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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. Prime Numbers:0x
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
A PERFECT SQUARE
A PERFECT SQUARE

2. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A MULTIPLE
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE

3. 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

4. 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.
ODD
41 -43 -47
15

5. In an evenly spaced set - the average can be found by finding ________.
13
The middle number
EVEN
1.4

6. v3˜
The sum of any two primes will be even - unless one of the two primes is 2.
16
11 -13 -17 -19
1.7

7. Prime Numbers:6x
3·3n = 3^{n+1}
61 -67
16
FACTOR

8. 3n + 3n + 3n = _____ = ______
41 -43 -47
3·3n = 3^{n+1}
A MULTIPLE
A non-multiple of N.

9. Let N be an integer. If you add two non-multiples of N - the result could be _______.
15
61 -67
Either a multiple of N or a non-multiple of N
25

10. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.
11 -13 -17 -19

11. Any integer with an EVEN number of total factors cannot be ______.
The middle number
A PERFECT SQUARE
1.7
16

12. 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
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.
71 -73 -79
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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

13. If 2 cannot be one of the primes in the sum - the sum must be _____.
97
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.

14. v256=
ODD
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Prime factorization
16

15. Positive integers with only two factors must be ___.
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.
N is a divisor of x+y
Prime

16. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set
FACTOR

17. N! is _____ of all integers from 1 to N.
ODD
A MULTIPLE
1.4
25

18. 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?
2.5
The average of an EVEN number of consecutive integers will NEVER be an integer.
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.
1.4

19. v196=
31 -37
A PERFECT SQUARE
The average of the set times the number of elements in the set
14

20. In an evenly spaced set - the ____ and the ____ are equal.
14
The same sign as the base
In an evenly spaced set - the average and the median are equal.
ODD

21. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE

22. ³v216 =
EVEN
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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.

23. v225=
71 -73 -79
15
13
Put the coefficient under the radical to get a better approximation

24. The average of an EVEN number of consecutive integers will ________ be an integer.
N is a divisor of x+y
13
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES

25. If N is a divisor of x and y - then _______.
N is a divisor of x+y
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.

26. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
16
2.5
The average of the set times the number of elements in the set

27. Positive integers with more than two factors are ____.
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Never prime
31 -37

28. Prime Numbers:5x
Prime factorization
53 -59
Either a multiple of N or a non-multiple of N
A non-multiple of N.

29. The average of an ODD number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.7
EVEN

30. Prime Numbers:8x
83 -89
1.4
[(last - first) / increment] + 1
1.7

31. Prime Numbers:1x
ODD
A non-multiple of N.
11 -13 -17 -19
[(last - first) / increment] + 1

32. The two statements in a data sufficiency problem will _______________.
Either a multiple of N or a non-multiple of N
41 -43 -47
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7

33. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
1.4
Put the coefficient under the radical to get a better approximation
25
ONLY the nonnegative root of the numberUNLIKE

34. v5˜
25
The average of an EVEN number of consecutive integers will NEVER be an integer.
2.5
Either a multiple of N or a non-multiple of N

35. 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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

36. For ODD ROOTS - the root has ______.
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.
Never prime
1. The smallest or largest element 2. The increment 3. The number of items in the set
The same sign as the base

37. If the problem states/assumes that a number is an integer - check to see if you can use _______.
EVEN
FACTOR
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime factorization

38. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
14
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

39. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
[(last - first) / increment] + 1
Put the coefficient under the radical to get a better approximation
A non-multiple of N.
EVEN

40. All perfect squares have a(n) _________ number of total factors.
[(last - first) / increment] + 1
ODD
If 2 cannot be one of the primes in the sum - the sum must be even.
Never prime

41. How to find the sum of consecutive integers:
25
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.
N is a divisor of x+y
2 -3 -5 -7

42. Prime factors of _____ must come in pairs of three.
The sum of any two primes will be even - unless one of the two primes is 2.
25
A non-multiple of N.
PERFECT CUBES

43. v625=
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 average of the set times the number of elements in the set
Prime factorization
25

44. In an evenly spaced set - the sum of the terms is equal to ____.
EVEN
The average of the set times the number of elements in the set
15
3·3n = 3^{n+1}

45. 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
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.
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.

46. The PRODUCT of n consecutive integers is divisible by ____.
23 -29
The middle number
The PRODUCT of n consecutive integers is divisible by n!.
13

47. v169=
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
N is a divisor of x+y
13
61 -67

48. The prime factorization of __________ contains only EVEN powers of primes.
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
2.5
PERFECT CUBES

49. Prime Numbers:4x
16
41 -43 -47
Prime factorization
3·3n = 3^{n+1}

50. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
15
[(last - first) / increment] + 1
11 -13 -17 -19