GMAT Number Properties

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. 3n + 3n + 3n = _____ = ______
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
3·3n = 3^{n+1}
If 2 cannot be one of the primes in the sum - the sum must be even.


2. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
25
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
[(last - first) / increment] + 1
A non-multiple of N.


3. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
EVEN
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE


4. The PRODUCT of n consecutive integers is divisible by ____.
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.
16
1.4


5. v625=
25
The average of an EVEN number of consecutive integers will NEVER be an integer.
[(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.


6. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
Never prime
11 -13 -17 -19
Put the coefficient under the radical to get a better approximation


7. Positive integers with more than two factors are ____.
16
Never prime
Put the coefficient under the radical to get a better approximation
2 -3 -5 -7


8. Prime Numbers:8x
[(last - first) / increment] + 1
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
A MULTIPLE
83 -89


9. Prime Numbers:9x
61 -67
A PERFECT SQUARE
97
Never prime


10. v196=
EVEN
71 -73 -79
ONLY the nonnegative root of the numberUNLIKE
14


11. Positive integers with only two factors must be ___.
16
EVEN
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime


12. Prime Numbers:7x
Prime
71 -73 -79
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.


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


14. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
[(last - first) / increment] + 1
The sum of any two primes will be even - unless one of the two primes is 2.
If 2 cannot be one of the primes in the sum - the sum must be even.


15. If 2 cannot be one of the primes in the sum - the sum must be _____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE
61 -67
If 2 cannot be one of the primes in the sum - the sum must be even.


16. The formula for finding the number of consecutive multiples in a set is _______.
In an evenly spaced set - the average and the median are equal.
[(last - first) / increment] + 1
31 -37
The sum of any two primes will be even - unless one of the two primes is 2.


17. v256=
Never prime
16
[(last - first) / increment] + 1
2.5


18. If estimating a root with a coefficient - _____ .
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.
Put the coefficient under the radical to get a better approximation


19. The average of an ODD number of consecutive integers will ________ be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.
3·3n = 3^{n+1}
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.


20. Prime Numbers:5x
The middle number
A PERFECT SQUARE
53 -59
N is a divisor of x+y


21. Any integer with an EVEN number of total factors cannot be ______.
83 -89
PERFECT CUBES
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
A PERFECT SQUARE


22. Prime Numbers:4x
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.
41 -43 -47
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6


23. v2˜
Either a multiple of N or a non-multiple of N
Never prime
1.4
ODD


24. v169=
2 -3 -5 -7
13
Put the coefficient under the radical to get a better approximation
25


25. 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.
23 -29
97
The middle number


26. How to find the sum of consecutive integers:
EVEN
2.5
11 -13 -17 -19
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.


27. v3˜
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.7
The sum of any two primes will be even - unless one of the two primes is 2.
FACTOR


28. ³v216 =
Prime
ONLY the nonnegative root of the numberUNLIKE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
41 -43 -47


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?
41 -43 -47
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. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
PERFECT CUBES


30. 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
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 gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
A PERFECT SQUARE


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


32. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
15
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
[(last - first) / increment] + 1


33. Prime Numbers:1x
11 -13 -17 -19
In an evenly spaced set - the average and the median are equal.
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.
Put the coefficient under the radical to get a better approximation


34. Prime Numbers:0x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.7
2 -3 -5 -7
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. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A non-multiple of N.
13


36. Prime Numbers:6x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
61 -67
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.
41 -43 -47


37. For ODD ROOTS - the root has ______.
14
A PERFECT SQUARE
The same sign as the base
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6


38. In an evenly spaced set - the average can be found by finding ________.
2.5
[(last - first) / increment] + 1
The middle number
1. The smallest or largest element 2. The increment 3. The number of items in the set


39. The two statements in a data sufficiency problem will _______________.
PERFECT CUBES
The sum of any two primes will be even - unless one of the two primes is 2.
NEVER CONTRADICT ONE ANOTHER
53 -59


40. Let N be an integer. If you add two non-multiples of N - the result could be _______.
53 -59
The average of an EVEN number of consecutive integers will NEVER be an integer.
Either a multiple of N or a non-multiple of N
1.7


41. The sum of any two primes will be ____ - unless ______.
61 -67
The sum of any two primes will be even - unless one of the two primes is 2.
97
A PERFECT SQUARE


42. v225=
15
The sum of any two primes will be even - unless one of the two primes is 2.
Either a multiple of N or a non-multiple of N
The average of an EVEN number of consecutive integers will NEVER be an integer.


43. N! is _____ of all integers from 1 to N.
A MULTIPLE
The sum of any two primes will be even - unless one of the two primes is 2.
83 -89
Prime


44. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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.
15
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.


45. Prime Numbers:3x
In an evenly spaced set - the average and the median are equal.
The same sign as the base
3·3n = 3^{n+1}
31 -37


46. Prime factors of _____ must come in pairs of three.
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.
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


47. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
PERFECT CUBES
1.7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6


48. Prime Numbers:2x
23 -29
The average of the set times the number of elements in the set
The middle number
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.


49. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
The sum of any two primes will be even - unless one of the two primes is 2.
71 -73 -79
11 -13 -17 -19


50. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
71 -73 -79
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1. The smallest or largest element 2. The increment 3. The number of items in the set
If 2 cannot be one of the primes in the sum - the sum must be even.