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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. Prime Numbers:3x
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 -13 -17 -19
31 -37
In an evenly spaced set - the average and the median are equal.

2. The formula for finding the number of consecutive multiples in a set is _______.
A PERFECT SQUARE
FACTOR
[(last - first) / increment] + 1
If 2 cannot be one of the primes in the sum - the sum must be even.

3. v256=
Never prime
16
2.5
PERFECT CUBES

4. The two statements in a data sufficiency problem will _______________.
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6
31 -37

5. 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 --2 2 3 --3 3 3 5 ---------5
NEVER CONTRADICT ONE ANOTHER
83 -89
1. The smallest or largest element 2. The increment 3. The number of items in the set

6. v169=
2.5
13
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The sum of any two primes will be even - unless one of the two primes is 2.

7. In an evenly spaced set - the sum of the terms is equal to ____.
If 2 cannot be one of the primes in the sum - the sum must be even.
The average of the set times the number of elements in the set
Prime factorization
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. Prime Numbers:6x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
61 -67
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

9. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
31 -37
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

10. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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.
The average of the set times the number of elements in the set
97
ONLY the nonnegative root of the numberUNLIKE

11. v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6
The middle number
13
15

12. 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 PERFECT SQUARE
A MULTIPLE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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

13. 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
The PRODUCT of n consecutive integers is divisible by n!.
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.
ONLY the nonnegative root of the numberUNLIKE

14. Prime Numbers:5x
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set
61 -67
83 -89

15. The sum of any two primes will be ____ - unless ______.
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 sum of any two primes will be even - unless one of the two primes is 2.
ODD
83 -89

16. v3
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
1.7
16

17. The prime factorization of __________ contains only EVEN powers of primes.
1.4
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
PERFECT CUBES

18. v2
1. The smallest or largest element 2. The increment 3. The number of items in the set
2.5
1.4
The PRODUCT of n consecutive integers is divisible by n!.

19. If N is a divisor of x and y - then _______.
A non-multiple of N.
16
N is a divisor of x+y
61 -67

20. 3n + 3n + 3n = _____ = ______
33n = 3^{n+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.
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER

21. In an evenly spaced set - the average can be found by finding ________.
The sum of any two primes will be even - unless one of the two primes is 2.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Put the coefficient under the radical to get a better approximation
The middle number

22. Prime Numbers:0x
Never prime
33n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.
2 -3 -5 -7

23. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
Prime factorization
FACTOR
41 -43 -47
15

24. v5
FACTOR
Put the coefficient under the radical to get a better approximation
Prime
2.5

25. Prime Numbers:1x
Prime factorization
11 -13 -17 -19
2 -3 -5 -7
Never prime

26. v196=
13
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
14

27. v625=
[(last - first) / increment] + 1
The same sign as the base
25
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.

28. If the problem states/assumes that a number is an integer - check to see if you can use _______.
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.
Put the coefficient under the radical to get a better approximation
Prime factorization
A PERFECT SQUARE

29. 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.
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
25

30. Prime Numbers:8x
11 -13 -17 -19
1.7
The average of an EVEN number of consecutive integers will NEVER be an integer.
83 -89

31. 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.
71 -73 -79
97
33n = 3^{n+1}

32. Let N be an integer. If you add two non-multiples of N - the result could be _______.
2.5
The PRODUCT of n consecutive integers is divisible by n!.
2 -3 -5 -7
Either a multiple of N or a non-multiple of N

33. v225=
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
15
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5

34. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
61 -67
Prime factorization
A non-multiple of N.

35. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set

36. Prime Numbers:4x
A PERFECT SQUARE
41 -43 -47
Never prime
The middle number

37. In an evenly spaced set - the ____ and the ____ are equal.
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.
1.4
A PERFECT SQUARE

38. All perfect squares have a(n) _________ number of total factors.
ODD
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
The average of an ODD number of consecutive integers will ALWAYS be an integer.

39. If estimating a root with a coefficient - _____ .
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 same sign as the base
Put the coefficient under the radical to get a better approximation
16

40. For ODD ROOTS - the root has ______.
23 -29
ODD
The same sign as the base
15

41. The average of an ODD number of consecutive integers will ________ be an integer.
11 -13 -17 -19
A non-multiple of N.
In an evenly spaced set - the average and the median are equal.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

42. Positive integers with more than two factors are ____.
14
Never prime
61 -67
PERFECT CUBES

43. Prime Numbers:9x
A PERFECT SQUARE
N is a divisor of x+y
97
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

44. The PRODUCT of n consecutive integers is divisible by ____.
Never prime
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N

45. 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.
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
The PRODUCT of n consecutive integers is divisible by n!.

46. Prime Numbers:2x
The same sign as the base
Put the coefficient under the radical to get a better approximation
ODD
23 -29

47. In an evenly spaced set - the mean and median are equal to the _____ of _________.
1.7
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.
2 -3 -5 -7

48. The prime factorization of a perfect square contains only ______ powers of primes.
Prime
A PERFECT SQUARE
FACTOR
EVEN

49. If 2 cannot be one of the primes in the sum - the sum must be _____.
25
The same sign as the base
Prime factorization
If 2 cannot be one of the primes in the sum - the sum must be even.

50. N! is _____ of all integers from 1 to N.
A MULTIPLE
1.7
14
ODD

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