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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. Positive integers with only two factors must be ___.
A MULTIPLE
Prime
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

2. In an evenly spaced set - the sum of the terms is equal to ____.
Either a multiple of N or a non-multiple of N
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
13

3. The average of an ODD number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
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
11 -13 -17 -19

4. Prime Numbers:6x
The same sign as the base
NEVER CONTRADICT ONE ANOTHER
61 -67
EVEN

5. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
23 -29
53 -59
83 -89
ONLY the nonnegative root of the numberUNLIKE

6. v169=
13
16
53 -59
A PERFECT SQUARE

7. v225=
15
In an evenly spaced set - the average and the median are equal.
97
41 -43 -47

8. In an evenly spaced set - the ____ and the ____ are equal.
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
In an evenly spaced set - the average and the median are equal.
15

9. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
A PERFECT SQUARE
FACTOR
23 -29
61 -67

10. v3˜
1.7
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.
Prime
A PERFECT SQUARE

11. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
ODD
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 PRODUCT of n consecutive integers is divisible by n!.

12. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
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.
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

13. How to find the sum of consecutive integers:
The middle number
A PERFECT SQUARE
53 -59
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.

14. If N is a divisor of x and y - then _______.
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.
[(last - first) / increment] + 1
1.4
N is a divisor of x+y

15. Prime Numbers:0x
2.5
A non-multiple of N.
2 -3 -5 -7
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.

16. 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

17. The formula for finding the number of consecutive multiples in a set is _______.
41 -43 -47
[(last - first) / increment] + 1
Either a multiple of N or a non-multiple of N
The same sign as the base

18. v196=
NEVER CONTRADICT ONE ANOTHER
14
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
25

19. The prime factorization of __________ contains only EVEN powers of primes.
The average of the set times the number of elements in the set
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

20. Prime Numbers:2x
EVEN
A MULTIPLE
23 -29
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. 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
71 -73 -79
NEVER CONTRADICT ONE ANOTHER
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
FACTOR

22. 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
1.4
A PERFECT SQUARE
The middle number

23. Prime Numbers:9x
NEVER CONTRADICT ONE ANOTHER
97
Prime
71 -73 -79

24. Prime Numbers:8x
The same sign as the base
83 -89
13
NEVER CONTRADICT ONE ANOTHER

25. In an evenly spaced set - the average can be found by finding ________.
A PERFECT SQUARE
The middle 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
The average of the set times the number of elements in the set

26. N! is _____ of all integers from 1 to N.
A MULTIPLE
41 -43 -47
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number

27. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Either a multiple of N or a non-multiple of N
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}

28. Prime factors of _____ must come in pairs of three.
[(last - first) / increment] + 1
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
PERFECT CUBES

29. If the problem states/assumes that a number is an integer - check to see if you can use _______.
NEVER CONTRADICT ONE ANOTHER
Prime factorization
PERFECT CUBES
ODD

30. Prime Numbers:3x
PERFECT CUBES
41 -43 -47
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
31 -37

31. The two statements in a data sufficiency problem will _______________.
Either a multiple of N or a non-multiple of N
EVEN
Prime
NEVER CONTRADICT ONE ANOTHER

32. Prime Numbers:7x
Put the coefficient under the radical to get a better approximation
The average of an ODD number of consecutive integers will ALWAYS be an integer.
71 -73 -79
Either a multiple of N or a non-multiple of N

33. Any integer with an EVEN number of total factors cannot be ______.
11 -13 -17 -19
97
Prime
A PERFECT SQUARE

34. 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.
97
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
A PERFECT SQUARE

35. The PRODUCT of n consecutive integers is divisible by ____.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The PRODUCT of n consecutive integers is divisible by n!.
Either a multiple of N or a non-multiple of N
Put the coefficient under the radical to get a better approximation

36. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
A PERFECT SQUARE
2.5
Either a multiple of N or a non-multiple of N
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

37. Positive integers with more than two factors are ____.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Either a multiple of N or a non-multiple of N
Never prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

38. Prime Numbers:5x
53 -59
41 -43 -47
Never prime
A PERFECT SQUARE

39. 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?
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.
The average of the set times the number of elements in the set
3·3n = 3^{n+1}

40. Prime Numbers:4x
1.4
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE

41. v256=
16
Prime
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.

42. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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 average of an ODD number of consecutive integers will ALWAYS be an integer.
[(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.

43. v2˜
A MULTIPLE
31 -37
1.4
14

44. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25
2 -3 -5 -7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

45. v5˜
2.5
ONLY the nonnegative root of the numberUNLIKE
PERFECT CUBES
1.4

46. The average of an EVEN number of consecutive integers will ________ be an integer.
83 -89
The average of an EVEN number of consecutive integers will NEVER be an integer.
2 -3 -5 -7
A PERFECT SQUARE

47. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
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
In an evenly spaced set - the average and the median are equal.

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
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
15
16
97

49. For ODD ROOTS - the root has ______.
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 average of the set times the number of elements in the set
The same sign as the base
25

50. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
PERFECT CUBES
The average of an EVEN number of consecutive integers will NEVER be an integer.
83 -89
A non-multiple of N.