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Test your basic knowledge 
GMAT Number Properties
Start Test
Study First
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 reenforces your understanding as you take the test each time.
1. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
Prime factorization
N is a divisor of x+y
15
2. Let N be an integer. If you add a multiple of N to a nonmultiple of N  the result is ________.
3·3n = 3^{n+1}
A nonmultiple of N.
11 13 17 19
A PERFECT SQUARE
3. The average of an EVEN number of consecutive integers will ________ be an integer.
A MULTIPLE
61 67
The average of an EVEN number of consecutive integers will NEVER be an integer.
1.4
4. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
Set up prime columns.  z 6 12 15 2 2¹ 2² 3 3¹ 3¹ 3¹ 5 5¹
PERFECT CUBES
NEVER CONTRADICT ONE ANOTHER
5. v3˜
1.4
1.7
53 59
13
6. ³v216 =
In an evenly spaced set  the mean and median are equal to the average of the first and the last number.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³  so ³v216 = ³v6³ = 6
41 43 47
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
7. Let N be an integer. If you add two nonmultiples of N  the result could be _______.
Look at the numbers from 1 to 30  inclusive  that have at least one factor of 3 and count up how many each has: 31; 61; 92; 121; 151; 182; 211; 241; 273; 301  The answer is 14.
Either a multiple of N or a nonmultiple of N
If 2 cannot be one of the primes in the sum  the sum must be even.
14
8. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
Never prime
In an evenly spaced set  the mean and median are equal to the average of the first and the last number.
9. Prime Numbers:7x
Set up prime columns.  z 6 12 15 2 2¹ 2² 3 3¹ 3¹ 3¹ 5 5¹
EVEN
[(last  first) / increment] + 1
71 73 79
10. How to find the sum of consecutive integers:
23 29
15
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.
11. v256=
Never prime
In an evenly spaced set  the average and the median are equal.
15
16
12. For ODD ROOTS  the root has ______.
16
A nonmultiple of N.
The same sign as the base
A MULTIPLE
13. Positive integers with only two factors must be ___.
Prime
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}
14. In an evenly spaced set  the ____ and the ____ are equal.
Never prime
The same sign as the base
In an evenly spaced set  the average and the median are equal.
A nonmultiple of N.
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
3·3n = 3^{n+1}
A MULTIPLE
The sum of any two primes will be even  unless one of the two primes is 2.
16. 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
17. Prime Numbers:5x
53 59
31 37
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 PRODUCT of n consecutive integers is divisible by n!.
18. Prime Numbers:8x
97
A PERFECT SQUARE
The average of the set times the number of elements in the set
83 89
19. 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.
1.7
41 43 47
Either a multiple of N or a nonmultiple of N
20. When we take an EVEN ROOT  a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
53 59
97
21. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
Prime
97
If 2 cannot be one of the primes in the sum  the sum must be even.
22. 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.
1.7
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.
EVEN
23. All perfect squares have a(n) _________ number of total factors.
23 29
In an evenly spaced set  the average and the median are equal.
ODD
A PERFECT SQUARE
24. If the problem states/assumes that a number is an integer  check to see if you can use _______.
The sum of any two primes will be even  unless one of the two primes is 2.
Prime factorization
15
The SUM of n consecutive integers is divisible by n if n is odd  but not if n is even.
25. In an evenly spaced set  the average can be found by finding ________.
Never prime
The middle number
14
In an evenly spaced set  the average and the median are equal.
26. v196=
The average of the set times the number of elements in the set
14
A PERFECT SQUARE
Never prime
27. Positive integers with more than two factors are ____.
ONLY the nonnegative root of the numberUNLIKE
1.7
Never prime
A MULTIPLE
28. 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
The average of an EVEN number of consecutive integers will NEVER be an integer.
If 2 cannot be one of the primes in the sum  the sum must be even.
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
FACTOR
29. v625=
The average of the set times the number of elements in the set
[(last  first) / increment] + 1
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
25
30. The formula for finding the number of consecutive multiples in a set is _______.
The PRODUCT of n consecutive integers is divisible by n!.
FACTOR
The sum of any two primes will be even  unless one of the two primes is 2.
[(last  first) / increment] + 1
31. v5˜
83 89
2.5
16
The SUM of n consecutive integers is divisible by n if n is odd  but not if n is even.
32. If N is a divisor of x and y  then _______.
Look at the numbers from 1 to 30  inclusive  that have at least one factor of 3 and count up how many each has: 31; 61; 92; 121; 151; 182; 211; 241; 273; 301  The answer is 14.
Prime
N is a divisor of x+y
1.4
33. Prime Numbers:1x
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.
11 13 17 19
A nonmultiple of N.
34. 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.
The sum of any two primes will be even  unless one of the two primes is 2.
N is a divisor of x+y
NEVER CONTRADICT ONE ANOTHER
35. How to solve: Is the integer z divisible by 6? (1) gcd(z 12) = 3 (2) gcd(z 15) = 15
The average of an ODD number of consecutive integers will ALWAYS be an integer.
83 89
A PERFECT SQUARE
Set up prime columns.  z 6 12 15 2 2¹ 2² 3 3¹ 3¹ 3¹ 5 5¹
36. 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?
If 2 cannot be one of the primes in the sum  the sum must be 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: 31; 61; 92; 121; 151; 182; 211; 241; 273; 301  The answer is 14.
97
The sum of any two primes will be even  unless one of the two primes is 2.
37. Prime Numbers:0x
If 2 cannot be one of the primes in the sum  the sum must be even.
A PERFECT SQUARE
2 3 5 7
Never prime
38. N! is _____ of all integers from 1 to N.
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.
N is a divisor of x+y
The SUM of n consecutive integers is divisible by n if n is odd  but not if n is even.
39. 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
A nonmultiple of N.
The SUM of n consecutive integers is divisible by n if n is odd  but not if n is even.
41 43 47
40. In an evenly spaced set  the sum of the terms is equal to ____.
The average of the set times the number of elements in the set
PERFECT CUBES
ODD
NEVER CONTRADICT ONE ANOTHER
41. 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.
15
Set up prime columns.  z 6 12 15 2 2¹ 2² 3 3¹ 3¹ 3¹ 5 5¹
11 13 17 19
42. On data sufficiency  ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
1.4
FACTOR
A nonmultiple of N.
Either a multiple of N or a nonmultiple of N
43. Prime Numbers:2x
In an evenly spaced set  the mean and median are equal to the average of the first and the last number.
14
23 29
ONLY the nonnegative root of the numberUNLIKE
44. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
31 37
The sum of any two primes will be even  unless one of the two primes is 2.
[(last  first) / increment] + 1
45. Prime Numbers:6x
61 67
The average of the set times the number of elements in the set
ONLY the nonnegative root of the numberUNLIKE
PERFECT CUBES
46. v225=
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³  so ³v216 = ³v6³ = 6
15
47. Any integer with an EVEN number of total factors cannot 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.
31 37
Either a multiple of N or a nonmultiple of N
A PERFECT SQUARE
48. Prime Numbers:4x
41 43 47
83 89
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.
49. If estimating a root with a coefficient  _____ .
41 43 47
Put the coefficient under the radical to get a better approximation
Prime
In an evenly spaced set  the average and the median are equal.
50. In an evenly spaced set  the mean and median are equal to the _____ of _________.
15
A nonmultiple of N.
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.
In an evenly spaced set  the mean and median are equal to the average of the first and the last number.