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GMAT Number Properties

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. In an evenly spaced set - the ____ and the ____ are equal.
71 -73 -79
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.
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.

2. The prime factorization of __________ contains only EVEN powers of primes.
A non-multiple of N.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE

3. Prime Numbers:1x
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.
1. The smallest or largest element 2. The increment 3. The number of items in the set
N is a divisor of x+y

4. Any integer with an ODD number of total factors must be _______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
97
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

5. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The middle number
3·3n = 3^{n+1}
Prime factorization
ONLY the nonnegative root of the numberUNLIKE

6. 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.
Put the coefficient under the radical to get a better approximation
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

7. In an evenly spaced set - the sum of the terms is equal to ____.
FACTOR
The average of the set times the number of elements in the set
In an evenly spaced set - the average and the median are equal.
53 -59

8. v5˜
Prime
2.5
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

9. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
Either a multiple of N or a non-multiple of N
The same sign as the base
23 -29

10. v2˜
61 -67
1.4
EVEN
13

11. In an evenly spaced set - the average can be found by finding ________.
The middle number
53 -59
2 -3 -5 -7
14

12. v625=
97
1.7
25
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. Prime Numbers:2x
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

14. Prime Numbers:4x
15
Either a multiple of N or a non-multiple of N
ODD
41 -43 -47

15. Let N be an integer. If you add two non-multiples of N - the result could be _______.
83 -89
15
13
Either a multiple of N or a non-multiple of N

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. All perfect squares have a(n) _________ number of total factors.
PERFECT CUBES
13
97
ODD

18. v3˜
The average of an EVEN number of consecutive integers will NEVER be an integer.
3·3n = 3^{n+1}
1.7
11 -13 -17 -19

19. 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
25
1.4
ONLY the nonnegative root of the numberUNLIKE

20. Positive integers with only two factors must be ___.
15
Prime
83 -89
Never prime

21. Prime Numbers:0x
Never prime
FACTOR
2 -3 -5 -7
1.7

22. Prime Numbers:7x
The PRODUCT of n consecutive integers is divisible by n!.
71 -73 -79
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
N is a divisor of x+y

23. The average of an EVEN number of consecutive integers will ________ be an integer.
NEVER CONTRADICT ONE ANOTHER
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.
The PRODUCT of n consecutive integers is divisible by n!.

24. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.
15
The average of an ODD number of consecutive integers will ALWAYS be an integer.

25. Any integer with an EVEN number of total factors cannot be ______.
15
A MULTIPLE
1.4
A PERFECT SQUARE

26. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The sum of any two primes will be even - unless one of the two primes is 2.
The same sign as the base
FACTOR
In an evenly spaced set - the average and the median are equal.

27. The formula for finding the number of consecutive multiples in a set is _______.
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
[(last - first) / increment] + 1

28. If N is a divisor of x and y - then _______.
[(last - first) / increment] + 1
N is a divisor of x+y
16
The average of an ODD number of consecutive integers will ALWAYS be an integer.

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.
Either a multiple of N or a non-multiple of N
71 -73 -79
23 -29

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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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 2 cannot be one of the primes in the sum - the sum must be even.
Prime

31. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
15
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 any two primes will be even - unless one of the two primes is 2.

32. v225=
3·3n = 3^{n+1}
15
2.5
71 -73 -79

33. Positive integers with more than two factors are ____.
A non-multiple of N.
83 -89
Never prime
61 -67

34. Prime Numbers:6x
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
1.7
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.

35. For ODD ROOTS - the root has ______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The same sign as the base
PERFECT CUBES
1.4

36. Prime factors of _____ must come in pairs of three.
71 -73 -79
A PERFECT SQUARE
PERFECT CUBES
The PRODUCT of n consecutive integers is divisible by n!.

37. The sum of any two primes will be ____ - unless ______.
In an evenly spaced set - the average and the median are equal.
FACTOR
2.5
The sum of any two primes will be even - unless one of the two primes is 2.

38. v169=
83 -89
1.7
13
23 -29

39. In an evenly spaced set - the mean and median are equal to the _____ of _________.
The average of an EVEN number of consecutive integers will NEVER be 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
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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

40. Prime Numbers:3x
31 -37
2.5
97
A PERFECT SQUARE

41. The average of an ODD number of consecutive integers will ________ be an integer.
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
16
The average of an ODD number of consecutive integers will ALWAYS be an integer.

42. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The same sign as the base
61 -67
A non-multiple of N.
2.5

43. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
23 -29
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Never prime
1. The smallest or largest element 2. The increment 3. The number of items in the set

44. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime factorization
71 -73 -79
31 -37

45. Prime Numbers:9x
25
97
41 -43 -47
If 2 cannot be one of the primes in the sum - the sum must be even.

46. How to find the sum of consecutive integers:
11 -13 -17 -19
Either a multiple of N or a non-multiple 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
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.

47. ³v216 =
2.5
25
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
61 -67

48. Prime Numbers:5x
[(last - first) / increment] + 1
53 -59
23 -29
83 -89

49. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
16

50. If 2 cannot be one of the primes in the sum - the sum must be _____.
31 -37
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.
71 -73 -79
If 2 cannot be one of the primes in the sum - the sum must be even.