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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:7x
83 -89
Put the coefficient under the radical to get a better approximation
The average of an ODD number of consecutive integers will ALWAYS be an integer.
71 -73 -79

2. Prime Numbers:2x
23 -29
FACTOR
EVEN
The middle number

3. All perfect squares have a(n) _________ number of total factors.
ODD
1.4
61 -67
2 -3 -5 -7

4. v5˜
2.5
Never prime
Prime factorization
25

5. The sum of any two primes will be ____ - unless ______.
FACTOR
61 -67
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE

6. Prime Numbers:4x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
41 -43 -47
11 -13 -17 -19
2.5

7. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
25
83 -89
The middle number

8. 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

9. v3˜
Prime
14
1.7
ODD

10. v625=
15
The middle number
25
[(last - first) / increment] + 1

11. 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
23 -29
PERFECT CUBES
A non-multiple of N.

12. Prime Numbers:5x
53 -59
The middle number
The PRODUCT of n consecutive integers is divisible by n!.
EVEN

13. v225=
14
13
15
16

14. For ODD ROOTS - the root has ______.
The same sign as the base
The sum of any two primes will be even - unless one of the two primes is 2.
1.7
23 -29

15. Any integer with an EVEN number of total factors cannot be ______.
ODD
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
A MULTIPLE

16. 3n + 3n + 3n = _____ = ______
13
3·3n = 3^{n+1}
25
1.7

17. Prime Numbers:0x
Either a multiple of N or a non-multiple of N
2 -3 -5 -7
1.7
23 -29

18. The prime factorization of __________ contains only EVEN powers of primes.
[(last - first) / increment] + 1
A PERFECT SQUARE
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.
NEVER CONTRADICT ONE ANOTHER

19. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an EVEN number of consecutive integers will NEVER be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.

20. Prime Numbers:3x
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.
PERFECT CUBES
31 -37
The PRODUCT of n consecutive integers is divisible by n!.

21. The formula for finding the number of consecutive multiples in a set is _______.
25
[(last - first) / increment] + 1
2.5
The middle number

22. Any integer with an ODD number of total factors must be _______.
EVEN
ODD
Prime factorization
A PERFECT SQUARE

23. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A PERFECT SQUARE
31 -37
1. The smallest or largest element 2. The increment 3. The number of items in the set
PERFECT CUBES

24. In an evenly spaced set - the sum of the terms is equal to ____.
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 average of the set times the number of elements in the set
Prime factorization
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

25. Positive integers with more than two factors are ____.
2 -3 -5 -7
Never prime
83 -89
53 -59

26. Prime Numbers:6x
1. The smallest or largest element 2. The increment 3. The number of items in the set
71 -73 -79
A PERFECT SQUARE
61 -67

27. 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
A PERFECT SQUARE
25
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

28. N! is _____ of all integers from 1 to N.
The sum of any two primes will be even - unless one of the two primes is 2.
23 -29
A MULTIPLE
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

29. 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. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
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.
3·3n = 3^{n+1}
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

30. v2˜
1.4
Prime factorization
A PERFECT SQUARE
14

31. If 2 cannot be one of the primes in the sum - the sum must be _____.
ONLY the nonnegative root of the numberUNLIKE
If 2 cannot be one of the primes in the sum - the sum must be 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.
11 -13 -17 -19

32. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
53 -59
61 -67

33. Prime Numbers:1x
1.4
14
11 -13 -17 -19
3·3n = 3^{n+1}

34. The prime factorization of a perfect square contains only ______ powers of primes.
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN
31 -37

35. If N is a divisor of x and y - then _______.
15
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
14
N is a divisor of x+y

36. Prime Numbers:8x
NEVER CONTRADICT ONE ANOTHER
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The middle number
83 -89

37. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
97
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
61 -67
A PERFECT SQUARE

38. In an evenly spaced set - the ____ and the ____ are equal.
61 -67
In an evenly spaced set - the average and the median are equal.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.4

39. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
Never prime
A non-multiple of N.
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

40. Prime factors of _____ must come in pairs of three.
61 -67
PERFECT CUBES
ODD
In an evenly spaced set - the average and the median are equal.

41. v196=
[(last - first) / increment] + 1
71 -73 -79
14
13

42. The average of an EVEN number of consecutive integers will ________ be an integer.
25
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 same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.

43. ³v216 =
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
2.5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
23 -29

44. v256=
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
16
23 -29
The middle number

45. v169=
83 -89
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.
13

46. In an evenly spaced set - the average can be found by finding ________.
The middle number
1. The smallest or largest element 2. The increment 3. The number of items in the set
16
A PERFECT SQUARE

47. How to find the sum of consecutive integers:
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.
14
In an evenly spaced set - the average and the median are equal.
97

48. 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.
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. 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!.

49. Prime Numbers:9x
Either a multiple of N or a non-multiple of N
Never prime
97
25

50. Positive integers with only two factors must be ___.
PERFECT CUBES
A MULTIPLE
Prime
The same sign as the base