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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.
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. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
In an evenly spaced set - the average and the median are equal.
11 -13 -17 -19
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
The middle number

2. v256=
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The same sign as the base
16
Prime factorization

3. v169=
61 -67
13
Either a multiple of N or a non-multiple of N
Prime factorization

4. The formula for finding the number of consecutive multiples in a set is _______.
The PRODUCT of n consecutive integers is divisible by n!.
A non-multiple of N.
[(last - first) / increment] + 1
97

5. For ODD ROOTS - the root has ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The same sign as the base
Prime factorization
14

6. v3
The PRODUCT of n consecutive integers is divisible by n!.
1.7
Prime
1.4

7. In an evenly spaced set - the sum of the terms is equal to ____.
1.4
Prime
The average of the set times the number of elements in the set
The PRODUCT of n consecutive integers is divisible by n!.

8. v216 =
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6
1.7

9. In an evenly spaced set - the average can be found by finding ________.
1.4
The middle number
71 -73 -79
Prime factorization

10. Prime Numbers:0x
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.
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.
2 -3 -5 -7
The average of an EVEN number of consecutive integers will NEVER be an integer.

11. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The middle number
13
Prime factorization
The average of an ODD number of consecutive integers will ALWAYS be an integer.

12. 3n + 3n + 3n = _____ = ______
33n = 3^{n+1}
2 -3 -5 -7
If 2 cannot be one of the primes in the sum - the sum must be even.
14

13. 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?
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.
83 -89
Never prime

14. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The average of the set times the number of elements in the set
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
FACTOR

15. Prime Numbers:6x
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.
ODD
61 -67

16. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
14
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

17. Prime factors of _____ must come in pairs of three.
FACTOR
71 -73 -79
Either a multiple of N or a non-multiple of N
PERFECT CUBES

18. Prime Numbers:5x
53 -59
33n = 3^{n+1}
A PERFECT SQUARE
71 -73 -79

19. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.
ONLY the nonnegative root of the numberUNLIKE
Never prime

20. The prime factorization of a perfect square contains only ______ powers of primes.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
EVEN
15
1. The smallest or largest element 2. The increment 3. The number of items in the set

21. 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
1.7
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. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER

22. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
If 2 cannot be one of the primes in the sum - the sum must be even.
A non-multiple of N.
The middle number
The PRODUCT of n consecutive integers is divisible by n!.

23. Let N be an integer. If you add two non-multiples of N - the result could be _______.
2.5
Either a multiple of N or a non-multiple of N
Prime factorization
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

24. Prime Numbers:7x
31 -37
25
71 -73 -79
The same sign as the base

25. v225=
A MULTIPLE
15
2.5
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

26. v196=
14
16
97
A non-multiple of N.

27. Prime Numbers:3x
31 -37
The middle number
N is a divisor of x+y
Prime factorization

28. v625=
PERFECT CUBES
25
Put the coefficient under the radical to get a better approximation
97

29. In an evenly spaced set - the mean and median are equal to the _____ of _________.
2 -3 -5 -7
31 -37
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

30. All perfect squares have a(n) _________ number of total factors.
If 2 cannot be one of the primes in the sum - the sum must be even.
ODD
N is a divisor of x+y
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

31. 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
33n = 3^{n+1}
Put the coefficient under the radical to get a better approximation
ONLY the nonnegative root of the numberUNLIKE
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.

32. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
1.7
Prime
The average of an EVEN number of consecutive integers will NEVER be an integer.
FACTOR

33. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The sum of any two primes will be even - unless one of the two primes is 2.
13
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE

34. Prime Numbers:2x
23 -29
The average of the set times the number of elements in the set
15
1. The smallest or largest element 2. The increment 3. The number of items in the set

35. 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
ONLY the nonnegative root of the numberUNLIKE
The average of the set times the number of elements in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.

36. The average of an ODD number of consecutive integers will ________ be an integer.
Prime factorization
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A non-multiple of N.

37. N! is _____ of all integers from 1 to 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.
15
PERFECT CUBES

38. Prime Numbers:8x
The sum of any two primes will be even - unless one of the two primes is 2.
61 -67
83 -89
If 2 cannot be one of the primes in the sum - the sum must be even.

39. Positive integers with more than two factors are ____.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime
16
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.

40. If estimating a root with a coefficient - _____ .
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
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.

41. The sum of any two primes will be ____ - unless ______.
Either a multiple of N or a non-multiple of N
13
The sum of any two primes will be even - unless one of the two primes is 2.
[(last - first) / increment] + 1

42. Any integer with an ODD number of total factors must be _______.
A MULTIPLE
A PERFECT SQUARE
31 -37
The average of an EVEN number of consecutive integers will NEVER be an integer.

43. 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last 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.
FACTOR

44. Prime Numbers:9x
97
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
13

45. If N is a divisor of x and y - then _______.
31 -37
97
N is a divisor of x+y
53 -59

46. Prime Numbers:4x
41 -43 -47
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.
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.

47. In an evenly spaced set - the ____ and the ____ are equal.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
Prime factorization
Put the coefficient under the radical to get a better approximation

48. Prime Numbers:1x
25
11 -13 -17 -19
Never prime
33n = 3^{n+1}

49. v5
16
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
A MULTIPLE
2.5

50. If 2 cannot be one of the primes in the sum - the sum must be _____.
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.
The average of an EVEN number of consecutive integers will NEVER be an integer.
11 -13 -17 -19
If 2 cannot be one of the primes in the sum - the sum must be even.

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