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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. v5˜
2.5
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE

2. If 2 cannot be one of the primes in the sum - the sum must be _____.
83 -89
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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 2 cannot be one of the primes in the sum - the sum must be even.

3. v196=
2.5
14
15
13

4. Any integer with an ODD number of total factors must be _______.
Put the coefficient under the radical to get a better approximation
Never prime
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE

5. Prime Numbers:8x
53 -59
ODD
23 -29
83 -89

6. Positive integers with more than two factors are ____.
25
Never prime
41 -43 -47
14

7. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
ONLY the nonnegative root of the numberUNLIKE
A MULTIPLE
A non-multiple of N.

8. Prime Numbers:2x
The PRODUCT of n consecutive integers is divisible by n!.
23 -29
Never prime
Put the coefficient under the radical to get a better approximation

9. v256=
23 -29
EVEN
ODD
16

10. Prime Numbers:4x
A MULTIPLE
A PERFECT SQUARE
41 -43 -47
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

11. How to find the sum of consecutive integers:
NEVER CONTRADICT ONE ANOTHER
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.
ONLY the nonnegative root of the numberUNLIKE
N is a divisor of x+y

12. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
Either a multiple of N or a non-multiple of N
1. The smallest or largest element 2. The increment 3. The number of items in the set

13. v625=
13
14
3·3n = 3^{n+1}
25

14. Prime Numbers:6x
61 -67
ONLY the nonnegative root of the numberUNLIKE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A non-multiple of N.

15. N! is _____ of all integers from 1 to N.
Either a multiple of N or a non-multiple of N
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
11 -13 -17 -19
A MULTIPLE

16. Prime Numbers:0x
83 -89
71 -73 -79
2 -3 -5 -7
PERFECT CUBES

17. 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
Never prime
83 -89
16

18. For ODD ROOTS - the root has ______.
Never prime
The same sign as the base
[(last - first) / increment] + 1
14

19. 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
The sum of any two primes will be even - unless one of the two primes is 2.
NEVER CONTRADICT ONE ANOTHER
61 -67

20. v225=
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
15
NEVER CONTRADICT ONE ANOTHER
2.5

21. v3˜
2.5
1.7
ODD
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.

22. The average of an ODD number of consecutive integers will ________ be an integer.
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The middle number

23. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
71 -73 -79
13
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.

24. The formula for finding the number of consecutive multiples in a set is _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN
[(last - first) / increment] + 1
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.

25. The sum of any two primes will be ____ - unless ______.
83 -89
A non-multiple of N.
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.

26. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
1. The smallest or largest element 2. The increment 3. The number of items in the set
Never prime
In an evenly spaced set - the average and the median are equal.

27. Prime Numbers:5x
53 -59
The average of an ODD number of consecutive integers will ALWAYS be an integer.
31 -37
Put the coefficient under the radical to get a better approximation

28. Positive integers with only two factors must be ___.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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
Prime

29. 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
EVEN
53 -59
In an evenly spaced set - the average and the median are equal.
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

30. Prime Numbers:7x
ONLY the nonnegative root of the numberUNLIKE
71 -73 -79
NEVER CONTRADICT ONE ANOTHER
EVEN

31. v169=
Prime
The middle number
13
25

32. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A MULTIPLE
The average of an EVEN number of consecutive integers will NEVER be an integer.
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set

33. 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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
15

34. 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?
1.4
3·3n = 3^{n+1}
11 -13 -17 -19
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.

35. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
NEVER CONTRADICT ONE ANOTHER
41 -43 -47
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The middle number

36. 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
ODD
1. The smallest or largest element 2. The increment 3. The number of items in the set
14
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

37. ³v216 =
Either a multiple of N or a non-multiple of N
EVEN
A PERFECT SQUARE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

38. Prime Numbers:3x
31 -37
In an evenly spaced set - the average and the median are equal.
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.

39. The prime factorization of a perfect square contains only ______ powers of primes.
53 -59
31 -37
A PERFECT SQUARE
EVEN

40. The prime factorization of __________ contains only EVEN powers of primes.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Never prime
PERFECT CUBES
A PERFECT SQUARE

41. All perfect squares have a(n) _________ number of total factors.
2.5
Never prime
1. The smallest or largest element 2. The increment 3. The number of items in the set
ODD

42. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
3·3n = 3^{n+1}
14
25

43. v2˜
The sum of any two primes will be even - unless one of the two primes is 2.
Prime
23 -29
1.4

44. 3n + 3n + 3n = _____ = ______
1. The smallest or largest element 2. The increment 3. The number of items in the set
Either a multiple of N or a non-multiple of N
3·3n = 3^{n+1}
11 -13 -17 -19

45. Prime Numbers:9x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25
97
31 -37

46. 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

47. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
31 -37
The middle number
Prime factorization

48. The two statements in a data sufficiency problem will _______________.
PERFECT CUBES
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER
61 -67

49. The PRODUCT of n consecutive integers is divisible by ____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The PRODUCT of n consecutive integers is divisible by n!.
A MULTIPLE
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.

50. 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.
A PERFECT SQUARE
N is a divisor of x+y
61 -67