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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. 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
The same sign as the base
The average of the set times the number of elements in the set
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

2. Positive integers with only two factors must be ___.
25
Prime
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

3. If 2 cannot be one of the primes in the sum - the sum must be _____.
The middle number
31 -37
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE

4. 3n + 3n + 3n = _____ = ______
FACTOR
Prime
3·3n = 3^{n+1}
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

5. 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.
A PERFECT SQUARE
A MULTIPLE
The average of the set times the number of elements in the set

6. All perfect squares have a(n) _________ number of total factors.
15
23 -29
In an evenly spaced set - the average and the median are equal.
ODD

7. Prime Numbers:9x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
A non-multiple of N.
97

8. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
11 -13 -17 -19
[(last - first) / increment] + 1
The PRODUCT of n consecutive integers is divisible by n!.

9. v256=
16
The middle 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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

10. If estimating a root with a coefficient - _____ .
EVEN
23 -29
16
Put the coefficient under the radical to get a better approximation

11. v2˜
1.4
NEVER CONTRADICT ONE ANOTHER
The middle number
If 2 cannot be one of the primes in the sum - the sum must be even.

12. Prime Numbers:1x
83 -89
11 -13 -17 -19
1.4
EVEN

13. The average of an EVEN number of consecutive integers will ________ be an integer.
2 -3 -5 -7
A non-multiple of N.
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES

14. For ODD ROOTS - the root has ______.
14
EVEN
1.7
The same sign as the base

15. 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?
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
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 same sign as the base

16. v225=
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
13
15

17. The prime factorization of __________ contains only EVEN powers of primes.
Prime factorization
The average of the set times the number of elements in the set
23 -29
A PERFECT SQUARE

18. Any integer with an EVEN number of total factors cannot be ______.
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
EVEN

19. The formula for finding the number of consecutive multiples in a set is _______.
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.
The same sign as the base
[(last - first) / increment] + 1

20. v5˜
2.5
The middle number
1.4
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.

21. Let N be an integer. If you add two non-multiples of N - the result could be _______.
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
Either a multiple of N or a non-multiple of N
3·3n = 3^{n+1}
ODD

22. v169=
14
The PRODUCT of n consecutive integers is divisible by n!.
13
83 -89

23. Prime Numbers:4x
FACTOR
41 -43 -47
EVEN
71 -73 -79

24. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
The sum of any two primes will be even - unless one of the two primes is 2.
The middle number
Either a multiple of N or a non-multiple of N
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

25. Prime Numbers:8x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
83 -89
Prime
14

26. Positive integers with more than two factors are ____.
61 -67
13
Never prime
A non-multiple of N.

27. In an evenly spaced set - the sum of the terms is equal to ____.
A PERFECT SQUARE
13
The average of the set times the number of elements in the set
41 -43 -47

28. Prime Numbers:2x
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.
23 -29
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

29. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
PERFECT CUBES
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
3·3n = 3^{n+1}

30. How to find the sum of consecutive integers:
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
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.

31. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
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
PERFECT CUBES
61 -67
FACTOR

32. 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.
15
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

33. v3˜
A MULTIPLE
NEVER CONTRADICT ONE ANOTHER
1.7
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.

34. 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.
41 -43 -47
25
Never prime

35. v625=
31 -37
In an evenly spaced set - the average and the median are equal.
25
2.5

36. ³v216 =
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
14
N is a divisor of x+y

37. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
PERFECT CUBES

38. If N is a divisor of x and y - then _______.
61 -67
97
The average of an EVEN number of consecutive integers will NEVER be an integer.
N is a divisor of x+y

39. Prime Numbers:0x
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7
The same sign as the base

40. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The PRODUCT of n consecutive integers is divisible by n!.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
31 -37
ONLY the nonnegative root of the numberUNLIKE

41. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.7
2.5

42. In an evenly spaced set - the ____ and the ____ are equal.
1.7
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the average and the median are equal.

43. In an evenly spaced set - the mean and median are equal to the _____ of _________.
If 2 cannot be one of the primes in the sum - the sum must be even.
ODD
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.7

44. In an evenly spaced set - the average can be found by finding ________.
The middle number
In an evenly spaced set - the average and the median are equal.
2.5
31 -37

45. Prime Numbers:7x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ONLY the nonnegative root of the numberUNLIKE
[(last - first) / increment] + 1
71 -73 -79

46. Prime Numbers:3x
31 -37
16
ODD
If 2 cannot be one of the primes in the sum - the sum must be even.

47. Prime factors of _____ must come in pairs of three.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
PERFECT CUBES

48. If the problem states/assumes that a number is an integer - check to see if you can use _______.
PERFECT CUBES
1.4
Prime factorization
[(last - first) / increment] + 1

49. Prime Numbers:5x
53 -59
ODD
1.7
The sum of any two primes will be even - unless one of the two primes is 2.

50. Prime Numbers:6x
97
31 -37
61 -67
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.