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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 average of an EVEN number of consecutive integers will ________ be an integer.
23 -29
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
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.

2. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
2.5
FACTOR
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}

3. How to find the sum of consecutive integers:
15
25
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

4. ³v216 =
31 -37
14
ONLY the nonnegative root of the numberUNLIKE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

5. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
3·3n = 3^{n+1}
The same sign as the base
2.5

6. In an evenly spaced set - the average can be found by finding ________.
A PERFECT SQUARE
The middle number
16
The average of an EVEN number of consecutive integers will NEVER be an integer.

7. Prime Numbers:3x
31 -37
Either a multiple of N or a non-multiple of 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.
Prime factorization

8. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
16
1.4
The same sign as the base
ONLY the nonnegative root of the numberUNLIKE

9. Prime factors of _____ must come in pairs of three.
1.4
3·3n = 3^{n+1}
PERFECT CUBES
ODD

10. Prime Numbers:1x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
11 -13 -17 -19
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.

11. In an evenly spaced set - the mean and median are equal to the _____ of _________.
If 2 cannot be one of the primes in the sum - the sum must be even.
16
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE

12. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
11 -13 -17 -19
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 2 cannot be one of the primes in the sum - the sum must be even.

13. The two statements in a data sufficiency problem will _______________.
FACTOR
NEVER CONTRADICT ONE ANOTHER
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
In an evenly spaced set - the average and the median are equal.

14. Positive integers with more than two factors are ____.
The sum of any two primes will be even - unless one of the two primes is 2.
15
Never prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

15. v169=
Never prime
53 -59
A PERFECT SQUARE
13

16. If N is a divisor of x and y - then _______.
31 -37
The average of an EVEN number of consecutive integers will NEVER be an integer.
N is a divisor of x+y
The same sign as the base

17. For ODD ROOTS - the root has ______.
The same sign as the base
ODD
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
PERFECT CUBES

18. 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 PERFECT SQUARE
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
1.7

19. All perfect squares have a(n) _________ number of total factors.
NEVER CONTRADICT ONE ANOTHER
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
2.5

20. v196=
Either a multiple of N or a non-multiple of N
The average of an EVEN number of consecutive integers will NEVER be an integer.
14
Prime factorization

21. If estimating a root with a coefficient - _____ .
15
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.
FACTOR

22. Prime Numbers:6x
23 -29
The sum of any two primes will be even - unless one of the two primes is 2.
61 -67
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. Prime Numbers:5x
Prime factorization
53 -59
The average of an EVEN number of consecutive integers will NEVER be an integer.
13

24. If 2 cannot be one of the primes in the sum - the sum must be _____.
N is a divisor of x+y
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
14

25. v256=
A PERFECT SQUARE
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.
16

26. 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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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}

27. The PRODUCT of n consecutive integers is divisible by ____.
31 -37
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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!.

28. Prime Numbers:4x
16
41 -43 -47
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime factorization

29. 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

30. 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
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
2 -3 -5 -7

31. Prime Numbers:8x
83 -89
25
15
[(last - first) / increment] + 1

32. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A MULTIPLE
1. The smallest or largest element 2. The increment 3. The number of items in the set
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

33. Positive integers with only two factors must be ___.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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
Prime
In an evenly spaced set - the average and the median are equal.

34. In an evenly spaced set - the sum of the terms is equal to ____.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
61 -67
PERFECT CUBES
The average of the set times the number of elements in the set

35. v2˜
Either a multiple of N or a non-multiple of N
13
1.4
16

36. v5˜
13
The same sign as the base
2.5
A non-multiple of N.

37. The prime factorization of __________ contains only EVEN powers of primes.
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
1.7

38. Prime Numbers:2x
PERFECT CUBES
11 -13 -17 -19
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
23 -29

39. v3˜
The same sign as the base
1.7
71 -73 -79
Prime factorization

40. Prime Numbers:7x
Prime
[(last - first) / increment] + 1
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

41. Prime Numbers:0x
2 -3 -5 -7
[(last - first) / increment] + 1
The same sign as the base
FACTOR

42. If the problem states/assumes that a number is an integer - check to see if you can use _______.
41 -43 -47
11 -13 -17 -19
The middle number
Prime factorization

43. The prime factorization of a perfect square contains only ______ powers of primes.
71 -73 -79
41 -43 -47
A PERFECT SQUARE
EVEN

44. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.
The same sign as the base
The middle number

45. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
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
A MULTIPLE
EVEN

46. The average of an ODD number of consecutive integers will ________ be an integer.
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS be an integer.
3·3n = 3^{n+1}
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

47. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
83 -89
97

48. 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
14
EVEN
3·3n = 3^{n+1}

49. 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?
13
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.
2 -3 -5 -7

50. N! is _____ of all integers from 1 to N.
Put the coefficient under the radical to get a better approximation
The PRODUCT of n consecutive integers is divisible by n!.
A MULTIPLE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹