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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 re-enforces your understanding as you take the test each time.
1. Prime Numbers:1x
11 -13 -17 -19
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the average and the median are equal.
Never prime
2. Any integer with an EVEN number of total factors cannot be ______.
1.4
A PERFECT SQUARE
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.
3. ³v216 =
A PERFECT SQUARE
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
2.5
4. For ODD ROOTS - the root has ______.
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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
5. In an evenly spaced set - the average can be found by finding ________.
The middle number
Prime
EVEN
15
6. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
7. If estimating a root with a coefficient - _____ .
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
Prime
1. The smallest or largest element 2. The increment 3. The number of items in the set
8. The prime factorization of __________ contains only EVEN powers of primes.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of the set times the number of elements in the set
A PERFECT SQUARE
9. N! is _____ of all integers from 1 to N.
A MULTIPLE
2 -3 -5 -7
A PERFECT SQUARE
PERFECT CUBES
10. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
Never prime
Prime
41 -43 -47
11. Prime Numbers:4x
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.
41 -43 -47
Prime
12. v2˜
11 -13 -17 -19
1.4
31 -37
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13. v3˜
Either a multiple of N or a non-multiple of N
61 -67
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.
1.7
14. Prime Numbers:9x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
14
61 -67
97
15. Let N be an integer. If you add two non-multiples of N - the result could be _______.
14
Either a multiple of N or a non-multiple of N
Prime
83 -89
16. 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
The same sign as the base
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
2 -3 -5 -7
2.5
17. Prime Numbers:7x
If 2 cannot be one of the primes in the sum - the sum must be even.
The average of an EVEN number of consecutive integers will NEVER be an integer.
71 -73 -79
[(last - first) / increment] + 1
18. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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.
Either a multiple of N or a non-multiple of N
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
19. Prime Numbers:2x
The PRODUCT of n consecutive integers is divisible by n!.
23 -29
11 -13 -17 -19
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
20. 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
21. The PRODUCT of n consecutive integers is divisible by ____.
25
The PRODUCT of n consecutive integers is divisible by n!.
1.7
ONLY the nonnegative root of the numberUNLIKE
22. If N is a divisor of x and y - then _______.
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: 3-1; 6-1; 9-2; 12-1; 15-1; 18-2; 21-1; 24-1; 27-3; 30-1 - The answer is 14.
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.
23. The average of an EVEN number of consecutive integers will ________ be an integer.
31 -37
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.
FACTOR
24. v196=
14
The middle number
A MULTIPLE
The same sign as the base
25. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
EVEN
Either a multiple of N or a non-multiple of N
A non-multiple of N.
15
26. Prime Numbers:8x
The average of an EVEN number of consecutive integers will NEVER be an integer.
[(last - first) / increment] + 1
83 -89
1. The smallest or largest element 2. The increment 3. The number of items in the set
27. The two statements in a data sufficiency problem will _______________.
The middle number
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
NEVER CONTRADICT ONE ANOTHER
28. Positive integers with only two factors must be ___.
FACTOR
NEVER CONTRADICT ONE ANOTHER
61 -67
Prime
29. Prime Numbers:5x
In an evenly spaced set - the mean and median are equal to the average of the first and the last 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
53 -59
71 -73 -79
30. v5˜
2 -3 -5 -7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2.5
31. The average of an ODD number of consecutive integers will ________ be an integer.
23 -29
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
PERFECT CUBES
32. If the problem states/assumes that a number is an integer - check to see if you can use _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Put the coefficient under the radical to get a better approximation
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.
33. 3n + 3n + 3n = _____ = ______
53 -59
13
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
3·3n = 3^{n+1}
34. In an evenly spaced set - the sum of the terms is equal to ____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
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 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.
35. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
ONLY the nonnegative root of the numberUNLIKE
A MULTIPLE
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
36. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
Never prime
[(last - first) / increment] + 1
The average of an EVEN number of consecutive integers will NEVER be an integer.
37. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of the set times the number of elements in the set
3·3n = 3^{n+1}
38. v625=
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25
39. Prime factors of _____ must come in pairs of three.
97
PERFECT CUBES
41 -43 -47
2.5
40. 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.
61 -67
41 -43 -47
14
41. Prime Numbers:6x
61 -67
A PERFECT SQUARE
1.7
The sum of any two primes will be even - unless one of the two primes is 2.
42. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
3·3n = 3^{n+1}
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
71 -73 -79
2 -3 -5 -7
43. 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?
Prime
97
A PERFECT SQUARE
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.
44. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
45. How to find the sum of consecutive integers:
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
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.
25
46. v169=
The same sign as the base
2 -3 -5 -7
41 -43 -47
13
47. All perfect squares have a(n) _________ number of total factors.
ODD
1.4
A MULTIPLE
Prime
48. v225=
The average of an EVEN number of consecutive integers will NEVER be an integer.
15
13
71 -73 -79
49. v256=
16
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
2.5
50. Prime Numbers:3x
The same sign as the base
The middle number
53 -59
31 -37