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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. v196=
Prime factorization
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37
14

2. If estimating a root with a coefficient - _____ .
2 -3 -5 -7
A MULTIPLE
Put the coefficient under the radical to get a better approximation
Never prime

3. All perfect squares have a(n) _________ number of total factors.
23 -29
ODD
1.7
A MULTIPLE

4. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE

5. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER

6. 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.
Prime
FACTOR
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

7. The PRODUCT of n consecutive integers is divisible by ____.
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.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
16

8. The average of an EVEN number of consecutive integers will ________ be an integer.
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
A non-multiple of N.
2 -3 -5 -7

9. Prime Numbers:0x
2 -3 -5 -7
The PRODUCT of n consecutive integers is divisible by n!.
Prime
A PERFECT SQUARE

10. N! is _____ of all integers from 1 to N.
If 2 cannot be one of the primes in the sum - the sum must be even.
A MULTIPLE
The same sign as the base
Put the coefficient under the radical to get a better approximation

11. 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?
53 -59
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.
FACTOR
16

12. Prime Numbers:8x
83 -89
2 -3 -5 -7
97
41 -43 -47

13. v256=
16
1.4
The average of an EVEN number of consecutive integers will NEVER be an integer.
The PRODUCT of n consecutive integers is divisible by n!.

14. The average of an ODD number of consecutive integers will ________ be an integer.
97
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS 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

15. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
1.4
Prime
PERFECT CUBES
FACTOR

16. v625=
The sum of any two primes will be even - unless one of the two primes is 2.
25
FACTOR
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

17. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Put the coefficient under the radical to get a better approximation
The middle number
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
FACTOR

18. In an evenly spaced set - the average can be found by finding ________.
A MULTIPLE
1.4
The middle number
41 -43 -47

19. Prime Numbers:3x
1. The smallest or largest element 2. The increment 3. The number of items in the set
23 -29
31 -37
A non-multiple of N.

20. Prime Numbers:4x
53 -59
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
31 -37

21. How to find the sum of consecutive integers:
83 -89
The same sign as the base
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.

22. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
PERFECT CUBES
N is a divisor of x+y
A non-multiple of N.
1.7

23. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
2 -3 -5 -7
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

24. Any integer with an EVEN number of total factors cannot be ______.
3·3n = 3^{n+1}
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
The average of the set times the number of elements in the set

25. Prime Numbers:1x
ONLY the nonnegative root of the numberUNLIKE
A MULTIPLE
11 -13 -17 -19
A PERFECT SQUARE

26. For ODD ROOTS - the root has ______.
The same sign as the base
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.
A non-multiple of N.

27. v169=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.
13
83 -89

28. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
[(last - first) / increment] + 1
The average of the set times the number of elements in the set

29. Prime Numbers:7x
71 -73 -79
83 -89
1.7
25

30. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The PRODUCT of n consecutive integers is divisible by n!.
23 -29

31. 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
ODD
1.7
NEVER CONTRADICT ONE ANOTHER
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

32. If 2 cannot be one of the primes in the sum - the sum must be _____.
41 -43 -47
N is a divisor of x+y
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.

33. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If 2 cannot be one of the primes in the sum - the sum must be even.
11 -13 -17 -19

34. 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
Prime
[(last - first) / increment] + 1
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
FACTOR

35. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
23 -29
A MULTIPLE
ONLY the nonnegative root of the numberUNLIKE
The average of an EVEN number of consecutive integers will NEVER be an integer.

36. If N is a divisor of x and y - then _______.
1.4
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
N is a divisor of x+y
A PERFECT SQUARE

37. v225=
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 PRODUCT of n consecutive integers is divisible by n!.
15
16

38. Prime Numbers:9x
15
The sum of any two primes will be even - unless one of the two primes is 2.
1.7
97

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
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ODD
ONLY the nonnegative root of the numberUNLIKE

40. Prime Numbers:2x
13
23 -29
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
N is a divisor of x+y

41. Prime Numbers:6x
83 -89
PERFECT CUBES
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.

42. Prime Numbers:5x
ONLY the nonnegative root of the numberUNLIKE
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.
Either a multiple of N or a non-multiple of N
53 -59

43. Positive integers with more than two factors are ____.
Never prime
83 -89
15
The PRODUCT of n consecutive integers is divisible by n!.

44. Positive integers with only two factors must be ___.
Prime
3·3n = 3^{n+1}
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

45. v2˜
16
ODD
1.4
41 -43 -47

46. If the problem states/assumes that a number is an integer - check to see if you can use _______.
2 -3 -5 -7
Prime factorization
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE

47. In an evenly spaced set - the sum of the terms is equal to ____.
EVEN
Prime factorization
14
The average of the set times the number of elements in the set

48. v5˜
23 -29
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
2.5
53 -59

49. v3˜
EVEN
1.7
Never prime
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

50. The prime factorization of __________ contains only EVEN powers of primes.
PERFECT CUBES
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
FACTOR