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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.
ONLY the nonnegative root of the numberUNLIKE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
83 -89
The middle number

2. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The average of the set times the number of elements in the set
A non-multiple of N.
41 -43 -47
16

3. N! is _____ of all integers from 1 to N.
A PERFECT SQUARE
A MULTIPLE
16
15

4. v169=
15
Prime factorization
Put the coefficient under the radical to get a better approximation
13

5. Prime Numbers:7x
53 -59
71 -73 -79
PERFECT CUBES
Either a multiple of N or a non-multiple of N

6. How to find the sum of consecutive integers:
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.
13
97
Prime

7. In an evenly spaced set - the average can be found by finding ________.
EVEN
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.
The middle number

8. v5˜
A PERFECT SQUARE
2.5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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.

9. 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 ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
EVEN
The middle number

10. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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.
N is a divisor of x+y
Prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

11. The prime factorization of a perfect square contains only ______ powers of primes.
2.5
EVEN
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
[(last - first) / increment] + 1

12. Prime Numbers:8x
23 -29
15
83 -89
Prime

13. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
53 -59
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47

14. The two statements in a data sufficiency problem will _______________.
[(last - first) / increment] + 1
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

15. Prime factors of _____ must come in pairs of three.
71 -73 -79
N is a divisor of x+y
PERFECT CUBES
25

16. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The same sign as the base
1.4

17. Prime Numbers:4x
83 -89
41 -43 -47
Either a multiple of N or a non-multiple of N
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

18. The formula for finding the number of consecutive multiples in a set is _______.
In an evenly spaced set - the average and the median are equal.
The same sign as the base
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
[(last - first) / increment] + 1

19. Positive integers with only two factors must be ___.
Prime
97
2 -3 -5 -7
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

20. The sum of any two primes will be ____ - unless ______.
A PERFECT SQUARE
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
ONLY the nonnegative root of the numberUNLIKE

21. For ODD ROOTS - the root has ______.
N is a divisor of x+y
The average of the set times the number of elements in the set
The same sign as the base
53 -59

22. Prime Numbers:0x
Either a multiple of N or a non-multiple of N
Prime factorization
2 -3 -5 -7
The PRODUCT of n consecutive integers is divisible by n!.

23. The prime factorization of __________ contains only EVEN powers of primes.
Never prime
ODD
EVEN
A PERFECT SQUARE

24. 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

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25. Prime Numbers:1x
ODD
A MULTIPLE
11 -13 -17 -19
71 -73 -79

26. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
A non-multiple of N.
Prime
1.4

27. 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.
Prime
41 -43 -47
The average of the set times the number of elements in the set

28. In an evenly spaced set - the ____ and the ____ are equal.
The same sign as the base
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the average and the median are equal.

29. All perfect squares have a(n) _________ number of total factors.
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
71 -73 -79
ODD
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

30. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
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.
Never prime

31. If N is a divisor of x and y - then _______.
N is a divisor of x+y
A PERFECT SQUARE
13
ODD

32. ³v216 =
61 -67
PERFECT CUBES
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

33. Prime Numbers:5x
The middle number
Never prime
53 -59
A PERFECT SQUARE

34. If the problem states/assumes that a number is an integer - check to see if you can use _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
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.
Prime factorization

35. If estimating a root with a coefficient - _____ .
The average of an EVEN number of consecutive integers will NEVER be an integer.
Put the coefficient under the radical to get a better approximation
Never prime
11 -13 -17 -19

36. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
FACTOR
N is a divisor of x+y

37. In an evenly spaced set - the mean and median are equal to the _____ of _________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
11 -13 -17 -19

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

39. v3˜
1.7
2 -3 -5 -7
A non-multiple of N.
FACTOR

40. 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
FACTOR
2 -3 -5 -7
Either a multiple of N or a non-multiple of N

41. v2˜
Prime factorization
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.4
The PRODUCT of n consecutive integers is divisible by n!.

42. v225=
15
3·3n = 3^{n+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.
83 -89

43. Prime Numbers:6x
In an evenly spaced set - the average and the median are equal.
61 -67
ONLY the nonnegative root of the numberUNLIKE
FACTOR

44. v196=
83 -89
The sum of any two primes will be even - unless one of the two primes is 2.
3·3n = 3^{n+1}
14

45. Positive integers with more than two factors are ____.
16
The average of the set times the number of elements in the set
The average of an EVEN number of consecutive integers will NEVER be an integer.
Never prime

46. v625=
23 -29
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.
25

47. Prime Numbers:2x
A MULTIPLE
23 -29
31 -37
[(last - first) / increment] + 1

48. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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
25

49. Prime Numbers:9x
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.
ONLY the nonnegative root of the numberUNLIKE
Put the coefficient under the radical to get a better approximation
97

50. Let N be an integer. If you add two non-multiples of N - the result could be _______.
15
Put the coefficient under the radical to get a better approximation
Either a multiple of N or a non-multiple of N
ONLY the nonnegative root of the numberUNLIKE