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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. v225=
2.5
A non-multiple of N.
15
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. 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
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN
The average of an ODD number of consecutive integers will ALWAYS be an integer.

3. N! is _____ of all integers from 1 to N.
[(last - first) / increment] + 1
A MULTIPLE
71 -73 -79
Prime factorization

4. For ODD ROOTS - the root has ______.
16
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The same sign as the base
A non-multiple of N.

5. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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
ONLY the nonnegative root of the numberUNLIKE
Prime

6. The two statements in a data sufficiency problem will _______________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
Either a multiple of N or a non-multiple of N
NEVER CONTRADICT ONE ANOTHER

7. The average of an EVEN number of consecutive integers will ________ be an integer.
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 average of an EVEN number of consecutive integers will NEVER be an integer.
The middle number
FACTOR

8. Prime Numbers:8x
83 -89
The average of an EVEN number of consecutive integers will NEVER be an integer.
11 -13 -17 -19
The same sign as the base

9. 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.
97
23 -29
14

10. 3n + 3n + 3n = _____ = ______
The middle number
The same sign as the base
41 -43 -47
3·3n = 3^{n+1}

11. v3˜
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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.7

12. ³v216 =
1.4
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

13. The PRODUCT of n consecutive integers is divisible by ____.
13
Put the coefficient under the radical to get a better approximation
[(last - first) / increment] + 1
The PRODUCT of n consecutive integers is divisible by n!.

14. The formula for finding the number of consecutive multiples in a set is _______.
53 -59
Never prime
[(last - first) / increment] + 1
Either a multiple of N or a non-multiple of N

15. In an evenly spaced set - the ____ and the ____ are equal.
EVEN
3·3n = 3^{n+1}
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the average and the median are equal.

16. Positive integers with only two factors must be ___.
15
Prime factorization
Prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

17. v625=
25
2 -3 -5 -7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER

18. Prime Numbers:0x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2 -3 -5 -7
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19

19. Any integer with an ODD number of total factors must be _______.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
The same sign as the base
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.

20. v2˜
1.4
FACTOR
31 -37
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

21. Let N be an integer. If you add two non-multiples of N - the result could be _______.
[(last - first) / increment] + 1
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Either a multiple of N or a non-multiple of N
83 -89

22. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A MULTIPLE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ODD

23. If 2 cannot be one of the primes in the sum - the sum must be _____.
[(last - first) / increment] + 1
NEVER CONTRADICT ONE ANOTHER
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN

24. If N is a divisor of x and y - then _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
61 -67
N is a divisor of x+y
Prime factorization

25. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
25
FACTOR
ONLY the nonnegative root of the numberUNLIKE
The PRODUCT of n consecutive integers is divisible by n!.

26. 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.
97
41 -43 -47
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.

27. The prime factorization of __________ contains only EVEN powers of primes.
The sum of any two primes will be even - unless one of the two primes is 2.
25
A PERFECT SQUARE
83 -89

28. The average of an ODD number of consecutive integers will ________ be an integer.
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.
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.

29. Prime factors of _____ must come in pairs of three.
A PERFECT SQUARE
PERFECT CUBES
A MULTIPLE
NEVER CONTRADICT ONE ANOTHER

30. Positive integers with more than two factors are ____.
3·3n = 3^{n+1}
Prime
The middle number
Never prime

31. Any integer with an EVEN number of total factors cannot be ______.
A MULTIPLE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The same sign as the base
A PERFECT SQUARE

32. 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
FACTOR
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47

33. If estimating a root with a coefficient - _____ .
The PRODUCT of n consecutive integers is divisible by n!.
41 -43 -47
Prime factorization
Put the coefficient under the radical to get a better approximation

34. If the problem states/assumes that a number is an integer - check to see if you can use _______.
1. The smallest or largest element 2. The increment 3. The number of items 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.
A PERFECT SQUARE
Prime factorization

35. 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
14
15
A MULTIPLE

36. The prime factorization of a perfect square contains only ______ powers of primes.
A non-multiple of N.
EVEN
11 -13 -17 -19
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

37. The sum of any two primes will be ____ - unless ______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The sum of any two primes will be even - unless one of the two primes is 2.
The middle number
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

38. 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
23 -29
71 -73 -79
Prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

39. All perfect squares have a(n) _________ number of total factors.
ODD
11 -13 -17 -19
2.5
71 -73 -79

40. Prime Numbers:6x
61 -67
ODD
11 -13 -17 -19
Never prime

41. In an evenly spaced set - the mean and median are equal to the _____ of _________.
25
A PERFECT SQUARE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime

42. v196=
16
A PERFECT SQUARE
Never prime
14

43. Prime Numbers:1x
11 -13 -17 -19
13
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set

44. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
EVEN
Never prime
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

45. Prime Numbers:3x
In an evenly spaced set - the average and the median are equal.
31 -37
61 -67
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

46. Prime Numbers:7x
71 -73 -79
Put the coefficient under the radical to get a better approximation
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.

47. Prime Numbers:4x
[(last - first) / increment] + 1
41 -43 -47
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

48. Prime Numbers:5x
53 -59
A MULTIPLE
The average of the set times the number of elements in the set
2.5

49. v256=
31 -37
13
In an evenly spaced set - the average and the median are equal.
16

50. In an evenly spaced set - the sum of the terms is equal to ____.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of the set times the number of elements in the set
23 -29
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.