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GMAT Number Properties

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. v2
If 2 cannot be one of the primes in the sum - the sum must be even.
ODD
1.4
Prime factorization

2. v5
16
61 -67
In an evenly spaced set - the average and the median are equal.
2.5

3. 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?
The average of an EVEN number of consecutive integers will NEVER 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

4. 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
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.
PERFECT CUBES
A PERFECT SQUARE
33n = 3^{n+1}

5. Prime Numbers:5x
1.7
41 -43 -47
Prime
53 -59

6. If the problem states/assumes that a number is an integer - check to see if you can use _______.
61 -67
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime

7. In an evenly spaced set - the average can be found by finding ________.
NEVER CONTRADICT ONE ANOTHER
N is a divisor of x+y
The middle number
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.

8. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the average and the median are equal.
The average of the set times the number of elements in the set
A PERFECT SQUARE

9. The prime factorization of a perfect square contains only ______ powers of primes.
The PRODUCT of n consecutive integers is divisible by n!.
FACTOR
2 -3 -5 -7
EVEN

10. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE
2.5
N is a divisor of x+y

11. N! is _____ of all integers from 1 to N.
A MULTIPLE
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.
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
71 -73 -79

12. If N is a divisor of x and y - then _______.
The middle number
2 -3 -5 -7
N is a divisor of x+y
25

13. The prime factorization of __________ contains only EVEN powers of primes.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
Prime factorization
A PERFECT SQUARE

14. The formula for finding the number of consecutive multiples in a set is _______.
1.4
Put the coefficient under the radical to get a better approximation
71 -73 -79
[(last - first) / increment] + 1

15. v3
1.7
The PRODUCT of n consecutive integers is divisible by n!.
FACTOR
16

16. Positive integers with more than two factors are ____.
A MULTIPLE
Never prime
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

17. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
The sum of any two primes will be even - unless one of the two primes is 2.
2 -3 -5 -7
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
The average of the set times the number of elements in the set

18. 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.
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.
31 -37
Never prime

19. Positive integers with only two factors must be ___.
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.
ODD
Prime

20. 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
25
13
61 -67
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

21. v196=
14
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Either a multiple of N or a non-multiple of N
A non-multiple of N.

22. Prime Numbers:0x
1.4
The average of an ODD number of consecutive integers will ALWAYS be an integer.
2 -3 -5 -7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6

23. Prime Numbers:2x
The PRODUCT of n consecutive integers is divisible by n!.
23 -29
The average of the set times the number of elements in the set
1.4

24. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The middle number
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
NEVER CONTRADICT ONE ANOTHER

25. All perfect squares have a(n) _________ number of total factors.
ODD
The middle number
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
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.

26. In an evenly spaced set - the mean and median are equal to the _____ of _________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER
83 -89
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

27. 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
1. The smallest or largest element 2. The increment 3. The number of items in the set
97
A non-multiple of N.

28. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
Never prime
ONLY the nonnegative root of the numberUNLIKE
71 -73 -79
23 -29

29. In an evenly spaced set - the sum of the terms is equal to ____.
The middle number
ONLY the nonnegative root of the numberUNLIKE
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

30. The PRODUCT of n consecutive integers is divisible by ____.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The middle number
1.7
The PRODUCT of n consecutive integers is divisible by n!.

31. v169=
PERFECT CUBES
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
13

32. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
41 -43 -47
ODD
The same sign as the base

33. Prime Numbers:7x
PERFECT CUBES
N is a divisor of x+y
Prime factorization
71 -73 -79

34. The two statements in a data sufficiency problem will _______________.
25
NEVER CONTRADICT ONE ANOTHER
33n = 3^{n+1}
61 -67

35. For ODD ROOTS - the root has ______.
14
The same sign as the base
ODD
A PERFECT SQUARE

36. In an evenly spaced set - the ____ and the ____ are equal.
1.4
In an evenly spaced set - the average and the median are equal.
In an evenly spaced set - the mean and median are equal to the average of the first and the last 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.

37. If estimating a root with a coefficient - _____ .
A PERFECT SQUARE
83 -89
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

38. The average of an EVEN number of consecutive integers will ________ be an integer.
61 -67
The middle number
The average of an EVEN number of consecutive integers will NEVER 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.

39. v216 =
61 -67
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6
The PRODUCT of n consecutive integers is divisible by n!.

40. 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.
1. The smallest or largest element 2. The increment 3. The number of items in the set
ODD
53 -59

41. Prime Numbers:4x
41 -43 -47
23 -29
A PERFECT SQUARE
83 -89

42. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
25
[(last - first) / increment] + 1
The middle number

43. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
13
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6
23 -29

44. v625=
25
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
23 -29

45. Prime Numbers:1x
11 -13 -17 -19
41 -43 -47
N is a divisor of x+y
The average of an EVEN number of consecutive integers will NEVER be an integer.

46. 3n + 3n + 3n = _____ = ______
1. The smallest or largest element 2. The increment 3. The number of items in the set
A MULTIPLE
FACTOR
33n = 3^{n+1}

47. 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
FACTOR
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
ODD
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.

48. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
PERFECT CUBES
FACTOR
A non-multiple of N.
A PERFECT SQUARE

49. 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.
Prime
ODD
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5

50. Prime Numbers:8x
EVEN
83 -89
53 -59
Prime

Test your basic knowledge |

GMAT Number Properties

250+ Skill Guides in 1 Book
13 Skills Types | 550 Pages | Only $9.95 | PDF / EPub, Kindle Ready

Link to This Test

Related Subjects

Test your basic knowledge |

GMAT Number Properties

250+ Skill Guides in 1 Book 13 Skills Types | 550 Pages | Only $9.95 | PDF / EPub, Kindle Ready

Link to This Test

Related Subjects

250+ Skill Guides in 1 Book
13 Skills Types | 550 Pages | Only $9.95 | PDF / EPub, Kindle Ready