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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 ODD number of total factors must be _______.
A PERFECT SQUARE
EVEN
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
2 -3 -5 -7

2. Prime Numbers:9x
97
61 -67
N is a divisor of x+y
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

3. Prime Numbers:5x
41 -43 -47
2 -3 -5 -7
53 -59
In an evenly spaced set - the average and the median are equal.

4. Prime Numbers:6x
The average of the set times the number of elements in the set
23 -29
The middle number
61 -67

5. Prime Numbers:1x
[(last - first) / increment] + 1
FACTOR
Prime factorization
11 -13 -17 -19

6. v2˜
PERFECT CUBES
11 -13 -17 -19
1.4
The average of an ODD number of consecutive integers will ALWAYS be an integer.

7. Positive integers with only two factors must be ___.
97
Prime factorization
Prime
Put the coefficient under the radical to get a better approximation

8. Prime Numbers:7x
Prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2.5
71 -73 -79

9. Any integer with an EVEN number of total factors cannot be ______.
11 -13 -17 -19
61 -67
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE

10. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
Prime
15
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.

11. v196=
3·3n = 3^{n+1}
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
25
14

12. 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
14
The same sign as the base
13

13. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER
The PRODUCT of n consecutive integers is divisible by n!.
FACTOR

14. All perfect squares have a(n) _________ number of total factors.
Prime
ODD
EVEN
2 -3 -5 -7

15. How to find the sum of consecutive integers:
15
31 -37
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.
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.

16. 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
31 -37
If 2 cannot be one of the primes in the sum - the sum must be even.
15
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

17. 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

18. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
2 -3 -5 -7

19. 3n + 3n + 3n = _____ = ______
13
61 -67
3·3n = 3^{n+1}
N is a divisor of x+y

20. 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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
97
FACTOR

21. Prime Numbers:2x
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.
NEVER CONTRADICT ONE ANOTHER
23 -29

22. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
The average of the set times the number of elements in the set
1.7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

23. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
1.4
97
Never prime

24. Let N be an integer. If you add two non-multiples of N - the result could be _______.
A PERFECT SQUARE
25
Either a multiple of N or a non-multiple of N
41 -43 -47

25. For ODD ROOTS - the root has ______.
[(last - first) / increment] + 1
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.
The same sign as the base

26. v225=
23 -29
Prime
15
NEVER CONTRADICT ONE ANOTHER

27. The PRODUCT of n consecutive integers is divisible by ____.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
15
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The PRODUCT of n consecutive integers is divisible by n!.

28. v3˜
2.5
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
1.7

29. If 2 cannot be one of the primes in the sum - the sum must be _____.
A MULTIPLE
16
Prime factorization
If 2 cannot be one of the primes in the sum - the sum must be even.

30. Prime Numbers:8x
2.5
1. The smallest or largest element 2. The increment 3. The number of items in the set
PERFECT CUBES
83 -89

31. 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.
If 2 cannot be one of the primes in the sum - the sum must be even.
The middle number
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

32. ³v216 =
2.5
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.
A MULTIPLE

33. v625=
25
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE

34. v256=
[(last - first) / increment] + 1
2 -3 -5 -7
16
ONLY the nonnegative root of the numberUNLIKE

35. Prime Numbers:4x
25
The same sign as the base
41 -43 -47
ODD

36. 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.
1.7
11 -13 -17 -19
N is a divisor of x+y

37. 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 factorization
Put the coefficient under the radical to get a better approximation
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

38. The formula for finding the number of consecutive multiples in a set is _______.
Either a multiple of N or a non-multiple of N
25
[(last - first) / increment] + 1
97

39. v169=
A MULTIPLE
13
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.

40. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
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 SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A non-multiple of N.
1.7

41. 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
25
If 2 cannot be one of the primes in the sum - the sum must be even.
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

42. 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
53 -59
31 -37
13

43. Positive integers with more than two factors are ____.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime
2 -3 -5 -7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

44. The prime factorization of a perfect square contains only ______ powers of primes.
Put the coefficient under the radical to get a better approximation
53 -59
EVEN
83 -89

45. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
Never prime
ONLY the nonnegative root of the numberUNLIKE
EVEN
Prime factorization

46. The average of an EVEN number of consecutive integers will ________ be an integer.
13
The average of an EVEN number of consecutive integers will NEVER be an integer.
[(last - first) / increment] + 1
2.5

47. The prime factorization of __________ contains only EVEN powers of primes.
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.
61 -67
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 PERFECT SQUARE

48. The two statements in a data sufficiency problem will _______________.
The average of an EVEN number of consecutive integers will NEVER be an integer.
NEVER CONTRADICT ONE ANOTHER
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.
61 -67

49. In an evenly spaced set - the average can be found by finding ________.
The same sign as the base
If 2 cannot be one of the primes in the sum - the sum must be even.
16
The middle number

50. 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?
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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
31 -37