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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. ³v216 =
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.
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation

2. In an evenly spaced set - the sum of the terms is equal to ____.
2.5
NEVER CONTRADICT ONE ANOTHER
ODD
The average of the set times the number of elements in the set

3. Prime Numbers:6x
Prime
A PERFECT SQUARE
31 -37
61 -67

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.
83 -89
13
2 -3 -5 -7

5. In an evenly spaced set - the ____ and the ____ are equal.
ODD
N is a divisor of x+y
In an evenly spaced set - the average and the median are equal.
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.

6. 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.
14
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

7. Prime Numbers:1x
2.5
11 -13 -17 -19
The PRODUCT of n consecutive integers is divisible by n!.
ONLY the nonnegative root of the numberUNLIKE

8. Prime factors of _____ must come in pairs of three.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
PERFECT CUBES
2 -3 -5 -7
ODD

9. 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

10. Prime Numbers:0x
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
FACTOR
2 -3 -5 -7

11. Prime Numbers:5x
53 -59
The same sign as the base
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.
23 -29

12. If estimating a root with a coefficient - _____ .
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
FACTOR
3·3n = 3^{n+1}

13. Prime Numbers:3x
31 -37
14
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER

14. v196=
14
2 -3 -5 -7
Never prime
ONLY the nonnegative root of the numberUNLIKE

15. For ODD ROOTS - the root has ______.
The average of the set times the number of elements in the set
The same sign as the base
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
15

16. Prime Numbers:8x
25
83 -89
23 -29
A PERFECT SQUARE

17. The two statements in a data sufficiency problem will _______________.
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
1.4
FACTOR

18. N! is _____ of all integers from 1 to N.
A PERFECT SQUARE
A MULTIPLE
[(last - first) / increment] + 1
The PRODUCT of n consecutive integers is divisible by n!.

19. All perfect squares have a(n) _________ number of total factors.
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES
ODD

20. v625=
ONLY the nonnegative root of the numberUNLIKE
25
97
Either a multiple of N or a non-multiple of N

21. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
Never prime
Prime
71 -73 -79

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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
83 -89
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25

23. 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.
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set
41 -43 -47

24. Positive integers with more than two factors are ____.
A PERFECT SQUARE
Never prime
53 -59
25

25. The average of an EVEN number of consecutive integers will ________ be an integer.
ODD
FACTOR
Never prime
The average of an EVEN number of consecutive integers will NEVER be an integer.

26. 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.
41 -43 -47
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
N is a divisor of x+y

27. If the problem states/assumes that a number is an integer - check to see if you can use _______.
NEVER CONTRADICT ONE ANOTHER
Prime factorization
EVEN
71 -73 -79

28. Prime Numbers:9x
53 -59
97
A PERFECT SQUARE
EVEN

29. v3˜
97
ODD
1.7
In an evenly spaced set - the average and the median are equal.

30. Prime Numbers:4x
14
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
41 -43 -47
A MULTIPLE

31. 3n + 3n + 3n = _____ = ______
PERFECT CUBES
3·3n = 3^{n+1}
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.
53 -59

32. Let N be an integer. If you add two non-multiples of N - the result could be _______.
A MULTIPLE
Either a multiple of N or a non-multiple of N
16
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.

33. v2˜
The PRODUCT of n consecutive integers is divisible by n!.
1.4
A MULTIPLE
Prime factorization

34. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Never prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Either a multiple of N or a non-multiple of 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.

35. If 2 cannot be one of the primes in the sum - the sum must be _____.
16
If 2 cannot be one of the primes in the sum - the sum must be even.
97
A PERFECT SQUARE

36. Prime Numbers:7x
25
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
71 -73 -79
EVEN

37. The prime factorization of __________ contains only EVEN powers of primes.
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 any two primes will be even - unless one of the two primes is 2.
Prime
A PERFECT SQUARE

38. Any integer with an EVEN number of total factors cannot be ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
If 2 cannot be one of the primes in the sum - the sum must be even.
97
A PERFECT SQUARE

39. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A non-multiple of N.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
PERFECT CUBES

40. Positive integers with only two factors must be ___.
A non-multiple of N.
31 -37
71 -73 -79
Prime

41. The prime factorization of a perfect square contains only ______ powers of primes.
In an evenly spaced set - the average and the median are equal.
ODD
EVEN
A non-multiple of N.

42. v169=
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.
13
Either a multiple of N or a non-multiple of N
2.5

43. In an evenly spaced set - the average can be found by finding ________.
1.7
1. The smallest or largest element 2. The increment 3. The number of items in the set
The middle number
61 -67

44. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
71 -73 -79
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.
Either a multiple of N or a non-multiple of N

45. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
N is a divisor of x+y
NEVER CONTRADICT ONE ANOTHER
ONLY the nonnegative root of the numberUNLIKE
The same sign as the base

46. v256=
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.
16
ONLY the nonnegative root of the numberUNLIKE
1.7

47. The sum of any two primes will be ____ - unless ______.
41 -43 -47
The sum of any two primes will be even - unless one of the two primes is 2.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
15

48. The PRODUCT of n consecutive integers is divisible by ____.
EVEN
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime

49. v5˜
The average of the set times the number of elements in the set
2.5
1. The smallest or largest element 2. The increment 3. The number of items 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

50. In an evenly spaced set - the mean and median are equal to the _____ of _________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.
23 -29
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.