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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. Prime Numbers:5x
53 59
The sum of any two primes will be even  unless one of the two primes is 2.
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.
PERFECT CUBES
2. Prime Numbers:8x
ODD
53 59
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
83 89
3. v5˜
The sum of any two primes will be even  unless one of the two primes is 2.
The average of the set times the number of elements in the set
2.5
13
4. The formula for finding the number of consecutive multiples in a set is _______.
In an evenly spaced set  the mean and median are equal to the average of the first and the last number.
[(last  first) / increment] + 1
In an evenly spaced set  the average and the median are equal.
71 73 79
5. Prime Numbers:1x
11 13 17 19
Prime factorization
If 2 cannot be one of the primes in the sum  the sum must be even.
31 37
6. When we take an EVEN ROOT  a radical sign means ________. This is _____ even exponents.
Put the coefficient under the radical to get a better approximation
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.
ONLY the nonnegative root of the numberUNLIKE
16
7. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}
A nonmultiple of N.
The average of the set times the number of elements in the set
8. Let N be an integer. If you add a multiple of N to a nonmultiple of N  the result is ________.
The PRODUCT of n consecutive integers is divisible by n!.
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
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.
A nonmultiple of N.
9. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
25
The PRODUCT of n consecutive integers is divisible by n!.
97
10. If N is a divisor of x and y  then _______.
1.4
A nonmultiple of N.
EVEN
N is a divisor of x+y
11. v256=
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
11 13 17 19
16
12. v2˜
41 43 47
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
1.4
13. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
16
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.
1. The smallest or largest element 2. The increment 3. The number of items in the set
14. v169=
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
13
PERFECT CUBES
15. How to find the sum of consecutive integers:
14
ODD
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 SUM of n consecutive integers is divisible by n if n is odd  but not if n is even.
16. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
2.5
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.
17. If the problem states/assumes that a number is an integer  check to see if you can use _______.
If 2 cannot be one of the primes in the sum  the sum must be even.
The PRODUCT of n consecutive integers is divisible by n!.
41 43 47
Prime factorization
18. 3n + 3n + 3n = _____ = ______
The same sign as the base
N is a divisor of x+y
3·3n = 3^{n+1}
Set up prime columns.  z 6 12 15 2 2¹ 2² 3 3¹ 3¹ 3¹ 5 5¹
19. Prime Numbers:4x
A PERFECT SQUARE
41 43 47
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
20. If 2 cannot be one of the primes in the sum  the sum must be _____.
41 43 47
16
25
If 2 cannot be one of the primes in the sum  the sum must be even.
21. Prime Numbers:6x
In an evenly spaced set  the average and the median are equal.
EVEN
61 67
13
22. In an evenly spaced set  the sum of the terms is equal to ____.
97
A nonmultiple of N.
The average of the set times the number of elements in the set
A MULTIPLE
23. 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 ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE
2.5
Look at the numbers from 1 to 30  inclusive  that have at least one factor of 3 and count up how many each has: 31; 61; 92; 121; 151; 182; 211; 241; 273; 301  The answer is 14.
24. Prime Numbers:3x
The average of the set times the number of elements in the set
23 29
31 37
PERFECT CUBES
25. Any integer with an ODD number of total factors must be _______.
1.4
EVEN
A PERFECT SQUARE
The average of the set times the number of elements in the set
26. In an evenly spaced set  the average can be found by finding ________.
A nonmultiple of N.
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 middle number
53 59
27. Prime Numbers:0x
2 3 5 7
The PRODUCT of n consecutive integers is divisible by n!.
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.
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
28. How to solve: Is the integer z divisible by 6? (1) gcd(z 12) = 3 (2) gcd(z 15) = 15
The middle number
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
In an evenly spaced set  the average and the median are equal.
Set up prime columns.  z 6 12 15 2 2¹ 2² 3 3¹ 3¹ 3¹ 5 5¹
29. 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
30. 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
Prime
ONLY the nonnegative root of the numberUNLIKE
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.
31. Let N be an integer. If you add two nonmultiples of N  the result could be _______.
3·3n = 3^{n+1}
25
A MULTIPLE
Either a multiple of N or a nonmultiple of N
32. v225=
15
A PERFECT SQUARE
83 89
If 2 cannot be one of the primes in the sum  the sum must be even.
33. 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.
1.7
15
71 73 79
34. Positive integers with only two factors must be ___.
Prime
FACTOR
31 37
1. The smallest or largest element 2. The increment 3. The number of items in the set
35. v196=
14
16
1.7
A PERFECT SQUARE
36. The average of an ODD number of consecutive integers will ________ be an integer.
The same sign as the base
The average of an ODD number of consecutive integers will ALWAYS be an integer.
[(last  first) / increment] + 1
15
37. For ODD ROOTS  the root has ______.
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
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 same sign as the base
23 29
38. 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 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
Prime
1. The smallest or largest element 2. The increment 3. The number of items in the set
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
39. Prime Numbers:9x
EVEN
25
14
97
40. If estimating a root with a coefficient  _____ .
Put the coefficient under the radical to get a better approximation
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.
41 43 47
The same sign as the base
41. v3˜
1.7
The PRODUCT of n consecutive integers is divisible by n!.
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.
83 89
42. 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.
16
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
43. The prime factorization of __________ contains only EVEN powers of primes.
83 89
Either a multiple of N or a nonmultiple of N
A PERFECT SQUARE
41 43 47
44. In an evenly spaced set  the ____ and the ____ are equal.
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set  the average and the median are equal.
97
Prime factorization
45. All perfect squares have a(n) _________ number of total factors.
Prime
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
ODD
Put the coefficient under the radical to get a better approximation
46. v625=
31 37
In an evenly spaced set  the average and the median are equal.
25
PERFECT CUBES
47. 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.
Set up prime columns.  z 6 12 15 2 2¹ 2² 3 3¹ 3¹ 3¹ 5 5¹
A PERFECT SQUARE
13
48. On data sufficiency  ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
Put the coefficient under the radical to get a better approximation
ONLY the nonnegative root of the numberUNLIKE
31 37
FACTOR
49. N! is _____ of all integers from 1 to N.
A nonmultiple of N.
71 73 79
83 89
A MULTIPLE
50. Any integer with an EVEN number of total factors cannot be ______.
31 37
A PERFECT SQUARE
If gcd(k1 n) ? 1 or gcd(k2 n) ? 1  this proves insufficiency.
[(last  first) / increment] + 1