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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
23 -29
53 -59
The average of the set times the number of elements in the set
83 -89

2. If N is a divisor of x and y - then _______.
16
N is a divisor of x+y
The PRODUCT of n consecutive integers is divisible by n!.
1.4

3. v625=
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
25
The sum of any two primes will be even - unless one of the two primes is 2.
The average of an EVEN number of consecutive integers will NEVER be an integer.

4. For ODD ROOTS - the root has ______.
The same sign as the base
83 -89
13
PERFECT CUBES

5. N! is _____ of all integers from 1 to N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE

6. v169=
15
13
41 -43 -47
A PERFECT SQUARE

7. The prime factorization of a perfect square contains only ______ powers of primes.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
N is a divisor of x+y
EVEN
2.5

8. ³v216 =
ONLY the nonnegative root of the numberUNLIKE
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

9. v3˜
1.7
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
1.4

10. 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
1.7
FACTOR
If 2 cannot be one of the primes in the sum - the sum must be even.

11. Prime Numbers:3x
1.7
97
31 -37
A PERFECT SQUARE

12. 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
A PERFECT SQUARE
23 -29
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.

13. Prime Numbers:1x
EVEN
FACTOR
The middle number
11 -13 -17 -19

14. The sum of any two primes will be ____ - unless ______.
15
41 -43 -47
The sum of any two primes will be even - unless one of the two primes is 2.
A non-multiple of N.

15. In an evenly spaced set - the sum of the terms is equal to ____.
A PERFECT SQUARE
The average of the set times the number of elements in the set
A non-multiple of N.
The same sign as the base

16. Any integer with an ODD number of total factors must be _______.
16
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
1.4

17. v5˜
1. The smallest or largest element 2. The increment 3. The number of items in the set
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19
2.5

18. Positive integers with more than two factors are ____.
NEVER CONTRADICT ONE ANOTHER
71 -73 -79
Never prime
1.7

19. 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.
41 -43 -47
97
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

20. In an evenly spaced set - the average can be found by finding ________.
The middle number
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47
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.

21. If estimating a root with a coefficient - _____ .
PERFECT CUBES
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.
2 -3 -5 -7

22. v2˜
Prime factorization
EVEN
1.4
23 -29

23. v196=
14
71 -73 -79
The middle number
The average of an ODD number of consecutive integers will ALWAYS be an integer.

24. 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
A MULTIPLE
ONLY the nonnegative root of the numberUNLIKE
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
A PERFECT SQUARE

25. 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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26. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
The middle number
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

27. Prime Numbers:0x
2 -3 -5 -7
71 -73 -79
61 -67
N is a divisor of x+y

28. Prime Numbers:4x
15
41 -43 -47
The average of the set times the number of elements in the set
N is a divisor of x+y

29. Prime Numbers:8x
The middle number
83 -89
PERFECT CUBES
Never prime

30. Any integer with an EVEN number of total factors cannot be ______.
3·3n = 3^{n+1}
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
The average of an ODD number of consecutive integers will ALWAYS be an integer.

31. Prime Numbers:6x
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
1.7
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.
61 -67

32. v256=
16
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
2 -3 -5 -7
1.7

33. The prime factorization of __________ contains only EVEN powers of primes.
15
Prime factorization
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE

34. How to find the sum of consecutive integers:
25
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
97

35. 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.
61 -67
13
2 -3 -5 -7

36. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
11 -13 -17 -19
1. The smallest or largest element 2. The increment 3. The number of items in the set
83 -89
A PERFECT SQUARE

37. In an evenly spaced set - the ____ and the ____ are equal.
83 -89
The sum of any two primes will be even - unless one of the two primes is 2.
The average of an EVEN number of consecutive integers will NEVER be an integer.
In an evenly spaced set - the average and the median are equal.

38. The formula for finding the number of consecutive multiples in a set is _______.
23 -29
[(last - first) / increment] + 1
41 -43 -47
Either a multiple of N or a non-multiple of N

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

40. The PRODUCT of n consecutive integers is divisible by ____.
A PERFECT SQUARE
Prime
The PRODUCT of n consecutive integers is divisible by n!.
71 -73 -79

41. Positive integers with only two factors must be ___.
Prime
The average of the set times the number of elements in the set
1.4
The sum of any two primes will be even - unless one of the two primes is 2.

42. Prime factors of _____ must come in pairs of three.
The PRODUCT of n consecutive integers is divisible by n!.
23 -29
PERFECT CUBES
25

43. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
11 -13 -17 -19
The average of an EVEN number of consecutive integers will NEVER be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The middle number

44. Prime Numbers:2x
EVEN
A non-multiple of N.
23 -29
If 2 cannot be one of the primes in the sum - the sum must be even.

45. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
23 -29
FACTOR
97

46. 3n + 3n + 3n = _____ = ______
1.4
Never prime
3·3n = 3^{n+1}
If 2 cannot be one of the primes in the sum - the sum must be even.

47. Prime Numbers:7x
Prime
61 -67
71 -73 -79
2 -3 -5 -7

48. 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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE
97

49. The two statements in a data sufficiency problem will _______________.
14
PERFECT CUBES
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
NEVER CONTRADICT ONE ANOTHER

50. 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.
2.5
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7