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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. For ODD ROOTS - the root has ______.
41 -43 -47
3·3n = 3^{n+1}
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set

2. 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 factorization
71 -73 -79
ONLY the nonnegative root of the numberUNLIKE
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.

3. v169=
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
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

4. 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
FACTOR
83 -89
53 -59

5. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
13
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.
[(last - first) / increment] + 1

6. In an evenly spaced set - the average can be found by finding ________.
The middle number
31 -37
The average of an EVEN number of consecutive integers will NEVER be an integer.
FACTOR

7. Positive integers with only two factors must be ___.
2.5
The middle number
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.

8. In an evenly spaced set - the sum of the terms is equal to ____.
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.
61 -67
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

9. v5˜
Prime
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.
41 -43 -47

10. The prime factorization of __________ contains only EVEN powers of primes.
25
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
N is a divisor of x+y
A PERFECT SQUARE

11. If 2 cannot be one of the primes in the sum - the sum must be _____.
The average of the set times the number of elements in the set
3·3n = 3^{n+1}
If 2 cannot be one of the primes in the sum - the sum must be even.
25

12. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Put the coefficient under the radical to get a better approximation
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The PRODUCT of n consecutive integers is divisible by n!.
Prime

13. ³v216 =
14
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
41 -43 -47
N is a divisor of x+y

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.
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 an ODD number of consecutive integers will ALWAYS be an integer.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

15. v3˜
N is a divisor of x+y
1.7
15
14

16. How to find the sum of consecutive integers:
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.
15
ONLY the nonnegative root of the numberUNLIKE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

17. The sum of any two primes will be ____ - unless ______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The sum of any two primes will be even - unless one of the two primes is 2.
PERFECT CUBES
The middle number

18. Prime Numbers:8x
13
Prime
3·3n = 3^{n+1}
83 -89

19. v2˜
14
2 -3 -5 -7
41 -43 -47
1.4

20. If the problem states/assumes that a number is an integer - check to see if you can use _______.
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!.
Prime factorization
Put the coefficient under the radical to get a better approximation

21. The two statements in a data sufficiency problem will _______________.
Prime
25
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7

22. Any integer with an ODD number of total factors must be _______.
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE
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.

23. N! is _____ of all integers from 1 to N.
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.
A MULTIPLE
53 -59
61 -67

24. v256=
ODD
Prime
16
Put the coefficient under the radical to get a better approximation

25. The average of an ODD number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
25
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE

26. Prime Numbers:0x
ONLY the nonnegative root of the numberUNLIKE
2 -3 -5 -7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

27. The average of an EVEN number of consecutive integers will ________ be an integer.
EVEN
Prime
The average of an EVEN number of consecutive integers will NEVER be an integer.
The same sign as the base

28. If N is a divisor of x and y - then _______.
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.
N is a divisor of x+y
FACTOR
Either a multiple of N or a non-multiple of N

29. 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

30. 3n + 3n + 3n = _____ = ______
25
1.4
3·3n = 3^{n+1}
PERFECT CUBES

31. Prime Numbers:5x
Prime factorization
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.
53 -59

32. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
41 -43 -47
A non-multiple of N.
25

33. Prime Numbers:2x
41 -43 -47
23 -29
Either a multiple of N or a non-multiple of N
71 -73 -79

34. Prime Numbers:4x
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE
41 -43 -47
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

35. Positive integers with more than two factors are ____.
16
Never prime
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

36. v225=
1. The smallest or largest element 2. The increment 3. The number of items in the set
23 -29
15
14

37. v196=
83 -89
Prime factorization
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

38. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.

39. Prime Numbers:7x
71 -73 -79
Put the coefficient under the radical to get a better approximation
The middle number
Never prime

40. Prime Numbers:9x
31 -37
97
16
In an evenly spaced set - the average and the median are equal.

41. Prime Numbers:1x
41 -43 -47
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

42. v625=
If 2 cannot be one of the primes in the sum - the sum must be even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25

43. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
15
23 -29
ONLY the nonnegative root of the numberUNLIKE

44. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
The sum of any two primes will be even - unless one of the two primes is 2.
2.5
16

45. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime factorization
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.

46. 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
23 -29
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
A non-multiple of N.

47. The formula for finding the number of consecutive multiples in a set is _______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
53 -59
15
[(last - first) / increment] + 1

48. Prime Numbers:6x
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
61 -67
11 -13 -17 -19

49. If estimating a root with a coefficient - _____ .
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The sum of any two primes will be even - unless one of the two primes is 2.
Put the coefficient under the radical to get a better approximation
The same sign as the base

50. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
13
11 -13 -17 -19
FACTOR