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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. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime
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.
[(last - first) / increment] + 1

2. v196=
1. The smallest or largest element 2. The increment 3. The number of items in the set
ODD
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
14

3. Prime Numbers:6x
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}
Either a multiple of N or a non-multiple of N
61 -67

4. v5˜
EVEN
2.5
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
15

5. Prime Numbers:5x
53 -59
If 2 cannot be one of the primes in the sum - the sum must be even.
N is a divisor of x+y
PERFECT CUBES

6. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The PRODUCT of n consecutive integers is divisible by n!.
11 -13 -17 -19
61 -67
Prime factorization

7. Prime Numbers:1x
11 -13 -17 -19
16
The same sign as the base
1.4

8. 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?
13
3·3n = 3^{n+1}
83 -89
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.

9. The average of an ODD number of consecutive integers will ________ be an integer.
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.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
14
FACTOR

10. v2˜
14
41 -43 -47
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

11. Prime Numbers:9x
Never prime
97
The PRODUCT of n consecutive integers is divisible by n!.
53 -59

12. ³v216 =
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
16
13

13. 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.
EVEN
2 -3 -5 -7
NEVER CONTRADICT ONE ANOTHER

14. 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.
23 -29
25
The average of the set times the number of elements in the set

15. All perfect squares have a(n) _________ number of total factors.
FACTOR
61 -67
N is a divisor of x+y
ODD

16. In an evenly spaced set - the sum of the terms is equal to ____.
The PRODUCT of n consecutive integers is divisible by n!.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of the set times the number of elements in the set
FACTOR

17. v3˜
25
1.7
61 -67
N is a divisor of x+y

18. Prime Numbers:3x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
31 -37
2.5
1.4

19. How to find the sum of consecutive integers:
The middle number
97
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.

20. 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 SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A non-multiple of N.
The average of an EVEN number of consecutive integers will NEVER be an integer.

21. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
61 -67
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 average of an ODD number of consecutive integers will ALWAYS be an integer.

22. v256=
1.7
Prime
71 -73 -79
16

23. For ODD ROOTS - the root has ______.
14
3·3n = 3^{n+1}
The same sign as the base
Put the coefficient under the radical to get a better approximation

24. The two statements in a data sufficiency problem will _______________.
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
[(last - first) / increment] + 1
NEVER CONTRADICT ONE ANOTHER

25. v169=
Put the coefficient under the radical to get a better approximation
ONLY the nonnegative root of the numberUNLIKE
13
The average of an EVEN number of consecutive integers will NEVER be an integer.

26. Positive integers with only two factors must be ___.
Prime
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.
A MULTIPLE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

27. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
13
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.
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.

28. 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
13
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The middle number

29. The prime factorization of __________ contains only EVEN powers of primes.
If 2 cannot be one of the primes in the sum - the sum must be even.
71 -73 -79
A PERFECT SQUARE
Prime

30. 3n + 3n + 3n = _____ = ______
23 -29
3·3n = 3^{n+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.
Either a multiple of N or a non-multiple of N

31. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Either a multiple of N or a non-multiple of N
23 -29
In an evenly spaced set - the average and the median are equal.
2 -3 -5 -7

32. Prime Numbers:0x
2 -3 -5 -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.
A MULTIPLE
EVEN

33. The sum of any two primes will be ____ - unless ______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The sum of any two primes will be even - unless one of the two primes is 2.
Prime factorization
14

34. In an evenly spaced set - the average can be found by finding ________.
The sum of any two primes will be even - unless one of the two primes is 2.
1.4
The middle number
N is a divisor of x+y

35. Prime Numbers:8x
83 -89
11 -13 -17 -19
A PERFECT SQUARE
14

36. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
25
1.7
2.5
ONLY the nonnegative root of the numberUNLIKE

37. If 2 cannot be one of the primes in the sum - the sum must be _____.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
ODD
A non-multiple of N.

38. 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
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
The PRODUCT of n consecutive integers is divisible by n!.
N is a divisor of x+y

39. 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

40. If N is a divisor of x and y - then _______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
FACTOR
31 -37
N is a divisor of x+y

41. v225=
15
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of an EVEN number of consecutive integers will NEVER be an integer.
25

42. Any integer with an EVEN number of total factors cannot be ______.
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
31 -37

43. N! is _____ of all integers from 1 to N.
Prime
A MULTIPLE
61 -67
FACTOR

44. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
ODD
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE
FACTOR

45. The PRODUCT of n consecutive integers is divisible by ____.
ODD
The PRODUCT of n consecutive integers is divisible by n!.
1.7
53 -59

46. Prime Numbers:4x
41 -43 -47
ODD
53 -59
1.4

47. If estimating a root with a coefficient - _____ .
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Put the coefficient under the radical to get a better approximation

48. The formula for finding the number of consecutive multiples in a set is _______.
Never prime
11 -13 -17 -19
[(last - first) / increment] + 1
15

49. Prime factors of _____ must come in pairs of three.
Never prime
A PERFECT SQUARE
ODD
PERFECT CUBES

50. The average of an EVEN number of consecutive integers will ________ be an integer.
Never prime
ONLY the nonnegative root of the numberUNLIKE
The average of an EVEN number of consecutive integers will NEVER be an integer.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹