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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. The PRODUCT of n consecutive integers is divisible by ____.
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.
2.5
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

2. Prime Numbers:5x
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set
ONLY the nonnegative root of the numberUNLIKE
Put the coefficient under the radical to get a better approximation

3. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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 SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The same sign as the base
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

4. The average of an ODD number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
16
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 average of an ODD number of consecutive integers will ALWAYS be an integer.

5. 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?
If 2 cannot be one of the primes in the sum - the sum must be even.
The middle number
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.
Never prime

6. ³v216 =
If 2 cannot be one of the primes in the sum - the sum must be even.
N is a divisor of x+y
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1. The smallest or largest element 2. The increment 3. The number of items in the set

7. For ODD ROOTS - the root has ______.
2.5
The same sign as the base
1.7
71 -73 -79

8. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
Prime
The average of the set times the number of elements in the set
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. The two statements in a data sufficiency problem will _______________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
NEVER CONTRADICT ONE ANOTHER
1. The smallest or largest element 2. The increment 3. The number of items in the set
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

10. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The PRODUCT of n consecutive integers is divisible by n!.
FACTOR
97
The middle number

11. Prime Numbers:4x
A MULTIPLE
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
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.

12. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The middle number
Never prime
71 -73 -79
ONLY the nonnegative root of the numberUNLIKE

13. v5˜
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
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
2.5

14. In an evenly spaced set - the ____ and the ____ are equal.
14
NEVER CONTRADICT ONE ANOTHER
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.

15. Prime Numbers:2x
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 an ODD number of consecutive integers will ALWAYS be an integer.
23 -29
EVEN

16. If estimating a root with a coefficient - _____ .
N is a divisor of x+y
41 -43 -47
Put the coefficient under the radical to get a better approximation
16

17. How to find the sum of consecutive integers:
41 -43 -47
15
61 -67
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.

18. In an evenly spaced set - the average can be found by finding ________.
The middle number
23 -29
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

19. 3n + 3n + 3n = _____ = ______
1.7
3·3n = 3^{n+1}
53 -59
A PERFECT SQUARE

20. Prime Numbers:9x
11 -13 -17 -19
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
83 -89
97

21. If N is a divisor of x and y - then _______.
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime
N is a divisor of x+y

22. Prime Numbers:1x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13
11 -13 -17 -19
The average of an ODD number of consecutive integers will ALWAYS be an integer.

23. All perfect squares have a(n) _________ number of total factors.
31 -37
ODD
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.
1.7

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

25. Positive integers with more than two factors are ____.
Never prime
2 -3 -5 -7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1. The smallest or largest element 2. The increment 3. The number of items in the set

26. The formula for finding the number of consecutive multiples in a set is _______.
ONLY the nonnegative root of the numberUNLIKE
14
[(last - first) / increment] + 1
2.5

27. v3˜
71 -73 -79
1. The smallest or largest element 2. The increment 3. The number of items in the set
53 -59
1.7

28. 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.
The middle number
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.
Prime

29. Prime Numbers:7x
The middle number
71 -73 -79
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.

30. Prime Numbers:6x
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.
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.
61 -67

31. Let N be an integer. If you add two non-multiples of N - the result could be _______.
31 -37
1.4
13
Either a multiple of N or a non-multiple of N

32. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The middle number
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
3·3n = 3^{n+1}

33. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The sum of any two primes will be even - unless one of the two primes is 2.
23 -29
97

34. N! is _____ of all integers from 1 to N.
N is a divisor of x+y
A MULTIPLE
2.5
61 -67

35. Prime factors of _____ must come in pairs of three.
Prime
Put the coefficient under the radical to get a better approximation
PERFECT CUBES
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.

36. v225=
2.5
41 -43 -47
1.7
15

37. 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.
ODD
The same sign as the base
A PERFECT SQUARE

38. v169=
1. The smallest or largest element 2. The increment 3. The number of items in the set
Either a multiple of N or a non-multiple of N
13
71 -73 -79

39. v2˜
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
2 -3 -5 -7
N is a divisor of x+y
1.4

40. v196=
16
14
PERFECT CUBES
2.5

41. 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
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.

42. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
1.4
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

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

44. The sum of any two primes will be ____ - unless ______.
71 -73 -79
A non-multiple of N.
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

45. The prime factorization of __________ contains only EVEN powers of primes.
14
A PERFECT SQUARE
N is a divisor of x+y
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

46. The prime factorization of a perfect square contains only ______ powers of primes.
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.
Put the coefficient under the radical to get a better approximation
EVEN
The average of an ODD number of consecutive integers will ALWAYS be an integer.

47. Positive integers with only two factors must be ___.
[(last - first) / increment] + 1
Prime
Put the coefficient under the radical to get a better approximation
97

48. v625=
25
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Put the coefficient under the radical to get a better approximation
41 -43 -47

49. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
ONLY the nonnegative root of the numberUNLIKE
1. The smallest or largest element 2. The increment 3. The number of items in the set
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

50. Prime Numbers:0x
A PERFECT SQUARE
2 -3 -5 -7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
EVEN