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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 ODD number of consecutive integers will ________ be an integer.
13
Put the coefficient under the radical to get a better approximation
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an ODD number of consecutive integers will ALWAYS be an integer.

2. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
N is a divisor of x+y
31 -37
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
41 -43 -47

3. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
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 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 factorization

4. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
97
31 -37
The average of an EVEN number of consecutive integers will NEVER be an integer.

5. 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?
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 same sign as the base
ODD
13

6. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
31 -37
The same sign as the base
ODD
ONLY the nonnegative root of the numberUNLIKE

7. v3˜
53 -59
1.7
13
In an evenly spaced set - the average and the median are equal.

8. The formula for finding the number of consecutive multiples in a set is _______.
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE
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.
[(last - first) / increment] + 1

9. In an evenly spaced set - the sum of the terms is equal to ____.
The average of the set times the number of elements in the set
61 -67
In an evenly spaced set - the average and the median are equal.
41 -43 -47

10. v625=
41 -43 -47
25
Put the coefficient under the radical to get a better approximation
15

11. 3n + 3n + 3n = _____ = ______
2 -3 -5 -7
71 -73 -79
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}

12. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.
ONLY the nonnegative root of the numberUNLIKE

13. v169=
N is a divisor of x+y
14
A PERFECT SQUARE
13

14. 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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
N is a divisor of x+y

15. N! is _____ of all integers from 1 to N.
Prime factorization
A PERFECT SQUARE
The same sign as the base
A MULTIPLE

16. Positive integers with only two factors must be ___.
Prime
71 -73 -79
13
Never prime

17. v5˜
15
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.
N is a divisor of x+y

18. Prime Numbers:6x
Either a multiple of N or a non-multiple of N
61 -67
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set

19. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
[(last - first) / increment] + 1
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE

20. The sum of any two primes will be ____ - unless ______.
53 -59
NEVER CONTRADICT ONE ANOTHER
ONLY the nonnegative root of the numberUNLIKE
The sum of any two primes will be even - unless one of the two primes is 2.

21. Positive integers with more than two factors are ____.
The same sign as the base
Prime
N is a divisor of x+y
Never prime

22. Prime Numbers:2x
23 -29
FACTOR
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.

23. 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

24. The prime factorization of __________ contains only EVEN powers of primes.
2.5
Never 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.
A PERFECT SQUARE

25. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by 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.
Never prime
97

26. Prime Numbers:9x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
53 -59
97

27. 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
EVEN
In an evenly spaced set - the average and the median are equal.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

28. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The sum of any two primes will be even - unless one of the two primes is 2.
Prime factorization
1. The smallest or largest element 2. The increment 3. The number of items in the set
[(last - first) / increment] + 1

29. v2˜
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.4
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

30. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25
The PRODUCT of n consecutive integers is divisible by n!.

31. Prime factors of _____ must come in pairs of three.
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A MULTIPLE
PERFECT CUBES

32. The prime factorization of a perfect square contains only ______ powers of primes.
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}
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
EVEN

33. v196=
N is a divisor of x+y
14
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

34. 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
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. 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 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

35. The two statements in a data sufficiency problem will _______________.
13
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
NEVER CONTRADICT ONE ANOTHER
The sum of any two primes will be even - unless one of the two primes is 2.

36. If 2 cannot be one of the primes in the sum - the sum must be _____.
EVEN
2.5
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime

37. All perfect squares have a(n) _________ number of total factors.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ODD
The average of the set times the number of elements in the set
A PERFECT SQUARE

38. 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
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The same sign as the base
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.

39. If N is a divisor of x and y - then _______.
N is a divisor of x+y
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.
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

40. In an evenly spaced set - the mean and median are equal to the _____ of _________.
A PERFECT SQUARE
PERFECT CUBES
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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

41. In an evenly spaced set - the average can be found by finding ________.
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.
[(last - first) / increment] + 1
Put the coefficient under the radical to get a better approximation
The middle number

42. 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
EVEN
A PERFECT SQUARE
PERFECT CUBES

43. v256=
If 2 cannot be one of the primes in the sum - the sum must be even.
16
2.5
The same sign as the base

44. v225=
15
ODD
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.
13

45. Prime Numbers:1x
A non-multiple of N.
2 -3 -5 -7
11 -13 -17 -19
41 -43 -47

46. Any integer with an ODD number of total factors must be _______.
15
1.4
A PERFECT SQUARE
The same sign as the base

47. ³v216 =
A non-multiple of N.
The PRODUCT of n consecutive integers is divisible by n!.
If 2 cannot be one of the primes in the sum - the sum must be even.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

48. Any integer with an EVEN number of total factors cannot be ______.
97
A PERFECT SQUARE
2.5
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

49. Prime Numbers:4x
FACTOR
41 -43 -47
Never prime
3·3n = 3^{n+1}

50. For ODD ROOTS - the root has ______.
Put the coefficient under the radical to get a better approximation
The same sign as the base
15
ONLY the nonnegative root of the numberUNLIKE