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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. The average of an EVEN number of consecutive integers will ________ be an integer.
Never prime
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
A MULTIPLE

2. Prime Numbers:6x
61 -67
1.7
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.

3. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
Prime factorization
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
14

4. Positive integers with only two factors must be ___.
97
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Prime
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.

5. In an evenly spaced set - the ____ and the ____ are equal.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
In an evenly spaced set - the average and the median are equal.
ONLY the nonnegative root of the numberUNLIKE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

6. v5˜
53 -59
1.7
2.5
11 -13 -17 -19

7. Prime Numbers:5x
A MULTIPLE
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
53 -59
PERFECT CUBES

8. Prime Numbers:2x
83 -89
23 -29
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.
EVEN

9. 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.
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

10. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
11 -13 -17 -19
1. The smallest or largest element 2. The increment 3. The number of items in the set
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The average of an ODD number of consecutive integers will ALWAYS be an integer.

11. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The same sign as the base
FACTOR
11 -13 -17 -19
3·3n = 3^{n+1}

12. Positive integers with more than two factors are ____.
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
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.
Never prime

13. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
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.
ODD
2.5

14. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
The average of the set times the number of elements in the set
Prime factorization
25

15. Any integer with an EVEN number of total factors cannot be ______.
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE
PERFECT CUBES

16. 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.
A MULTIPLE
Either a multiple of N or 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.

17. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
A non-multiple of N.
A MULTIPLE
A PERFECT SQUARE

18. v196=
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
Never prime
14

19. If N is a divisor of x and y - then _______.
NEVER CONTRADICT ONE ANOTHER
11 -13 -17 -19
N is a divisor of x+y
FACTOR

20. 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
A MULTIPLE
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
FACTOR
The average of an EVEN number of consecutive integers will NEVER be an integer.

21. Prime Numbers:0x
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
A PERFECT SQUARE
A MULTIPLE

22. In an evenly spaced set - the sum of the terms is equal to ____.
Put the coefficient under the radical to get a better approximation
ONLY the nonnegative root of the numberUNLIKE
13
The average of the set times the number of elements in the set

23. Prime Numbers:9x
97
Prime factorization
The middle number
2 -3 -5 -7

24. If 2 cannot be one of the primes in the sum - the sum must be _____.
2.5
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.
If 2 cannot be one of the primes in the sum - the sum must be even.
Either a multiple of N or a non-multiple of N

25. All perfect squares have a(n) _________ number of total factors.
83 -89
Prime
41 -43 -47
ODD

26. How to find the sum of consecutive integers:
The sum of any two primes will be even - unless one of the two primes is 2.
2 -3 -5 -7
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

27. The average of an ODD number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
23 -29
31 -37
The average of an ODD number of consecutive integers will ALWAYS be an integer.

28. Prime Numbers:3x
N is a divisor of x+y
Put the coefficient under the radical to get a better approximation
31 -37
11 -13 -17 -19

29. The prime factorization of __________ contains only EVEN powers of primes.
13
A PERFECT SQUARE
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.

30. v2˜
The average of the set times the number of elements in the set
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.4
14

31. v3˜
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.7
31 -37
Either a multiple of N or a non-multiple of N

32. v625=
The average of an EVEN number of consecutive integers will NEVER be an integer.
25
83 -89
In an evenly spaced set - the average and the median are equal.

33. Prime Numbers:7x
The middle number
1.7
71 -73 -79
1.4

34. The PRODUCT of n consecutive integers is divisible by ____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
11 -13 -17 -19
ONLY the nonnegative root of the numberUNLIKE
The PRODUCT of n consecutive integers is divisible by n!.

35. In an evenly spaced set - the average can be found by finding ________.
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE
The middle number
FACTOR

36. N! is _____ of all integers from 1 to N.
1. The smallest or largest element 2. The increment 3. The number of items in the set
83 -89
A PERFECT SQUARE
A MULTIPLE

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?
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Never 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.
If 2 cannot be one of the primes in the sum - the sum must be even.

38. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
14
N is a divisor of x+y
[(last - first) / increment] + 1

39. v256=
11 -13 -17 -19
16
PERFECT CUBES
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

40. If estimating a root with a coefficient - _____ .
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
The average of an EVEN number of consecutive integers will NEVER be an integer.
3·3n = 3^{n+1}

41. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
14
If 2 cannot be one of the primes in the sum - the sum must be even.
31 -37

42. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
3·3n = 3^{n+1}
1.7

43. For ODD ROOTS - the root has ______.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
A MULTIPLE
The same sign as the base

44. ³v216 =
14
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
A MULTIPLE

45. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.

46. Prime Numbers:8x
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.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A non-multiple of N.

47. 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.
2 -3 -5 -7
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

48. 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

49. Prime factors of _____ must come in pairs of three.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A non-multiple of N.
Prime
PERFECT CUBES

50. Prime Numbers:1x
Prime
A PERFECT SQUARE
2 -3 -5 -7
11 -13 -17 -19