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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. v5˜
N is a divisor of x+y
A MULTIPLE
1.7
2.5

2. v2˜
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.4
NEVER CONTRADICT ONE ANOTHER
A non-multiple of N.

3. Let N be an integer. If you add two non-multiples of N - the result could be _______.
14
A MULTIPLE
Either a multiple of N or a non-multiple of 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.

4. In an evenly spaced set - the ____ and the ____ are equal.
53 -59
83 -89
In an evenly spaced set - the average and the median are equal.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

5. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
15
2 -3 -5 -7
Prime

6. For ODD ROOTS - the root has ______.
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
31 -37

7. Prime Numbers:6x
The average of an EVEN number of consecutive integers will NEVER be an integer.
FACTOR
61 -67
2.5

8. v625=
ODD
2.5
25
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

9. The two statements in a data sufficiency problem will _______________.
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
71 -73 -79
NEVER CONTRADICT ONE ANOTHER

10. v196=
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
14

11. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
3·3n = 3^{n+1}
1. The smallest or largest element 2. The increment 3. The number of items in the set
The middle number
FACTOR

12. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
2.5
ONLY the nonnegative root of the numberUNLIKE
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.

13. Prime Numbers:3x
31 -37
A PERFECT SQUARE
83 -89
FACTOR

14. Prime Numbers:9x
2 -3 -5 -7
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ONLY the nonnegative root of the numberUNLIKE
97

15. 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
41 -43 -47
The PRODUCT of n consecutive integers is divisible by 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 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

16. 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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

17. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
71 -73 -79
83 -89
15

18. v169=
13
EVEN
25
1.4

19. N! is _____ of all integers from 1 to N.
A MULTIPLE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE

20. Positive integers with more than two factors are ____.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Never prime
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

21. Prime Numbers:2x
1.7
If 2 cannot be one of the primes in the sum - the sum must be even.
The middle number
23 -29

22. Any integer with an EVEN number of total factors cannot be ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
N is a divisor of x+y
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. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The average of the set times the number of elements 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.
13
FACTOR

24. The average of an ODD number of consecutive integers will ________ be an integer.
97
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
31 -37

25. The prime factorization of a perfect square contains only ______ powers of primes.
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
11 -13 -17 -19
31 -37

26. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
If 2 cannot be one of the primes in the sum - the sum must be even.
83 -89
A non-multiple of N.
[(last - first) / increment] + 1

27. Any integer with an ODD number of total factors must be _______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE
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.

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?
11 -13 -17 -19
1.7
A PERFECT SQUARE
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.

29. If N is a divisor of x and y - then _______.
97
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
N is a divisor of x+y

30. Prime Numbers:1x
31 -37
15
11 -13 -17 -19
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.

31. Prime Numbers:5x
25
31 -37
53 -59
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.

32. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.
61 -67

33. In an evenly spaced set - the sum of the terms is equal to ____.
The average of the set times the number of elements in the set
15
53 -59
23 -29

34. v3˜
Prime
53 -59
1.7
Either a multiple of N or a non-multiple of N

35. Prime factors of _____ must come in pairs of three.
ONLY the nonnegative root of the numberUNLIKE
PERFECT CUBES
3·3n = 3^{n+1}
[(last - first) / increment] + 1

36. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
The PRODUCT of n consecutive integers is divisible by n!.
14
71 -73 -79

37. How to find the sum of consecutive integers:
A PERFECT SQUARE
The average of the set times the number of elements in the set
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.
ODD

38. Positive integers with only two factors must be ___.
15
A MULTIPLE
The average of the set times the number of elements in the set
Prime

39. 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

40. Prime Numbers:4x
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.
41 -43 -47
N is a divisor of x+y

41. The average of an EVEN number of consecutive integers will ________ be an integer.
31 -37
A PERFECT SQUARE
1.4
The average of an EVEN number of consecutive integers will NEVER be an integer.

42. Prime Numbers:7x
Prime
16
The average of an ODD number of consecutive integers will ALWAYS be an integer.
71 -73 -79

43. In an evenly spaced set - the average can be found by finding ________.
53 -59
25
A non-multiple of N.
The middle number

44. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
16
A PERFECT SQUARE
25

45. ³v216 =
16
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
FACTOR
NEVER CONTRADICT ONE ANOTHER

46. v225=
If 2 cannot be one of the primes in the sum - the sum must be even.
15
1.7
A non-multiple of N.

47. The PRODUCT of n consecutive integers is divisible by ____.
1.7
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

48. All perfect squares have a(n) _________ number of total factors.
Put the coefficient under the radical to get a better approximation
1. The smallest or largest element 2. The increment 3. The number of items in the set
ODD
The same sign as the base

49. Prime Numbers:8x
1. The smallest or largest element 2. The increment 3. The number of items in the set
A non-multiple of N.
A MULTIPLE
83 -89

50. v256=
97
The average of the set times the number of elements in the set
16
A MULTIPLE