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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:5x
2.5
53 -59
15
A PERFECT SQUARE

2. Prime Numbers:3x
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 -29
Prime factorization
31 -37

3. ³v216 =
The sum of any two primes will be even - unless one of the two primes is 2.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
14

4. In an evenly spaced set - the mean and median are equal to the _____ of _________.
1.7
Prime factorization
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.

5. 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.
ONLY the nonnegative root of the numberUNLIKE
[(last - first) / increment] + 1
Prime factorization

6. v225=
15
2.5
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.

7. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime
15

8. v2˜
A PERFECT SQUARE
1.7
1.4
A non-multiple of N.

9. For ODD ROOTS - the root has ______.
15
The same sign as the base
Prime
3·3n = 3^{n+1}

10. v3˜
Prime factorization
Either a multiple of N or a non-multiple of N
NEVER CONTRADICT ONE ANOTHER
1.7

11. 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
The PRODUCT of n consecutive integers is divisible by n!.
2.5
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

12. If the problem states/assumes that a number is an integer - check to see if you can use _______.
14
The average of the set times the number of elements in the set
Prime factorization
A PERFECT SQUARE

13. Prime Numbers:6x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
61 -67
NEVER CONTRADICT ONE ANOTHER
53 -59

14. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
61 -67
The sum of any two primes will be even - unless one of the two primes is 2.
53 -59

15. 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?
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29
83 -89
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.

16. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
A MULTIPLE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

17. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
The average of the set times the number of elements in the set
NEVER CONTRADICT ONE ANOTHER
Either a multiple of N or a non-multiple of N

18. N! is _____ of all integers from 1 to N.
A MULTIPLE
1.4
1. The smallest or largest element 2. The increment 3. The number of items in the set
Put the coefficient under the radical to get a better approximation

19. Positive integers with only two factors must be ___.
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.
Prime
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.

20. 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.
31 -37
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
15

21. 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

22. 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
The PRODUCT of n consecutive integers is divisible by n!.
25
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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

23. Prime Numbers:8x
If 2 cannot be one of the primes in the sum - the sum must be even.
14
3·3n = 3^{n+1}
83 -89

24. 3n + 3n + 3n = _____ = ______
Either a multiple of N or a non-multiple of N
EVEN
13
3·3n = 3^{n+1}

25. If 2 cannot be one of the primes in the sum - the sum must be _____.
The middle number
If 2 cannot be one of the primes in the sum - the sum must be even.
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
EVEN

26. v5˜
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
2.5
A PERFECT SQUARE

27. v169=
13
2.5
Prime
The same sign as the base

28. 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.
Prime
NEVER CONTRADICT ONE ANOTHER
ONLY the nonnegative root of the numberUNLIKE

29. 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
Put the coefficient under the radical to get a better approximation
53 -59
The average of the set times the number of elements in the set
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

30. The PRODUCT of n consecutive integers is divisible by ____.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
The same sign as the base
The PRODUCT of n consecutive integers is divisible by n!.

31. In an evenly spaced set - the ____ and the ____ are equal.
A PERFECT SQUARE
13
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the average and the median are equal.

32. v625=
The average of the set times the number of elements in the set
25
PERFECT CUBES
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

33. 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.
25
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
FACTOR

34. Positive integers with more than two factors are ____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
14
A MULTIPLE
Never prime

35. Prime Numbers:1x
23 -29
2 -3 -5 -7
11 -13 -17 -19
Prime

36. Prime Numbers:2x
23 -29
ONLY the nonnegative root of the numberUNLIKE
EVEN
25

37. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
NEVER CONTRADICT ONE ANOTHER
97
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
11 -13 -17 -19

38. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
2 -3 -5 -7
PERFECT CUBES

39. The average of an EVEN number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
97
The average of an EVEN number of consecutive integers will NEVER be an integer.
A MULTIPLE

40. The sum of any two primes will be ____ - unless ______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.
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.

41. In an evenly spaced set - the sum of the terms is equal to ____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set
2.5

42. Prime Numbers:4x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
41 -43 -47
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 n consecutive integers is divisible by n if n is odd - but not if n is even.

43. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
61 -67
The average of an EVEN number of consecutive integers will NEVER 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

44. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of the set times the number of elements in the set
Put the coefficient under the radical to get a better approximation
Either a multiple of N or a non-multiple of N
16

45. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
The average of an EVEN number of consecutive integers will NEVER be an integer.
1.7
A PERFECT SQUARE

46. Prime factors of _____ must come in pairs of three.
A PERFECT SQUARE
PERFECT CUBES
11 -13 -17 -19
A PERFECT SQUARE

47. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
NEVER CONTRADICT ONE ANOTHER

48. If N is a divisor of x and y - then _______.
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
The average of the set times the number of elements in the set
N is a divisor of x+y

49. All perfect squares have a(n) _________ number of total factors.
ODD
A PERFECT SQUARE
The average of the set times the number of elements in the set
If 2 cannot be one of the primes in the sum - the sum must be even.

50. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
14
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER