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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. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
16
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

2. v2˜
Never prime
The average of the set times the number of elements in the set
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.

3. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
NEVER CONTRADICT ONE ANOTHER

4. Prime Numbers:4x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The sum of any two primes will be even - unless one of the two primes is 2.
41 -43 -47
A PERFECT SQUARE

5. All perfect squares have a(n) _________ number of total factors.
Prime
ODD
A PERFECT SQUARE
31 -37

6. The sum of any two primes will be ____ - unless ______.
FACTOR
16
The sum of any two primes will be even - unless one of the two primes is 2.
PERFECT CUBES

7. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
A PERFECT SQUARE

8. Prime Numbers:6x
1.7
Never prime
61 -67
The same sign as the base

9. For ODD ROOTS - the root has ______.
15
The average of an EVEN number of consecutive integers will NEVER be an integer.
23 -29
The same sign as the base

10. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
16

11. v169=
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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 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

12. Prime Numbers:9x
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 an ODD number of consecutive integers will ALWAYS be an integer.
2 -3 -5 -7
97

13. v225=
A non-multiple of N.
The middle number
15
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. Prime Numbers:0x
31 -37
13
1.4
2 -3 -5 -7

15. 3n + 3n + 3n = _____ = ______
2.5
A PERFECT SQUARE
3·3n = 3^{n+1}
1. The smallest or largest element 2. The increment 3. The number of items in the set

16. The prime factorization of a perfect square contains only ______ powers of primes.
23 -29
EVEN
In an evenly spaced set - the average and the median are equal.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

17. 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?
Put the coefficient under the radical to get a better approximation
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.
61 -67
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.

18. ³v216 =
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.
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.

19. v256=
16
2 -3 -5 -7
NEVER CONTRADICT ONE ANOTHER
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.

20. Prime Numbers:1x
11 -13 -17 -19
25
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

21. In an evenly spaced set - the average can be found by finding ________.
EVEN
The middle number
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE

22. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
Prime factorization
Prime
A non-multiple of N.
EVEN

23. Let N be an integer. If you add two non-multiples of N - the result could be _______.
71 -73 -79
Either a multiple of N or a non-multiple of N
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
2.5

24. If 2 cannot be one of the primes in the sum - the sum must be _____.
Either a multiple of N or a non-multiple of N
The middle number
15
If 2 cannot be one of the primes in the sum - the sum must be even.

25. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
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.
1.7
14

26. 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
97

27. 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

28. v196=
2 -3 -5 -7
14
The sum of any two primes will be even - unless one of the two primes is 2.
3·3n = 3^{n+1}

29. The two statements in a data sufficiency problem will _______________.
PERFECT CUBES
NEVER CONTRADICT ONE ANOTHER
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.
16

30. v3˜
[(last - first) / increment] + 1
1.7
16
31 -37

31. Prime Numbers:8x
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.
83 -89
A non-multiple of N.
1. The smallest or largest element 2. The increment 3. The number of items in the set

32. Positive integers with only two factors must be ___.
A PERFECT SQUARE
Prime
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE

33. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ONLY the nonnegative root of the numberUNLIKE
83 -89

34. The formula for finding the number of consecutive multiples in a set is _______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
If 2 cannot be one of the primes in the sum - the sum must be even.
[(last - first) / increment] + 1
The same sign as the base

35. In an evenly spaced set - the ____ and the ____ are equal.
The PRODUCT of n consecutive integers is divisible by n!.
Prime factorization
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the average and the median are equal.

36. The average of an ODD number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN
2 -3 -5 -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.

37. The average of an EVEN number of consecutive integers will ________ be an integer.
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 EVEN number of consecutive integers will NEVER be an integer.
The average of the set times the number of elements in the set
1.7

38. Any integer with an ODD number of total factors must be _______.
1.4
A PERFECT SQUARE
Prime
Prime factorization

39. 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
In an evenly spaced set - the average and the median are equal.
13
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The same sign as the base

40. The prime factorization of __________ contains only EVEN powers of primes.
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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ONLY the nonnegative root of the numberUNLIKE

41. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
25
If 2 cannot be one of the primes in the sum - the sum must be even.
FACTOR
ONLY the nonnegative root of the numberUNLIKE

42. Prime Numbers:3x
If 2 cannot be one of the primes in the sum - the sum must be even.
13
41 -43 -47
31 -37

43. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

44. v5˜
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
11 -13 -17 -19
The average of the set times the number of elements in the set
2.5

45. In an evenly spaced set - the sum of the terms is equal to ____.
EVEN
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
71 -73 -79

46. Prime Numbers:5x
If 2 cannot be one of the primes in the sum - the sum must be even.
71 -73 -79
23 -29
53 -59

47. Positive integers with more than two factors are ____.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Never prime
Prime
The average of the set times the number of elements in the set

48. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of an EVEN number of consecutive integers will NEVER be an integer.
1.4
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

49. N! is _____ of all integers from 1 to N.
A PERFECT SQUARE
The middle number
A MULTIPLE
16

50. v625=
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.
A PERFECT SQUARE
25
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.