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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. 3n + 3n + 3n = _____ = ______
Either a multiple of N or a non-multiple of N
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.
3·3n = 3^{n+1}

2. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
Never prime
In an evenly spaced set - the average and the median are equal.
ODD

3. Prime Numbers:0x
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7
11 -13 -17 -19
1.7

4. Prime Numbers:4x
41 -43 -47
1.7
In an evenly spaced set - the average and the median are equal.
15

5. Prime Numbers:2x
Put the coefficient under the radical to get a better approximation
A MULTIPLE
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

6. v5˜
2.5
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
N is a divisor of x+y
In an evenly spaced set - the average and the median are equal.

7. v169=
PERFECT CUBES
13
The average of the set times the number of elements 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

8. Prime Numbers:9x
16
The average of an EVEN number of consecutive integers will NEVER be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97

9. N! is _____ of all integers from 1 to N.
A MULTIPLE
A PERFECT SQUARE
The average of the set times the number of elements in the set
23 -29

10. v256=
The average of the set times the number of elements in the set
2 -3 -5 -7
16
14

11. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.4
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

12. 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
Prime factorization
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.

13. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE
1. The smallest or largest element 2. The increment 3. The number of items in the set

14. v196=
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
14
41 -43 -47
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.

15. Prime Numbers:1x
Prime factorization
In an evenly spaced set - the average and the median are equal.
11 -13 -17 -19
ODD

16. Prime Numbers:7x
PERFECT CUBES
71 -73 -79
53 -59
A PERFECT SQUARE

17. Prime Numbers:5x
2 -3 -5 -7
1.7
53 -59
Put the coefficient under the radical to get a better approximation

18. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
EVEN
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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

19. Positive integers with only two factors must be ___.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
EVEN
Prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.

20. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
31 -37
25
EVEN

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. v625=
The average of an EVEN number of consecutive integers will NEVER be an integer.
25
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.

23. Prime Numbers:6x
61 -67
1. The smallest or largest element 2. The increment 3. The number of items in the set
A MULTIPLE
The sum of any two primes will be even - unless one of the two primes is 2.

24. The sum of any two primes will be ____ - unless ______.
Either a multiple of N or a non-multiple of N
Put the coefficient under the radical to get a better approximation
PERFECT CUBES
The sum of any two primes will be even - unless one of the two primes is 2.

25. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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 prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
EVEN

26. 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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
23 -29
Never prime

27. In an evenly spaced set - the ____ and the ____ are equal.
The same sign as the base
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
97

28. 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.
ODD
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

29. The formula for finding the number of consecutive multiples in a set is _______.
25
[(last - first) / increment] + 1
16
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

30. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The same sign as the base
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
EVEN
1. The smallest or largest element 2. The increment 3. The number of items in the set

31. If estimating a root with a coefficient - _____ .
71 -73 -79
Put the coefficient under the radical to get a better approximation
25
NEVER CONTRADICT ONE ANOTHER

32. How to find the sum of consecutive integers:
11 -13 -17 -19
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

33. v2˜
11 -13 -17 -19
1.4
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

34. 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
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
The same sign as the base
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

35. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Put the coefficient under the radical to get a better approximation
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.
FACTOR

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

37. The average of an EVEN number of consecutive integers will ________ be an integer.
13
In an evenly spaced set - the average and the median are equal.
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.

38. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
In an evenly spaced set - the average and the median are equal.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
A non-multiple of N.

39. v225=
61 -67
15
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19

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

41. Any integer with an EVEN number of total factors cannot be ______.
1.4
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.

42. If 2 cannot be one of the primes in the sum - the sum must be _____.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
11 -13 -17 -19
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 2 cannot be one of the primes in the sum - the sum must be even.

43. v3˜
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.
1.7
1. The smallest or largest element 2. The increment 3. The number of items in the set

44. In an evenly spaced set - the average can be found by finding ________.
Never prime
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.
If 2 cannot be one of the primes in the sum - the sum must be even.

45. If N is a divisor of x and y - then _______.
71 -73 -79
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set
N is a divisor of x+y

46. ³v216 =
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
2.5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

47. The PRODUCT of n consecutive integers is divisible by ____.
N is a divisor of x+y
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 PRODUCT of n consecutive integers is divisible by n!.
PERFECT CUBES

48. For ODD ROOTS - the root has ______.
3·3n = 3^{n+1}
The same sign as the base
A PERFECT SQUARE
PERFECT CUBES

49. The prime factorization of __________ contains only EVEN powers of primes.
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

50. The two statements in a data sufficiency problem will _______________.
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
NEVER CONTRADICT ONE ANOTHER
[(last - first) / increment] + 1