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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. Any integer with an EVEN number of total factors cannot be ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.

2. v196=
61 -67
Prime
PERFECT CUBES
14

3. v169=
The average of an ODD number of consecutive integers will ALWAYS be an integer.
3·3n = 3^{n+1}
The average of the set times the number of elements in the set
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.
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
[(last - first) / increment] + 1
Prime

5. Prime Numbers:8x
83 -89
1.7
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.
13

6. If 2 cannot be one of the primes in the sum - the sum must be _____.
1.7
If 2 cannot be one of the primes in the sum - the sum must be even.
A MULTIPLE
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.

7. ³v216 =
53 -59
71 -73 -79
N is a divisor of x+y
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

8. v5˜
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2.5

9. In an evenly spaced set - the ____ and the ____ are equal.
16
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.

10. 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 average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime factorization
61 -67

11. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
15
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ODD
A non-multiple of N.

12. In an evenly spaced set - the mean and median are equal to the _____ of _________.
N is a divisor of x+y
In an evenly spaced set - the average and the median are equal.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
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.

13. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
ONLY the nonnegative root of the numberUNLIKE
FACTOR
1. The smallest or largest element 2. The increment 3. The number of items in the set
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

14. Any integer with an ODD number of total factors must be _______.
16
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.
Never prime

15. For ODD ROOTS - the root has ______.
The same sign as the base
EVEN
16
A MULTIPLE

16. v625=
The average of the set times the number of elements in the set
Prime
25
1.4

17. Prime Numbers:3x
N is a divisor of x+y
31 -37
83 -89
3·3n = 3^{n+1}

18. The prime factorization of a perfect square contains only ______ powers of primes.
PERFECT CUBES
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN
The same sign as the base

19. Prime Numbers:0x
A PERFECT SQUARE
11 -13 -17 -19
2 -3 -5 -7
N is a divisor of x+y

20. Prime Numbers:4x
A MULTIPLE
71 -73 -79
97
41 -43 -47

21. The average of an ODD number of consecutive integers will ________ be an integer.
[(last - first) / increment] + 1
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.
41 -43 -47
The average of an ODD number of consecutive integers will ALWAYS be an integer.

22. Prime Numbers:2x
23 -29
The middle number
PERFECT CUBES
2 -3 -5 -7

23. 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 SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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!.
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.

24. v2˜
The average of the set times the number of elements in the set
1.4
97
Prime factorization

25. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
EVEN
97
ONLY the nonnegative root of the numberUNLIKE
71 -73 -79

26. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
3·3n = 3^{n+1}
Prime factorization
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE

27. v3˜
Either a multiple of N or a non-multiple of N
1.7
16
In an evenly spaced set - the average and the median are equal.

28. The PRODUCT of n consecutive integers is divisible by ____.
[(last - first) / increment] + 1
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}
The middle number

29. In an evenly spaced set - the average can be found by finding ________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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
14

30. Prime Numbers:9x
ONLY the nonnegative root of the numberUNLIKE
97
The middle number
1.4

31. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Put the coefficient under the radical to get a better approximation
Either a multiple of N or a non-multiple of N
PERFECT CUBES
15

32. In an evenly spaced set - the sum of the terms is equal to ____.
NEVER CONTRADICT ONE ANOTHER
Never prime
The average of the set times the number of elements in the set
A MULTIPLE

33. Prime Numbers:6x
61 -67
1.7
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

34. The prime factorization of __________ contains only EVEN powers of primes.
3·3n = 3^{n+1}
The sum of any two primes will be even - unless one of the two primes is 2.
11 -13 -17 -19
A PERFECT SQUARE

35. 3n + 3n + 3n = _____ = ______
PERFECT CUBES
Prime
3·3n = 3^{n+1}
Put the coefficient under the radical to get a better approximation

36. If N is a divisor of x and y - then _______.
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
14
N is a divisor of x+y

37. If estimating a root with a coefficient - _____ .
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
Put the coefficient under the radical to get a better approximation
83 -89
41 -43 -47

38. The two statements in a data sufficiency problem will _______________.
25
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER

39. N! is _____ of all integers from 1 to N.
The middle number
The average of an EVEN number of consecutive integers will NEVER be an integer.
Either a multiple of N or a non-multiple of N
A MULTIPLE

40. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Either a multiple of N or a non-multiple of N

41. 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?
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
71 -73 -79
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.

42. Positive integers with more than two factors are ____.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Never prime
ONLY the nonnegative root of the numberUNLIKE
The same sign as the base

43. How to find the sum of consecutive integers:
The sum of any two primes will be even - unless one of the two primes is 2.
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.
NEVER CONTRADICT ONE ANOTHER
71 -73 -79

44. The average of an EVEN number of consecutive integers will ________ be an integer.
53 -59
83 -89
N is a divisor of x+y
The average of an EVEN number of consecutive integers will NEVER be an integer.

45. All perfect squares have a(n) _________ number of total factors.
A non-multiple of N.
2 -3 -5 -7
If 2 cannot be one of the primes in the sum - the sum must be even.
ODD

46. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A non-multiple of N.
Never prime
The PRODUCT of n consecutive integers is divisible by n!.
97

47. 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
Either a multiple of N or a non-multiple of N
16
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER

48. v256=
PERFECT CUBES
1.7
3·3n = 3^{n+1}
16

49. Prime Numbers:1x
N is a divisor of x+y
11 -13 -17 -19
PERFECT CUBES
[(last - first) / increment] + 1

50. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
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.
53 -59
23 -29