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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 any two primes will be ____ - unless ______.
A PERFECT SQUARE
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

2. v169=
13
If 2 cannot be one of the primes in the sum - the sum must be even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A non-multiple of N.

3. The prime factorization of __________ contains only EVEN powers of primes.
23 -29
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
The average of an EVEN number of consecutive integers will NEVER be an integer.

4. Prime Numbers:9x
97
A non-multiple of N.
N is a divisor of x+y
[(last - first) / increment] + 1

5. v256=
The middle number
In an evenly spaced set - the average and the median are equal.
The same sign as the base
16

6. Prime Numbers:8x
NEVER CONTRADICT ONE ANOTHER
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.
83 -89
2 -3 -5 -7

7. 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.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N

8. v2˜
The sum of any two primes will be even - unless one of the two primes is 2.
31 -37
[(last - first) / increment] + 1
1.4

9. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The same sign as the base
The average of the set times the number of elements in the set
A non-multiple of N.
In an evenly spaced set - the average and the median are equal.

10. Let N be an integer. If you add two non-multiples of N - the result could be _______.
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.
Either a multiple of N or a non-multiple of N
Put the coefficient under the radical to get a better approximation

11. Prime Numbers:7x
25
The average of an EVEN number of consecutive integers will NEVER be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
71 -73 -79

12. ³v216 =
In an evenly spaced set - the average and the median are equal.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The sum of any two primes will be even - unless one of the two primes is 2.
2 -3 -5 -7

13. v625=
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.
EVEN
25
41 -43 -47

14. If the problem states/assumes that a number is an integer - check to see if you can use _______.
23 -29
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime factorization
N is a divisor of x+y

15. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
41 -43 -47
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
The middle number

16. Prime Numbers:6x
14
16
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
61 -67

17. 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.
NEVER CONTRADICT ONE ANOTHER
In an evenly spaced set - the average and the median are equal.
15

18. N! is _____ of all integers from 1 to N.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
A MULTIPLE

19. Prime factors of _____ must come in pairs of three.
EVEN
PERFECT CUBES
25
2 -3 -5 -7

20. 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 same sign as the base
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 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

21. 3n + 3n + 3n = _____ = ______
FACTOR
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}
14

22. If estimating a root with a coefficient - _____ .
A PERFECT SQUARE
Prime
3·3n = 3^{n+1}
Put the coefficient under the radical to get a better approximation

23. v225=
15
16
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.

24. v3˜
83 -89
Either a multiple of N or a non-multiple of N
1.7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

25. 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.
14
PERFECT CUBES
A PERFECT SQUARE

26. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Never prime
83 -89
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

27. The two statements in a data sufficiency problem will _______________.
1.7
NEVER CONTRADICT ONE ANOTHER
Never prime
PERFECT CUBES

28. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
2.5
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2 -3 -5 -7
ONLY the nonnegative root of the numberUNLIKE

29. Prime Numbers:4x
NEVER CONTRADICT ONE ANOTHER
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N
41 -43 -47

30. For ODD ROOTS - the root has ______.
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of the set times the number of elements in the set
Put the coefficient under the radical to get a better approximation

31. Positive integers with only two factors must be ___.
3·3n = 3^{n+1}
Put the coefficient under the radical to get a better approximation
Prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.

32. Positive integers with more than two factors are ____.
A PERFECT SQUARE
N is a divisor of x+y
Never prime
The average of the set times the number of elements in the set

33. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
[(last - first) / increment] + 1
The middle number
The average of an ODD number of consecutive integers will ALWAYS be an integer.

34. Prime Numbers:2x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
23 -29
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.
31 -37

35. 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?
1.7
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
A non-multiple of N.

36. Prime Numbers:3x
2 -3 -5 -7
The average of the set times the number of elements in the set
31 -37
53 -59

37. The formula for finding the number of consecutive multiples in a set is _______.
23 -29
[(last - first) / increment] + 1
Prime factorization
41 -43 -47

38. v196=
61 -67
14
25
ODD

39. The prime factorization of a perfect square contains only ______ powers of primes.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN
FACTOR

40. If N is a divisor of x and y - then _______.
16
N is a divisor of x+y
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19

41. The PRODUCT of n consecutive integers is divisible by ____.
3·3n = 3^{n+1}
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set
A PERFECT SQUARE

42. Prime Numbers:5x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
53 -59
1.7

43. Prime Numbers:1x
ONLY the nonnegative root of the numberUNLIKE
11 -13 -17 -19
The PRODUCT of n consecutive integers is divisible by n!.
The same sign as the base

44. 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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45. Prime Numbers:0x
If 2 cannot be one of the primes in the sum - the sum must be even.
2 -3 -5 -7
EVEN
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.

46. 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.
The middle number
[(last - first) / increment] + 1
ODD

47. All perfect squares have a(n) _________ number of total factors.
1.4
97
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.
ODD

48. Any integer with an EVEN number of total factors cannot be ______.
25
A PERFECT SQUARE
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

49. How to find the sum of consecutive integers:
A PERFECT SQUARE
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.
Prime

50. v5˜
2.5
Either a multiple of N or a non-multiple of N
31 -37
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.