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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:3x
2.5
A PERFECT SQUARE
31 -37
ODD

2. If estimating a root with a coefficient - _____ .
13
ODD
14
Put the coefficient under the radical to get a better approximation

3. v225=
The same sign as the base
15
ODD
A PERFECT SQUARE

4. 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

5. If the problem states/assumes that a number is an integer - check to see if you can use _______.
41 -43 -47
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
97

6. If N is a divisor of x and y - then _______.
Prime
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
Prime factorization

7. The sum of any two primes will be ____ - unless ______.
FACTOR
31 -37
71 -73 -79
The sum of any two primes will be even - unless one of the two primes is 2.

8. The two statements in a data sufficiency problem will _______________.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE
The average of an EVEN number of consecutive integers will NEVER be an integer.
NEVER CONTRADICT ONE ANOTHER

9. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
[(last - first) / increment] + 1
97
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1. The smallest or largest element 2. The increment 3. The number of items in the set

10. The formula for finding the number of consecutive multiples in a set is _______.
1.7
A MULTIPLE
[(last - first) / increment] + 1
2.5

11. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
EVEN

12. Prime Numbers:5x
14
A PERFECT SQUARE
53 -59
The PRODUCT of n consecutive integers is divisible by n!.

13. 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?
1.7
2 -3 -5 -7
[(last - first) / increment] + 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.

14. v3˜
71 -73 -79
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.7
The average of an ODD number of consecutive integers will ALWAYS be an integer.

15. In an evenly spaced set - the average can be found by finding ________.
23 -29
Never prime
A non-multiple of N.
The middle number

16. If 2 cannot be one of the primes in the sum - the sum must be _____.
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.
If 2 cannot be one of the primes in the sum - the sum must be even.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

17. The prime factorization of a perfect square contains only ______ powers of primes.
N is a divisor of x+y
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
EVEN

18. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Prime
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

19. v625=
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

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
FACTOR
PERFECT CUBES
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.

21. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
The same sign as the base
A non-multiple of N.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

22. Prime Numbers:4x
Prime factorization
[(last - first) / increment] + 1
41 -43 -47
Either a multiple of N or a non-multiple of N

23. The average of an EVEN number of consecutive integers will ________ be an integer.
N is a divisor of x+y
The average of an EVEN number of consecutive integers will NEVER be an integer.
97
PERFECT CUBES

24. Prime Numbers:7x
1.4
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
71 -73 -79
25

25. v256=
16
83 -89
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

26. 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.
EVEN
2 -3 -5 -7
Prime factorization

27. v2˜
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If 2 cannot be one of the primes in the sum - the sum must be even.
A MULTIPLE
1.4

28. 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
EVEN
A MULTIPLE
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.
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

29. 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.
ONLY the nonnegative root of the numberUNLIKE
NEVER CONTRADICT ONE ANOTHER
The same sign as the base

30. N! is _____ of all integers from 1 to N.
FACTOR
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.
31 -37

31. Any integer with an ODD number of total factors must be _______.
3·3n = 3^{n+1}
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13
A PERFECT SQUARE

32. The prime factorization of __________ contains only EVEN powers of primes.
ODD
Put the coefficient under the radical to get a better approximation
The same sign as the base
A PERFECT SQUARE

33. For ODD ROOTS - the root has ______.
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.
The same sign as the base
31 -37
ONLY the nonnegative root of the numberUNLIKE

34. The PRODUCT of n consecutive integers is divisible by ____.
ONLY the nonnegative root of the numberUNLIKE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The PRODUCT of n consecutive integers is divisible by n!.
1. The smallest or largest element 2. The increment 3. The number of items in the set

35. Prime Numbers:0x
The sum of any two primes will be even - unless one of the two primes is 2.
Prime factorization
2 -3 -5 -7
Put the coefficient under the radical to get a better approximation

36. How to find the sum of consecutive integers:
ONLY the nonnegative root of the numberUNLIKE
83 -89
The PRODUCT of n consecutive integers is divisible by 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.

37. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Either a multiple of N or a non-multiple of N
1.4
14

38. v5˜
3·3n = 3^{n+1}
2.5
The sum of any two primes will be even - unless one of the two primes is 2.
25

39. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
23 -29

40. Positive integers with more than two factors are ____.
Never prime
A MULTIPLE
The same sign as the base
FACTOR

41. In an evenly spaced set - the sum of the terms is equal to ____.
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
FACTOR
The average of the set times the number of elements in the set

42. 3n + 3n + 3n = _____ = ______
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 PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
3·3n = 3^{n+1}

43. Prime Numbers:1x
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.
25
11 -13 -17 -19
FACTOR

44. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
Either a multiple of N or a non-multiple of N
31 -37
A non-multiple of N.
The sum of any two primes will be even - unless one of the two primes is 2.

45. v169=
25
EVEN
13
The sum of any two primes will be even - unless one of the two primes is 2.

46. Prime Numbers:9x
16
97
A MULTIPLE
11 -13 -17 -19

47. All perfect squares have a(n) _________ number of total factors.
ONLY the nonnegative root of the numberUNLIKE
2 -3 -5 -7
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ODD

48. Prime Numbers:6x
13
11 -13 -17 -19
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
61 -67

49. Prime Numbers:8x
14
1. The smallest or largest element 2. The increment 3. The number of items in the set
15
83 -89

50. Prime Numbers:2x
Prime
The average of an EVEN number of consecutive integers will NEVER be an integer.
23 -29
The PRODUCT of n consecutive integers is divisible by n!.