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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 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.
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
53 -59
[(last - first) / increment] + 1

2. In an evenly spaced set - the average can be found by finding ________.
Put the coefficient under the radical to get a better approximation
The middle number
The sum of any two primes will be even - unless one of the two primes is 2.
EVEN

3. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
31 -37
The same sign as the base
ONLY the nonnegative root of the numberUNLIKE
2 -3 -5 -7

4. v2˜
13
1.4
If 2 cannot be one of the primes in the sum - the sum must be even.
N is a divisor of x+y

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

6. The sum of any two primes will be ____ - unless ______.
NEVER CONTRADICT ONE ANOTHER
[(last - first) / increment] + 1
83 -89
The sum of any two primes will be even - unless one of the two primes is 2.

7. v196=
1.7
The average of the set times the number of elements in the set
PERFECT CUBES
14

8. Prime Numbers:8x
71 -73 -79
83 -89
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.
53 -59

9. 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
Prime
[(last - first) / increment] + 1
Prime factorization

10. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
14
Put the coefficient under the radical to get a better approximation
FACTOR

11. If N is a divisor of x and y - then _______.
N is a divisor of x+y
Prime factorization
PERFECT CUBES
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

12. 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.
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
31 -37

13. Prime Numbers:0x
15
2 -3 -5 -7
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

14. 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.
ODD
53 -59
The sum of any two primes will be even - unless one of the two primes is 2.

15. For ODD ROOTS - the root has ______.
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
The same sign as the base
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

16. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
13
ODD
83 -89

17. The two statements in a data sufficiency problem will _______________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
NEVER CONTRADICT ONE ANOTHER
16
97

18. Prime Numbers:3x
31 -37
13
Either a multiple of N or a non-multiple of N
11 -13 -17 -19

19. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.
31 -37
53 -59

20. Prime Numbers:1x
Either a multiple of N or a non-multiple of N
23 -29
The middle number
11 -13 -17 -19

21. 3n + 3n + 3n = _____ = ______
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.
14
1.7
3·3n = 3^{n+1}

22. Any integer with an ODD number of total factors must be _______.
ODD
PERFECT CUBES
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER

23. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.
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

24. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
Never prime
14
1.4

25. v256=
2.5
16
3·3n = 3^{n+1}
The same sign as the base

26. Prime Numbers:5x
53 -59
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37

27. In an evenly spaced set - the ____ and the ____ are equal.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
1.4
The same sign as the base

28. N! is _____ of all integers from 1 to 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.
A MULTIPLE
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation

29. Prime Numbers:7x
Prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
71 -73 -79
Either a multiple of N or a non-multiple of N

30. Prime Numbers:4x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
11 -13 -17 -19
41 -43 -47
N is a divisor of x+y

31. v625=
ODD
[(last - first) / increment] + 1
25
FACTOR

32. The PRODUCT of n consecutive integers is divisible by ____.
A non-multiple of N.
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.
ODD

33. v5˜
2.5
14
The sum of any two primes will be even - unless one of the two primes is 2.
The PRODUCT of n consecutive integers is divisible by n!.

34. 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.
Either a multiple of N or a non-multiple of N
The sum of any two primes will be even - unless one of the two primes is 2.

35. Any integer with an EVEN number of total factors cannot be ______.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
25

36. 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?
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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

37. Prime Numbers:9x
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER
1.7
97

38. In an evenly spaced set - the sum of the terms is equal to ____.
FACTOR
25
The average of the set times the number of elements in the set
The PRODUCT of n consecutive integers is divisible by n!.

39. If 2 cannot be one of the primes in the sum - the sum must be _____.
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.
The PRODUCT of n consecutive integers is divisible by n!.
61 -67

40. v225=
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.
15
NEVER CONTRADICT ONE ANOTHER
16

41. The prime factorization of __________ contains only EVEN powers of primes.
53 -59
A PERFECT SQUARE
FACTOR
1.4

42. 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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43. Prime factors of _____ must come in pairs of three.
A PERFECT SQUARE
PERFECT CUBES
The middle number
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

44. The formula for finding the number of consecutive multiples in a set is _______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
3·3n = 3^{n+1}
[(last - first) / increment] + 1
A PERFECT SQUARE

45. In an evenly spaced set - the mean and median are equal to the _____ of _________.
71 -73 -79
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.
2.5
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

46. v169=
Prime
13
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

47. 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 sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE
53 -59

48. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime

49. Prime Numbers:6x
61 -67
A non-multiple of N.
Prime
83 -89

50. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
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
16
PERFECT CUBES