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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. Prime Numbers:0x
Prime factorization
2 -3 -5 -7
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47

2. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97
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.

3. 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 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.
In an evenly spaced set - the average and the median are equal.

4. Positive integers with more than two factors are ____.
NEVER CONTRADICT ONE ANOTHER
Never prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.

5. In an evenly spaced set - the ____ and the ____ are equal.
Prime factorization
In an evenly spaced set - the average and the median are equal.
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.
1.4

6. Prime Numbers:8x
83 -89
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.
3·3n = 3^{n+1}

7. The average of an ODD number of consecutive integers will ________ be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
71 -73 -79
The average of an EVEN number of consecutive integers will NEVER be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

8. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
The middle number
97
PERFECT CUBES

9. The formula for finding the number of consecutive multiples in a set is _______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If 2 cannot be one of the primes in the sum - the sum must be even.
[(last - first) / increment] + 1
A PERFECT SQUARE

10. If estimating a root with a coefficient - _____ .
61 -67
The average of an EVEN number of consecutive integers will NEVER be an integer.
A non-multiple of N.
Put the coefficient under the radical to get a better approximation

11. 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
23 -29
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 PRODUCT of n consecutive integers is divisible by n!.
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. 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

13. v256=
16
Prime
PERFECT CUBES
1.4

14. Let N be an integer. If you add two non-multiples of N - the result could be _______.
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Either a multiple of N or a non-multiple of N
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.

15. N! is _____ of all integers from 1 to N.
41 -43 -47
A MULTIPLE
1.7
PERFECT CUBES

16. 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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
25
3·3n = 3^{n+1}

17. v2˜
1.4
ONLY the nonnegative root of the numberUNLIKE
The sum of any two primes will be even - unless one of the two primes is 2.
15

18. v196=
11 -13 -17 -19
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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

19. Prime Numbers:2x
If 2 cannot be one of the primes in the sum - the sum must be even.
23 -29
In an evenly spaced set - the average and the median are equal.
NEVER CONTRADICT ONE ANOTHER

20. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
FACTOR
1.4
If 2 cannot be one of the primes in the sum - the sum must be even.

21. In an evenly spaced set - the sum of the terms is equal to ____.
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
1.4
ONLY the nonnegative root of the numberUNLIKE

22. For ODD ROOTS - the root has ______.
71 -73 -79
The same sign as the base
The middle number
Prime

23. Any integer with an EVEN number of total factors cannot be ______.
41 -43 -47
N is a divisor of x+y
The same sign as the base
A PERFECT SQUARE

24. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
ODD
71 -73 -79
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.

25. 3n + 3n + 3n = _____ = ______
A non-multiple of N.
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.
The PRODUCT of n consecutive integers is divisible by n!.

26. v5˜
2.5
83 -89
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

27. Prime Numbers:3x
83 -89
ODD
N is a divisor of x+y
31 -37

28. Prime Numbers:9x
97
If 2 cannot be one of the primes in the sum - the sum must be even.
41 -43 -47
83 -89

29. In an evenly spaced set - the mean and median are equal to the _____ of _________.
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

30. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
1.4
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A MULTIPLE
The average of an EVEN number of consecutive integers will NEVER be an integer.

31. The average of an EVEN number of consecutive integers will ________ be an integer.
71 -73 -79
Put the coefficient under the radical to get a better approximation
A non-multiple of N.
The average of an EVEN number of consecutive integers will NEVER be an integer.

32. 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.
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.

33. The prime factorization of a perfect square contains only ______ powers of primes.
The middle number
EVEN
Prime
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.

34. 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
Prime factorization
The average of an EVEN number of consecutive integers will NEVER 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.

35. All perfect squares have a(n) _________ number of total factors.
ODD
71 -73 -79
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29

36. 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
1.4
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
97

37. v225=
15
83 -89
Prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

38. Prime Numbers:4x
25
NEVER CONTRADICT ONE ANOTHER
14
41 -43 -47

39. ³v216 =
Prime
61 -67
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

40. Prime Numbers:1x
A MULTIPLE
EVEN
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19

41. Prime Numbers:7x
The sum of any two primes will be even - unless one of the two primes is 2.
71 -73 -79
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.
ODD

42. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
In an evenly spaced set - the average and the median are equal.
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.
1.7

43. How to find the sum of consecutive integers:
NEVER CONTRADICT ONE ANOTHER
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
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.

44. The prime factorization of __________ contains only EVEN powers of primes.
3·3n = 3^{n+1}
A PERFECT SQUARE
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.
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.

45. Prime Numbers:5x
Either a multiple of N or a non-multiple of N
ONLY the nonnegative root of the numberUNLIKE
ODD
53 -59

46. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
15
53 -59
The same sign as the base

47. In an evenly spaced set - the average can be found by finding ________.
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 middle number
3·3n = 3^{n+1}
The sum of any two primes will be even - unless one of the two primes is 2.

48. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
53 -59
ONLY the nonnegative root of the numberUNLIKE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
PERFECT CUBES

49. Prime Numbers:6x
NEVER CONTRADICT ONE ANOTHER
61 -67
Prime factorization
EVEN

50. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
1.4
In an evenly spaced set - the average and the median are equal.
31 -37