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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. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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

2. The prime factorization of __________ contains only EVEN powers of primes.
FACTOR
ODD
A PERFECT SQUARE
A MULTIPLE

3. v2˜
41 -43 -47
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.
FACTOR
1.4

4. 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
Put the coefficient under the radical to get a better approximation
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
3·3n = 3^{n+1}

5. 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
The middle number
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
The average of the set times the number of elements in the set

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!.
Prime factorization
ODD
1.4

7. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A non-multiple of N.
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

8. The sum of any two primes will be ____ - unless ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The sum of any two primes will be even - unless one of the two primes is 2.
1.7
If 2 cannot be one of the primes in the sum - the sum must be even.

9. If N is a divisor of x and y - then _______.
11 -13 -17 -19
The average of an EVEN number of consecutive integers will NEVER be an integer.
N is a divisor of x+y
41 -43 -47

10. 3n + 3n + 3n = _____ = ______
14
16
3·3n = 3^{n+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.

11. Prime Numbers:7x
71 -73 -79
2 -3 -5 -7
83 -89
The sum of any two primes will be even - unless one of the two primes is 2.

12. Prime Numbers:6x
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
97
83 -89

13. v169=
13
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE
2.5

14. Prime Numbers:5x
53 -59
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the average and the median are equal.
97

15. For ODD ROOTS - the root has ______.
2 -3 -5 -7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The same sign as the base
NEVER CONTRADICT ONE ANOTHER

16. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an EVEN number of consecutive integers will NEVER be an integer.

17. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A PERFECT SQUARE
A non-multiple of N.
3·3n = 3^{n+1}
1.4

18. 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
11 -13 -17 -19
3·3n = 3^{n+1}
97

19. Prime Numbers:8x
83 -89
[(last - first) / increment] + 1
FACTOR
23 -29

20. v256=
Either a multiple of N or a non-multiple of N
The average of an ODD number of consecutive integers will ALWAYS be an integer.
16
PERFECT CUBES

21. v3˜
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.
1.7
[(last - first) / increment] + 1

22. If estimating a root with a coefficient - _____ .
A MULTIPLE
Put the coefficient under the radical to get a better approximation
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

23. Any integer with an EVEN number of total factors cannot be ______.
The same sign as the base
Prime factorization
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

24. Prime Numbers:4x
A MULTIPLE
41 -43 -47
[(last - first) / increment] + 1
11 -13 -17 -19

25. Prime Numbers:2x
Put the coefficient under the radical to get a better approximation
ODD
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

26. The prime factorization of a perfect square contains only ______ powers of primes.
PERFECT CUBES
[(last - first) / increment] + 1
EVEN
25

27. Any integer with an ODD number of total factors must be _______.
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
1. The smallest or largest element 2. The increment 3. The number of items in the set
Put the coefficient under the radical to get a better approximation

28. v5˜
The same sign as the base
2.5
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 PERFECT SQUARE

29. Prime Numbers:1x
11 -13 -17 -19
The PRODUCT of n consecutive integers is divisible by n!.
A MULTIPLE
41 -43 -47

30. Prime Numbers:3x
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25
31 -37

31. 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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
[(last - first) / increment] + 1

32. The PRODUCT of n consecutive integers is divisible by ____.
53 -59
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set
16

33. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
31 -37
97
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ONLY the nonnegative root of the numberUNLIKE

34. v225=
A PERFECT SQUARE
15
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

35. All perfect squares have a(n) _________ number of total factors.
1. The smallest or largest element 2. The increment 3. The number of items in the set
53 -59
ODD
The sum of any two primes will be even - unless one of the two primes is 2.

36. ³v216 =
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE

37. The average of an EVEN number of consecutive integers will ________ be an integer.
2 -3 -5 -7
2.5
The average of an EVEN number of consecutive integers will NEVER be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

38. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
23 -29
The average of the set times the number of elements in the set
83 -89

39. Prime Numbers:0x
The average of the set times the number of elements in the set
The average of an EVEN number of consecutive integers will NEVER be an integer.
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.
2 -3 -5 -7

40. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Never prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Either a multiple of N or a non-multiple of N
15

41. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Either a multiple of N or a non-multiple of N
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
3·3n = 3^{n+1}

42. N! is _____ of all integers from 1 to N.
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A MULTIPLE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

43. Positive integers with only two factors must be ___.
2.5
53 -59
Prime
A MULTIPLE

44. 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

45. v625=
25
PERFECT CUBES
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.

46. The two statements in a data sufficiency problem will _______________.
2.5
The average of an EVEN number of consecutive integers will NEVER be an integer.
ONLY the nonnegative root of the numberUNLIKE
NEVER CONTRADICT ONE ANOTHER

47. 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 sum of any two primes will be even - unless one of the two primes is 2.
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set

48. v196=
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.
A MULTIPLE
14
NEVER CONTRADICT ONE ANOTHER

49. 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
25
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.

50. The average of an ODD number of consecutive integers will ________ be an integer.
71 -73 -79
The average of an EVEN number of consecutive integers will NEVER be an integer.
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.