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GMAT Number Properties

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. The two statements in a data sufficiency problem will _______________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
71 -73 -79
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

2. ³v216 =
11 -13 -17 -19
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
1.4

3. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
2 -3 -5 -7
The same sign as the base
A PERFECT SQUARE

4. Prime Numbers:2x
A PERFECT SQUARE
23 -29
N is a divisor of x+y
If 2 cannot be one of the primes in the sum - the sum must be even.

5. v225=
15
[(last - first) / increment] + 1
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

6. The formula for finding the number of consecutive multiples in a set is _______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
83 -89
[(last - first) / increment] + 1

7. How to find the sum of consecutive integers:
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.
N is a divisor of x+y
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.

8. 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
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 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 PERFECT SQUARE
Prime factorization

9. Prime Numbers:0x
2 -3 -5 -7
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
The same sign as the base

10. In an evenly spaced set - the sum of the terms is equal to ____.
1.4
A PERFECT SQUARE
The average of the set times the number of elements in the set
The same sign as the base

11. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
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.
1.4
1. The smallest or largest element 2. The increment 3. The number of items in the set

12. Any integer with an EVEN number of total factors cannot be ______.
41 -43 -47
A PERFECT SQUARE
A non-multiple of N.
1.7

13. The average of an EVEN number of consecutive integers will ________ be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Put the coefficient under the radical to get a better approximation
11 -13 -17 -19

14. Prime factors of _____ must come in pairs of three.
The middle number
PERFECT CUBES
In an evenly spaced set - the average and the median are equal.
14

15. The PRODUCT of n consecutive integers is divisible by ____.
EVEN
The PRODUCT of n consecutive integers is divisible by n!.
ONLY the nonnegative root of the numberUNLIKE
FACTOR

16. v5˜
25
2.5
15
1.7

17. Prime Numbers:8x
13
The average of the set times the number of elements in the set
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

18. 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
FACTOR
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD

19. 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.
2 -3 -5 -7
NEVER CONTRADICT ONE ANOTHER
The sum of any two primes will be even - unless one of the two primes is 2.

20. v256=
3·3n = 3^{n+1}
EVEN
61 -67
16

21. Prime Numbers:7x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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.
71 -73 -79
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 ________.
2 -3 -5 -7
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A non-multiple of N.
[(last - first) / increment] + 1

23. If 2 cannot be one of the primes in the sum - the sum must be _____.
PERFECT CUBES
97
ODD
If 2 cannot be one of the primes in the sum - the sum must be even.

24. v196=
ODD
14
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES

25. If the problem states/assumes that a number is an integer - check to see if you can use _______.
EVEN
Prime factorization
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
PERFECT CUBES

26. v2˜
3·3n = 3^{n+1}
53 -59
1.4
ODD

27. v625=
A PERFECT SQUARE
61 -67
11 -13 -17 -19
25

28. Prime Numbers:9x
31 -37
97
15
The sum of any two primes will be even - unless one of the two primes is 2.

29. If N is a divisor of x and y - then _______.
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS be an integer.
[(last - first) / increment] + 1
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.

30. Positive integers with only two factors must be ___.
Prime
The sum of any two primes will be even - unless one of the two primes is 2.
If 2 cannot be one of the primes in the sum - the sum must be even.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

31. 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.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER

32. 3n + 3n + 3n = _____ = ______
The PRODUCT of n consecutive integers is divisible by 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.
3·3n = 3^{n+1}
A PERFECT SQUARE

33. In an evenly spaced set - the average can be found by finding ________.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
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 middle number

34. 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
A MULTIPLE
[(last - first) / increment] + 1
The middle number

35. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
31 -37
97
NEVER CONTRADICT ONE ANOTHER

36. 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
1.4
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.
2 -3 -5 -7

37. v169=
13
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 PERFECT SQUARE
23 -29

38. All perfect squares have a(n) _________ number of total factors.
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
FACTOR
ODD

39. Prime Numbers:4x
41 -43 -47
[(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.
14

40. 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.
71 -73 -79
53 -59
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.

41. N! is _____ of all integers from 1 to N.
15
A MULTIPLE
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.
Prime

42. For ODD ROOTS - the root has ______.
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
The same sign as the base
In an evenly spaced set - the average and the median are equal.

43. The sum of any two primes will be ____ - unless ______.
The middle number
The sum of any two primes will be even - unless one of the two primes is 2.
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.
ODD

44. Positive integers with more than two factors are ____.
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
Never prime
71 -73 -79
A PERFECT SQUARE

45. Prime Numbers:3x
41 -43 -47
31 -37
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 mean and median are equal to the average of the first and the last number.

46. In an evenly spaced set - the ____ and the ____ are equal.
Prime
13
In an evenly spaced set - the average and the median are equal.
If 2 cannot be one of the primes in the sum - the sum must be even.

47. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set
FACTOR
15

48. 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

49. Prime Numbers:6x
A PERFECT SQUARE
14
Never prime
61 -67

50. 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
The average of an ODD number of consecutive integers will ALWAYS be an integer.
23 -29
Prime factorization