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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 two statements in a data sufficiency problem will _______________.
13
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER
23 -29

2. If 2 cannot be one of the primes in the sum - the sum must be _____.
Never prime
Put the coefficient under the radical to get a better approximation
If 2 cannot be one of the primes in the sum - the sum must be even.
71 -73 -79

3. Positive integers with only two factors must be ___.
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37
Prime
23 -29

4. 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

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5. Prime Numbers:4x
16
41 -43 -47
53 -59
EVEN

6. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
13
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.

7. 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?
16
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 non-multiple of N.
[(last - first) / increment] + 1

8. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ODD
53 -59
The PRODUCT of n consecutive integers is divisible by n!.
ONLY the nonnegative root of the numberUNLIKE

9. v196=
14
25
97
Put the coefficient under the radical to get a better approximation

10. For ODD ROOTS - the root has ______.
The middle number
The same sign as the base
61 -67
If 2 cannot be one of the primes in the sum - the sum must be even.

11. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
23 -29
The average of an ODD number of consecutive integers will ALWAYS be an integer.
FACTOR
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

12. Prime factors of _____ must come in pairs of three.
1.7
PERFECT CUBES
2 -3 -5 -7
The same sign as the base

13. If estimating a root with a coefficient - _____ .
ONLY the nonnegative root of the numberUNLIKE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
EVEN
Put the coefficient under the radical to get a better approximation

14. Any integer with an EVEN number of total factors cannot be ______.
41 -43 -47
1.4
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

15. v5˜
2.5
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE

16. v225=
1.4
15
31 -37
The middle number

17. In an evenly spaced set - the average can be found by finding ________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
3·3n = 3^{n+1}
The middle number
The PRODUCT of n consecutive integers is divisible by n!.

18. Prime Numbers:7x
14
71 -73 -79
15
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

19. Prime Numbers:9x
FACTOR
A PERFECT SQUARE
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

20. The average of an ODD number of consecutive integers will ________ be an integer.
1.4
ONLY the nonnegative root of the numberUNLIKE
2 -3 -5 -7
The average of an ODD number of consecutive integers will ALWAYS be an integer.

21. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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
15

22. The average of an EVEN number of consecutive integers will ________ be an integer.
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
ODD
PERFECT CUBES

23. 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
The average of an ODD number of consecutive integers will ALWAYS be an integer.
FACTOR
71 -73 -79

24. N! is _____ of all integers from 1 to N.
16
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.
41 -43 -47

25. If the problem states/assumes that a number is an integer - check to see if you can use _______.
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 sum of any two primes will be even - unless one of the two primes is 2.
Prime factorization
EVEN

26. In an evenly spaced set - the ____ and the ____ are equal.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1.7
In an evenly spaced set - the average and the median are equal.
2.5

27. 3n + 3n + 3n = _____ = ______
A MULTIPLE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
3·3n = 3^{n+1}
A non-multiple of N.

28. 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
[(last - first) / increment] + 1
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
1. The smallest or largest element 2. The increment 3. The number of items in the set
13

29. If N is a divisor of x and y - then _______.
N is a divisor of x+y
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.
31 -37
71 -73 -79

30. Prime Numbers:6x
71 -73 -79
3·3n = 3^{n+1}
61 -67
A MULTIPLE

31. The prime factorization of __________ contains only EVEN powers of primes.
Either a multiple of N or a non-multiple of N
The average of the set times the number of elements in the set
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE

32. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
[(last - first) / increment] + 1
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

33. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
97
25
A non-multiple of N.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

34. 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
3·3n = 3^{n+1}
11 -13 -17 -19
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Put the coefficient under the radical to get a better approximation

35. v625=
A PERFECT SQUARE
1.4
25
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.

36. Prime Numbers:1x
[(last - first) / increment] + 1
13
11 -13 -17 -19
The average of an EVEN number of consecutive integers will NEVER be an integer.

37. Let N be an integer. If you add two non-multiples of N - the result could be _______.
N is a divisor of x+y
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

38. The sum of any two primes will be ____ - unless ______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The sum of any two primes will be even - unless one of the two primes is 2.
31 -37
A PERFECT SQUARE

39. In an evenly spaced set - the sum of the terms is equal to ____.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
The average of the set times the number of elements in the set
1. The smallest or largest element 2. The increment 3. The number of items in the set

40. How to find the sum of consecutive integers:
2.5
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 non-multiple of N.
The average of the set times the number of elements in the set

41. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

42. The PRODUCT of n consecutive integers is divisible by ____.
25
The PRODUCT of n consecutive integers is divisible by n!.
97
53 -59

43. Prime Numbers:5x
Prime
97
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.
53 -59

44. All perfect squares have a(n) _________ number of total factors.
PERFECT CUBES
1.7
ODD
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

45. The formula for finding the number of consecutive multiples in a set is _______.
15
41 -43 -47
Either a multiple of N or a non-multiple of N
[(last - first) / increment] + 1

46. v169=
Never prime
13
The middle number
Prime factorization

47. Positive integers with more than two factors are ____.
Prime factorization
61 -67
PERFECT CUBES
Never prime

48. Prime Numbers:2x
13
Prime
23 -29
41 -43 -47

49. v3˜
31 -37
1.7
25
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:8x
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
Never prime
83 -89