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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. v169=
3·3n = 3^{n+1}
13
Prime
1.4

2. Prime Numbers:4x
15
The average of an ODD number of consecutive integers will ALWAYS be an integer.
41 -43 -47
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.

3. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
The middle number
83 -89
A PERFECT SQUARE

4. The prime factorization of a perfect square contains only ______ powers of primes.
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.
Put the coefficient under the radical to get a better approximation
13
EVEN

5. 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
PERFECT CUBES
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

6. Positive integers with only two factors must be ___.
15
A PERFECT SQUARE
Prime
61 -67

7. N! is _____ of all integers from 1 to N.
71 -73 -79
A MULTIPLE
83 -89
Either a multiple of N or a non-multiple of N

8. The PRODUCT of n consecutive integers is divisible by ____.
25
NEVER CONTRADICT ONE ANOTHER
The PRODUCT of n consecutive integers is divisible by n!.
Prime

9. 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
23 -29
2.5

10. 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 n consecutive integers is divisible by n if n is odd - but not if n is even.
Prime
A PERFECT SQUARE

11. Prime Numbers:7x
23 -29
FACTOR
A PERFECT SQUARE
71 -73 -79

12. If estimating a root with a coefficient - _____ .
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
The average of the set times the number of elements in the set
[(last - first) / increment] + 1

13. v225=
53 -59
A PERFECT SQUARE
A non-multiple of N.
15

14. The average of an EVEN number of consecutive integers will ________ be an integer.
[(last - first) / increment] + 1
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
11 -13 -17 -19

15. v625=
16
[(last - first) / increment] + 1
25
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

16. Prime Numbers:8x
83 -89
A PERFECT SQUARE
41 -43 -47
The sum of any two primes will be even - unless one of the two primes is 2.

17. v196=
14
The middle number
FACTOR
Either a multiple of N or a non-multiple of N

18. v5˜
N is a divisor of x+y
2.5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.4

19. 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.
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
3·3n = 3^{n+1}

20. 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

21. If N is a divisor of x and y - then _______.
N is a divisor of x+y
53 -59
A MULTIPLE
PERFECT CUBES

22. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.

23. v256=
15
16
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

24. Any integer with an EVEN number of total factors cannot be ______.
Never prime
1.7
A PERFECT SQUARE
2.5

25. 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
25
Prime
1.4

26. Prime Numbers:6x
41 -43 -47
Put the coefficient under the radical to get a better approximation
The PRODUCT of n consecutive integers is divisible by n!.
61 -67

27. In an evenly spaced set - the ____ and the ____ are equal.
14
1.7
In an evenly spaced set - the average and the median are equal.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

28. Prime Numbers:2x
23 -29
41 -43 -47
97
NEVER CONTRADICT ONE ANOTHER

29. In an evenly spaced set - the sum of the terms is equal to ____.
A non-multiple of N.
Put the coefficient under the radical to get a better approximation
The average of the set times the number of elements in the set
The sum of any two primes will be even - unless one of the two primes is 2.

30. Prime Numbers:3x
EVEN
Prime
83 -89
31 -37

31. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
16
A non-multiple of N.
15

32. Prime factors of _____ must come in pairs of three.
A PERFECT SQUARE
PERFECT CUBES
Never prime
The average of an EVEN number of consecutive integers will NEVER be an integer.

33. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
53 -59
61 -67
EVEN
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

34. 3n + 3n + 3n = _____ = ______
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.
25
3·3n = 3^{n+1}
EVEN

35. Prime Numbers:1x
31 -37
ODD
11 -13 -17 -19
61 -67

36. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
97
A non-multiple of N.

37. 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?
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.
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.
23 -29

38. In an evenly spaced set - the average can be found by finding ________.
The middle number
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
PERFECT CUBES

39. All perfect squares have a(n) _________ number of total factors.
NEVER CONTRADICT ONE ANOTHER
ODD
2.5
A non-multiple of N.

40. The average of an ODD number of consecutive integers will ________ be an integer.
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.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The PRODUCT of n consecutive integers is divisible by n!.

41. Any integer with an ODD number of total factors must be _______.
EVEN
The average of the set times the number of elements in the set
A PERFECT SQUARE
41 -43 -47

42. Prime Numbers:5x
1. The smallest or largest element 2. The increment 3. The number of items in the set
23 -29
83 -89
53 -59

43. Positive integers with more than two factors are ____.
3·3n = 3^{n+1}
A non-multiple of N.
FACTOR
Never prime

44. The two statements in a data sufficiency problem will _______________.
3·3n = 3^{n+1}
NEVER CONTRADICT ONE ANOTHER
13
15

45. 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.
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
23 -29

46. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
31 -37
In an evenly spaced set - the average and the median are equal.
ONLY the nonnegative root of the numberUNLIKE
23 -29

47. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
EVEN
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.7
The PRODUCT of n consecutive integers is divisible by n!.

48. v3˜
EVEN
1.7
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.
Either a multiple of N or a non-multiple of N

49. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
A PERFECT SQUARE
FACTOR
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.
A PERFECT SQUARE

50. 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
N is a divisor of x+y
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.