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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. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
83 -89
The middle number
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

2. 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
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.
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
The sum of any two primes will be even - unless one of the two primes is 2.

3. v3˜
The average of the set times the number of elements in the set
1.7
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N

4. Prime Numbers:4x
1.7
The average of an EVEN number of consecutive integers will NEVER be an integer.
41 -43 -47
In an evenly spaced set - the average and the median are equal.

5. In an evenly spaced set - the average can be found by finding ________.
The middle number
Put the coefficient under the radical to get a better approximation
Either a multiple of N or a non-multiple of N
A MULTIPLE

6. ³v216 =
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
A PERFECT SQUARE

7. v5˜
[(last - first) / increment] + 1
2 -3 -5 -7
The PRODUCT of n consecutive integers is divisible by n!.
2.5

8. Let N be an integer. If you add two non-multiples of N - the result could be _______.
71 -73 -79
The same sign as the base
97
Either a multiple of N or a non-multiple of N

9. All perfect squares have a(n) _________ number of total factors.
ODD
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
23 -29
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

10. 3n + 3n + 3n = _____ = ______
N is a divisor of x+y
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set

11. 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
13
71 -73 -79

12. v256=
41 -43 -47
1.7
16
If 2 cannot be one of the primes in the sum - the sum must be even.

13. Positive integers with only two factors must be ___.
31 -37
The average of the set times the number of elements in the set
EVEN
Prime

14. 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
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

15. 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

16. If estimating a root with a coefficient - _____ .
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
Put the coefficient under the radical to get a better approximation
A non-multiple of N.

17. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
N is a divisor of x+y
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
83 -89
25

18. Prime Numbers:9x
25
The sum of any two primes will be even - unless one of the two primes is 2.
11 -13 -17 -19
97

19. In an evenly spaced set - the sum of the terms is equal to ____.
ODD
The average of an EVEN number of consecutive integers will NEVER be an integer.
NEVER CONTRADICT ONE ANOTHER
The average of the set times the number of elements in the set

20. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.
Put the coefficient under the radical to get a better approximation
83 -89

21. For ODD ROOTS - the root has ______.
15
The same sign as the base
FACTOR
25

22. v169=
71 -73 -79
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.
13

23. Any integer with an EVEN number of total factors cannot be ______.
11 -13 -17 -19
13
A PERFECT SQUARE
N is a divisor of x+y

24. v2˜
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.
3·3n = 3^{n+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
1.4

25. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set
ONLY the nonnegative root of the numberUNLIKE
Never prime

26. v225=
N is a divisor of x+y
ONLY the nonnegative root of the numberUNLIKE
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

27. 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
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

28. Positive integers with more than two factors are ____.
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 prime
15
14

29. The sum of any two primes will be ____ - unless ______.
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
The sum of any two primes will be even - unless one of the two primes is 2.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

30. Prime Numbers:1x
PERFECT CUBES
Prime factorization
2 -3 -5 -7
11 -13 -17 -19

31. Prime Numbers:7x
71 -73 -79
A non-multiple of N.
31 -37
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.

32. The prime factorization of __________ contains only EVEN powers of primes.
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.
2 -3 -5 -7
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

33. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
N is a divisor of x+y
Prime factorization
The average of an ODD number of consecutive integers will ALWAYS be an integer.

34. How to find the sum of consecutive integers:
11 -13 -17 -19
2.5
The average of an ODD number of consecutive integers will ALWAYS be 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.

35. Prime Numbers:5x
Prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
83 -89
53 -59

36. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
[(last - first) / increment] + 1
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime

37. Prime Numbers:6x
61 -67
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.
PERFECT CUBES
The same sign as the base

38. 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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set

39. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
13
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the average and the median are equal.
FACTOR

40. The average of an EVEN number of consecutive integers will ________ be an integer.
N is a divisor of x+y
[(last - first) / increment] + 1
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE

41. 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
14
[(last - first) / increment] + 1

42. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
71 -73 -79
A PERFECT SQUARE
41 -43 -47
A non-multiple of N.

43. The formula for finding the number of consecutive multiples in a set is _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
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
23 -29

44. v196=
13
Prime
14
71 -73 -79

45. The two statements in a data sufficiency problem will _______________.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.
NEVER CONTRADICT ONE ANOTHER

46. If N is a divisor of x and y - then _______.
[(last - first) / increment] + 1
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
13
N is a divisor of x+y

47. N! is _____ of all integers from 1 to N.
1.7
A MULTIPLE
14
11 -13 -17 -19

48. Prime Numbers:8x
23 -29
83 -89
25
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.

49. Prime factors of _____ must come in pairs of three.
25
PERFECT CUBES
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

50. 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 average of an EVEN number of consecutive integers will NEVER be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
FACTOR
31 -37