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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. The prime factorization of __________ contains only EVEN powers of primes.
EVEN
53 -59
A PERFECT SQUARE
ODD

2. Prime Numbers:1x
The sum of any two primes will be even - unless one of the two primes is 2.
11 -13 -17 -19
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.
25

3. Prime Numbers:0x
15
61 -67
2 -3 -5 -7
FACTOR

4. Prime Numbers:9x
97
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.
15
23 -29

5. Prime Numbers:2x
A MULTIPLE
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
23 -29

6. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
71 -73 -79
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.

7. If 2 cannot be one of the primes in the sum - the sum must be _____.
The same sign as the base
If 2 cannot be one of the primes in the sum - the sum must be 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
The average of an ODD number of consecutive integers will ALWAYS be an integer.

8. Positive integers with only two factors must be ___.
Prime
83 -89
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set

9. Any integer with an EVEN number of total factors cannot be ______.
1.4
A PERFECT SQUARE
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. The smallest or largest element 2. The increment 3. The number of items in the set

10. 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 average of an ODD number of consecutive integers will ALWAYS be an integer.
Put the coefficient under the radical to get a better approximation
FACTOR

11. v3˜
53 -59
31 -37
1.7
15

12. v225=
15
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime factorization
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

13. If N is a divisor of x and y - then _______.
A MULTIPLE
Put the coefficient under the radical to get a better approximation
N is a divisor of x+y
ODD

14. ³v216 =
14
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The average of the set times the number of elements in the set
2 -3 -5 -7

15. In an evenly spaced set - the average can be found by finding ________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
The middle number
NEVER CONTRADICT ONE ANOTHER

16. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
41 -43 -47
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

17. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
71 -73 -79
FACTOR
2.5
97

18. Let N be an integer. If you add two non-multiples of N - the result could be _______.
ODD
The middle number
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

19. 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

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20. v196=
NEVER CONTRADICT ONE ANOTHER
14
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of an EVEN number of consecutive integers will NEVER be an integer.

21. For ODD ROOTS - the root has ______.
The same sign as the base
23 -29
[(last - first) / increment] + 1
14

22. v256=
2.5
16
Either a multiple of N or a non-multiple of N
ODD

23. Prime Numbers:3x
FACTOR
53 -59
ONLY the nonnegative root of the numberUNLIKE
31 -37

24. Prime Numbers:8x
83 -89
FACTOR
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
3·3n = 3^{n+1}

25. If estimating a root with a coefficient - _____ .
2.5
11 -13 -17 -19
Put the coefficient under the radical to get a better approximation
61 -67

26. Prime Numbers:4x
41 -43 -47
A non-multiple of N.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
NEVER CONTRADICT ONE ANOTHER

27. 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.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime
Prime factorization

28. The average of an EVEN number of consecutive integers will ________ be an integer.
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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47

29. 3n + 3n + 3n = _____ = ______
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.
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER

30. v169=
The PRODUCT of n consecutive integers is divisible by n!.
13
2.5
EVEN

31. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
The middle number

32. Prime Numbers:6x
The average of the set times the number of elements in the set
61 -67
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
71 -73 -79

33. N! is _____ of all integers from 1 to N.
23 -29
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
13
A MULTIPLE

34. 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.
In an evenly spaced set - the average and the median are equal.
NEVER CONTRADICT ONE ANOTHER
The sum of any two primes will be even - unless one of the two primes is 2.

35. v2˜
A PERFECT SQUARE
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
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.

36. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
The same sign as the base
1.7
3·3n = 3^{n+1}

37. Prime Numbers:7x
FACTOR
71 -73 -79
Never prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

38. Positive integers with more than two factors are ____.
Never prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

39. All perfect squares have a(n) _________ number of total factors.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.7
71 -73 -79
ODD

40. In an evenly spaced set - the ____ and the ____ are equal.
13
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.
23 -29

41. In an evenly spaced set - the sum of the terms is equal to ____.
13
NEVER CONTRADICT ONE ANOTHER
The average of the set times the number of elements in the set
Either a multiple of N or a non-multiple of N

42. 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
11 -13 -17 -19
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.
2.5

43. v5˜
A PERFECT SQUARE
The same sign as the base
2.5
A non-multiple of N.

44. The two statements in a data sufficiency problem will _______________.
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.
NEVER CONTRADICT ONE ANOTHER
Prime factorization
31 -37

45. How to find the sum of consecutive integers:
FACTOR
ODD
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.

46. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
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.
ONLY the nonnegative root of the numberUNLIKE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

47. 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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
25
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

48. In an evenly spaced set - the mean and median are equal to the _____ of _________.
PERFECT CUBES
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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
41 -43 -47

49. 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
PERFECT CUBES
1.7
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 average of the set times the number of elements in the set

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?
15
14
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.