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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. 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 gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
14
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.

2. Prime Numbers:0x
31 -37
2 -3 -5 -7
The average of the set times the number of elements in the set
16

3. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
ODD
PERFECT CUBES
A PERFECT SQUARE

4. v256=
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
16
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A MULTIPLE

5. In an evenly spaced set - the sum of the terms is equal to ____.
ONLY the nonnegative root of the numberUNLIKE
15
A PERFECT SQUARE
The average of the set times the number of elements in the set

6. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The sum of any two primes will be even - unless one of the two primes is 2.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13
ONLY the nonnegative root of the numberUNLIKE

7. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A non-multiple of N.
Prime factorization
61 -67

8. The formula for finding the number of consecutive multiples in a set is _______.
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 PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
1. The smallest or largest element 2. The increment 3. The number of items in the set

9. Prime Numbers:5x
53 -59
13
The middle number
Never prime

10. For ODD ROOTS - the root has ______.
31 -37
NEVER CONTRADICT ONE ANOTHER
The same sign as the base
83 -89

11. 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.
16
1. The smallest or largest element 2. The increment 3. The number of items in the set
61 -67

12. The PRODUCT of n consecutive integers is divisible by ____.
2.5
A PERFECT SQUARE
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.

13. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD
FACTOR
14

14. Prime Numbers:8x
ONLY the nonnegative root of the numberUNLIKE
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The same sign as the base

15. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A non-multiple of N.
A MULTIPLE
1. The smallest or largest element 2. The increment 3. The number of items in the set
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

16. All perfect squares have a(n) _________ number of total factors.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
23 -29
ODD

17. Any integer with an ODD number of total factors must be _______.
The sum of any two primes will be even - unless one of the two primes is 2.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

18. The prime factorization of a perfect square contains only ______ powers of primes.
Prime
EVEN
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A non-multiple of N.

19. 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

20. 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.
53 -59
Prime factorization
A PERFECT SQUARE

21. The average of an ODD number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The same sign as the base

22. v169=
13
16
31 -37
The average of an ODD number of consecutive integers will ALWAYS be an integer.

23. v2˜
13
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.
1.4
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.

24. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
71 -73 -79
1.7

25. Prime Numbers:1x
61 -67
11 -13 -17 -19
FACTOR
25

26. Prime Numbers:4x
71 -73 -79
15
2 -3 -5 -7
41 -43 -47

27. Prime Numbers:9x
NEVER CONTRADICT ONE ANOTHER
Put the coefficient under the radical to get a better approximation
16
97

28. The two statements in a data sufficiency problem will _______________.
The PRODUCT of n consecutive integers is divisible by n!.
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an ODD number of consecutive integers will ALWAYS be an integer.

29. v625=
The average of an EVEN number of consecutive integers will NEVER be an integer.
EVEN
PERFECT CUBES
25

30. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A MULTIPLE
2 -3 -5 -7
1. The smallest or largest element 2. The increment 3. The number of items in the set

31. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
3·3n = 3^{n+1}
1.4

32. 3n + 3n + 3n = _____ = ______
1.4
31 -37
11 -13 -17 -19
3·3n = 3^{n+1}

33. Prime Numbers:6x
61 -67
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.
41 -43 -47

34. If 2 cannot be one of the primes in the sum - the sum must be _____.
61 -67
Prime
If 2 cannot be one of the primes in the sum - the sum must be even.
[(last - first) / increment] + 1

35. If N is a divisor of x and y - then _______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an EVEN number of consecutive integers will NEVER be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.
N is a divisor of x+y

36. 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 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
53 -59
The sum of any two primes will be even - unless one of the two primes is 2.

37. Prime factors of _____ must come in pairs of three.
A PERFECT SQUARE
2.5
PERFECT CUBES
The average of an ODD number of consecutive integers will ALWAYS be an integer.

38. Positive integers with only two factors must be ___.
61 -67
PERFECT CUBES
Prime
Prime factorization

39. Positive integers with more than two factors are ____.
A PERFECT SQUARE
14
Never prime
31 -37

40. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
97
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 2 cannot be one of the primes in the sum - the sum must be even.

41. v225=
15
14
The sum of any two primes will be even - unless one of the two primes is 2.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

42. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
A non-multiple of N.
FACTOR
2.5

43. In an evenly spaced set - the average can be found by finding ________.
The middle number
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!.
A PERFECT SQUARE

44. N! is _____ of all integers from 1 to N.
A MULTIPLE
13
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

45. v5˜
The middle number
A PERFECT SQUARE
97
2.5

46. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
16
31 -37
23 -29
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

47. v196=
14
23 -29
53 -59
A PERFECT SQUARE

48. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
1.7
25
A PERFECT SQUARE

49. v3˜
The average of an ODD number of consecutive integers will ALWAYS be an integer.
31 -37
97
1.7

50. Prime Numbers:2x
23 -29
A MULTIPLE
ONLY the nonnegative root of the numberUNLIKE
The sum of any two primes will be even - unless one of the two primes is 2.