of N.
83 -89
25
The middle number

6. Positive integers with more than two factors are ____.
53 -59
Never prime
A PERFECT SQUARE
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

7. If estimating a root with a coefficient - _____ .
N is a divisor of x+y
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime
Put the coefficient under the radical to get a better approximation

8. v625=
The average of an EVEN number of consecutive integers will NEVER be an integer.
25
53 -59
The PRODUCT of n consecutive integers is divisible by n!.

9. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
In an evenly spaced set - the average and the median are equal.
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.
ONLY the nonnegative root of the numberUNLIKE
97

10. v5˜
83 -89
31 -37
2.5
The sum of any two primes will be even - unless one of the two primes is 2.

11. In an evenly spaced set - the ____ and the ____ are equal.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
13
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.

12. 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

13. Prime Numbers:0x
NEVER CONTRADICT ONE ANOTHER
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
31 -37

14. Prime Numbers:1x
[(last - first) / increment] + 1
1.4
11 -13 -17 -19
The average of an ODD number of consecutive integers will ALWAYS be an integer.

15. The prime factorization of a perfect square contains only ______ powers of primes.
31 -37
EVEN
The PRODUCT of n consecutive integers is divisible by n!.
A MULTIPLE

16. N! is _____ of all integers from 1 to N.
Never prime
A MULTIPLE
The average of the set times the number of elements in the set
1.4

17. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
1. The smallest or largest element 2. The increment 3. The number of items in the set
15
The middle number
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

18. The prime factorization of __________ contains only EVEN powers of primes.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
61 -67
In an evenly spaced set - the average and the median are equal.

19. v2˜
In an evenly spaced set - the average and the median are equal.
Prime
The average of the set times the number of elements in the set
1.4

20. If the problem states/assumes that a number is an integer - check to see if you can use _______.
EVEN
The average of an EVEN number of consecutive integers will NEVER be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
Prime factorization

21. v196=
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
14
15
The average of an ODD number of consecutive integers will ALWAYS be an integer.

22. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.

23. 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
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 gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.
ONLY the nonnegative root of the numberUNLIKE

24. Prime Numbers:5x
In an evenly spaced set - the average and the median are equal.
16
53 -59
83 -89

25. Prime Numbers:2x
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
23 -29
In an evenly spaced set - the average and the median are equal.

26. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime
[(last - first) / increment] + 1
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

27. v225=
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
15
53 -59
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

28. ³v216 =
Either a multiple of N or a non-multiple of 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
Prime factorization
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

29. For ODD ROOTS - the root has ______.
The average of the set times the number of elements in the set
1.7
11 -13 -17 -19
The same sign as the base

30. Any integer with an EVEN number of total factors cannot be ______.
2.5
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
83 -89

31. Prime Numbers:3x
31 -37
FACTOR
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

32. Prime Numbers:6x
Either a multiple of N or a non-multiple of N
61 -67
FACTOR
If 2 cannot be one of the primes in the sum - the sum must be even.

33. The formula for finding the number of consecutive multiples in a set is _______.
A PERFECT SQUARE
EVEN
[(last - first) / increment] + 1
PERFECT CUBES

34. If N is a divisor of x and y - then _______.
N is a divisor of x+y
Prime factorization
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number

35. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
ONLY the nonnegative root of the numberUNLIKE
Put the coefficient under the radical to get a better approximation
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

36. 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.
53 -59
2.5
A PERFECT SQUARE

37. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
The same sign as the base
A PERFECT SQUARE
A PERFECT SQUARE

38. The average of an EVEN number of consecutive integers will ________ be an integer.
15
The average of an EVEN number of consecutive integers will NEVER be an integer.
Put the coefficient under the radical to get a better approximation
41 -43 -47

39. All perfect squares have a(n) _________ number of total factors.
A non-multiple of N.
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
ODD

40. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
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
11 -13 -17 -19
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. The sum of any two primes will be ____ - unless ______.
Never prime
ONLY the nonnegative root of the numberUNLIKE
15
The sum of any two primes will be even - unless one of the two primes is 2.

42. v169=
13
The middle number
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.
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.

43. v256=
25
1.7
3·3n = 3^{n+1}
16

44. In an evenly spaced set - the mean and median are equal to the _____ of _________.
The middle number
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
15
3·3n = 3^{n+1}

45. The PRODUCT of n consecutive integers is divisible by ____.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The sum of any two primes will be even - unless one of the two primes is 2.
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.

46. 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 the set times the number of elements in the set
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

47. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE
The average of the set times the number of elements in the set
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

48. Prime factors of _____ must come in pairs of three.
The average of the set times the number of elements in the set
83 -89
14
PERFECT CUBES

49. Prime Numbers:9x
41 -43 -47
Never prime
97
EVEN

50. 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
ODD
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
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.