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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:1x
11 -13 -17 -19
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.
[(last - first) / increment] + 1

2. Any integer with an ODD number of total factors must be _______.
The average of the set times the number of elements in the set
Never prime
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

3. In an evenly spaced set - the sum of the terms is equal to ____.
71 -73 -79
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of the set times the number of elements in the set
EVEN

4. Prime Numbers:6x
The sum of any two primes will be even - unless one of the two primes is 2.
15
Put the coefficient under the radical to get a better approximation
61 -67

5. v2˜
[(last - first) / increment] + 1
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.
14
1.4

6. How to find the sum of consecutive integers:
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.
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. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A non-multiple of N.
The same sign as the base
A PERFECT SQUARE

8. Prime Numbers:4x
41 -43 -47
1.7
31 -37
ONLY the nonnegative root of the numberUNLIKE

9. Prime Numbers:3x
3·3n = 3^{n+1}
A MULTIPLE
FACTOR
31 -37

10. v225=
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.
15
1.4
97

11. v5˜
2.5
A MULTIPLE
71 -73 -79
Put the coefficient under the radical to get a better approximation

12. 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
53 -59
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.

13. v256=
16
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A MULTIPLE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

14. Prime factors of _____ must come in pairs of three.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
PERFECT CUBES
The average of an EVEN number of consecutive integers will NEVER be an integer.
3·3n = 3^{n+1}

15. v169=
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
13
[(last - first) / increment] + 1

16. Prime Numbers:2x
A non-multiple of N.
15
23 -29
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

17. 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.
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
The same sign as the base

18. Prime Numbers:5x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
53 -59
25
41 -43 -47

19. Prime Numbers:7x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
71 -73 -79

20. 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
2.5
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime factorization
14

21. 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

22. 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.
13
EVEN
The same sign as the base

23. For ODD ROOTS - the root has ______.
The same sign as the base
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.
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

24. v625=
61 -67
25
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE

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?
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
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 same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set

26. ³v216 =
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.
N is a divisor of x+y
The sum of any two primes will be even - unless one of the two primes is 2.

27. In an evenly spaced set - the average can be found by finding ________.
The middle number
The sum of any two primes will be even - unless one of the two primes is 2.
ONLY the nonnegative root of the numberUNLIKE
Prime

28. The prime factorization of a perfect square contains only ______ powers of primes.
Either a multiple of N or a non-multiple of N
EVEN
61 -67
97

29. N! is _____ of all integers from 1 to N.
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.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A MULTIPLE

30. In an evenly spaced set - the mean and median are equal to the _____ of _________.
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.
83 -89
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

31. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
[(last - first) / increment] + 1
1.7
61 -67

32. The sum of any two primes will be ____ - unless ______.
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
The sum of any two primes will be even - unless one of the two primes is 2.
The middle number
1. The smallest or largest element 2. The increment 3. The number of items in the set

33. The average of an EVEN number of consecutive integers will ________ be an integer.
ONLY the nonnegative root of the numberUNLIKE
The average of an EVEN number of consecutive integers will NEVER be an integer.
N is a divisor of x+y
A PERFECT SQUARE

34. All perfect squares have a(n) _________ number of total factors.
The average of the set times the number of elements in the set
ODD
In an evenly spaced set - the average and the median are equal.
2.5

35. Prime Numbers:8x
1.4
The middle number
83 -89
[(last - first) / increment] + 1

36. Prime Numbers:9x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.
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.
97

37. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
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.
83 -89
FACTOR

38. v196=
14
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE
Prime

39. Let N be an integer. If you add two non-multiples of N - the result could be _______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Either a multiple of N or a non-multiple of N
NEVER CONTRADICT ONE ANOTHER
11 -13 -17 -19

40. 3n + 3n + 3n = _____ = ______
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
3·3n = 3^{n+1}
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

41. Prime Numbers:0x
16
2 -3 -5 -7
2.5
Put the coefficient under the radical to get a better approximation

42. If the problem states/assumes that a number is an integer - check to see if you can use _______.
41 -43 -47
NEVER CONTRADICT ONE ANOTHER
Prime factorization
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

43. Any integer with an EVEN number of total factors cannot be ______.
[(last - first) / increment] + 1
A PERFECT SQUARE
The average of an EVEN number of consecutive integers will NEVER be an integer.
16

44. 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
[(last - first) / increment] + 1
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
61 -67

45. The two statements in a data sufficiency problem will _______________.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER
23 -29

46. Positive integers with more than two factors are ____.
Prime
Never prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97

47. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A non-multiple of N.

48. If estimating a root with a coefficient - _____ .
16
83 -89
EVEN
Put the coefficient under the radical to get a better approximation

49. Positive integers with only two factors must be ___.
Prime
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.

50. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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 ODD number of consecutive integers will ALWAYS be an integer.
71 -73 -79
ONLY the nonnegative root of the numberUNLIKE