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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. If N is a divisor of x and y - then _______.
N is a divisor of x+y
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.
1.4

2. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
3·3n = 3^{n+1}
ONLY the nonnegative root of the numberUNLIKE
EVEN

3. Prime Numbers:0x
2 -3 -5 -7
Never prime
11 -13 -17 -19
N is a divisor of x+y

4. 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
1.4
61 -67
The same sign as the base

5. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
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

6. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The same sign as the base
ODD

7. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
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 non-multiple of N.
71 -73 -79
FACTOR

8. Positive integers with only two factors must be ___.
2 -3 -5 -7
The same sign as the base
EVEN
Prime

9. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The PRODUCT of n consecutive integers is divisible by n!.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE

10. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
The same sign as the base
PERFECT CUBES
FACTOR

11. Prime Numbers:6x
61 -67
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.
ONLY the nonnegative root of the numberUNLIKE

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.
ODD
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
23 -29

13. N! is _____ of all integers from 1 to N.
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.
2 -3 -5 -7
A MULTIPLE

14. The two statements in a data sufficiency problem will _______________.
The sum of any two primes will be even - unless one of the two primes is 2.
NEVER CONTRADICT ONE ANOTHER
Prime factorization
97

15. v5˜
2.5
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.
The PRODUCT of n consecutive integers is divisible by n!.

16. Prime Numbers:7x
71 -73 -79
N is a divisor of x+y
25
41 -43 -47

17. v3˜
Prime
2.5
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.7

18. 3n + 3n + 3n = _____ = ______
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
41 -43 -47
3·3n = 3^{n+1}

19. How to find the sum of consecutive integers:
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.
The average of an EVEN number of consecutive integers will NEVER be an integer.
41 -43 -47

20. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The average of the set times the number of elements in the set
1.7
[(last - first) / increment] + 1
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

21. If estimating a root with a coefficient - _____ .
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
Put the coefficient under the radical to get a better approximation
16

22. v625=
53 -59
A PERFECT SQUARE
25
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

23. Prime Numbers:3x
23 -29
ODD
31 -37
The same sign as the base

24. v196=
A MULTIPLE
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set
14

25. Prime factors of _____ must come in pairs of three.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
PERFECT CUBES
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

26. v2˜
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
FACTOR
If 2 cannot be one of the primes in the sum - the sum must be even.

27. v169=
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.
If 2 cannot be one of the primes in the sum - the sum must be even.
13

28. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
1.7
The average of an ODD number of consecutive integers will ALWAYS be an integer.
25

29. All perfect squares have a(n) _________ number of total factors.
ODD
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

30. 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
1.7
Prime factorization
Either a multiple of N or a non-multiple of N
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

31. Positive integers with more than two factors are ____.
41 -43 -47
1.4
97
Never prime

32. For ODD ROOTS - the root has ______.
15
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
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

33. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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 -29
97
ONLY the nonnegative root of the numberUNLIKE

34. Let N be an integer. If you add two non-multiples of N - the result could be _______.
15
Either a multiple of N or a non-multiple of N
Put the coefficient under the radical to get a better approximation
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

35. v256=
16
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
1. The smallest or largest element 2. The increment 3. The number of items in the set

36. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
PERFECT CUBES
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.

37. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
23 -29
Prime factorization
ODD

38. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
53 -59
ODD
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE

39. The prime factorization of a perfect square contains only ______ powers of primes.
FACTOR
31 -37
EVEN
Prime

40. In an evenly spaced set - the average can be found by finding ________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The middle number
A PERFECT SQUARE
2.5

41. Prime Numbers:9x
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.
15
41 -43 -47
97

42. The prime factorization of __________ contains only EVEN powers of primes.
The same sign as the base
PERFECT CUBES
A PERFECT SQUARE
3·3n = 3^{n+1}

43. 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

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44. The average of an ODD number of consecutive integers will ________ be an integer.
NEVER CONTRADICT ONE ANOTHER
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.

45. The sum of any two primes will be ____ - unless ______.
Never prime
14
The sum of any two primes will be even - unless one of the two primes is 2.
83 -89

46. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 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.
A PERFECT SQUARE
31 -37

47. Prime Numbers:2x
23 -29
1.7
Prime
71 -73 -79

48. v225=
2.5
15
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
PERFECT CUBES

49. Prime Numbers:1x
71 -73 -79
14
The sum of any two primes will be even - unless one of the two primes is 2.
11 -13 -17 -19

50. Prime Numbers:4x
41 -43 -47
If 2 cannot be one of the primes in the sum - the sum must be even.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
In an evenly spaced set - the average and the median are equal.