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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. If the problem states/assumes that a number is an integer - check to see if you can use _______.
FACTOR
11 -13 -17 -19
Prime factorization
61 -67

2. Prime Numbers:5x
53 -59
2 -3 -5 -7
A PERFECT SQUARE
PERFECT CUBES

3. Positive integers with only two factors must be ___.
Prime
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.
A MULTIPLE
1.4

4. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
1.4
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.

5. Prime Numbers:1x
11 -13 -17 -19
14
1. The smallest or largest element 2. The increment 3. The number of items in the set
3·3n = 3^{n+1}

6. The prime factorization of a perfect square contains only ______ powers of primes.
PERFECT CUBES
EVEN
11 -13 -17 -19
1. The smallest or largest element 2. The increment 3. The number of items in the set

7. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
41 -43 -47
23 -29
2.5
ONLY the nonnegative root of the numberUNLIKE

8. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
23 -29
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.4
A PERFECT SQUARE

9. The average of an ODD number of consecutive integers will ________ be an integer.
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.
A MULTIPLE
16

10. For ODD ROOTS - the root has ______.
The same sign as the base
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
97
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

11. Prime Numbers:8x
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.
16
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

12. v196=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.
14

13. Any integer with an EVEN number of total factors cannot be ______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25
A PERFECT SQUARE
ODD

14. Prime Numbers:6x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Never prime
61 -67
A PERFECT SQUARE

15. Prime Numbers:4x
41 -43 -47
1.7
25
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

16. N! is _____ of all integers from 1 to N.
EVEN
11 -13 -17 -19
A MULTIPLE
NEVER CONTRADICT ONE ANOTHER

17. The sum of any two primes will be ____ - unless ______.
1.7
25
The sum of any two primes will be even - unless one of the two primes is 2.
3·3n = 3^{n+1}

18. v3˜
The sum of any two primes will be even - unless one of the two primes is 2.
1.7
FACTOR
ODD

19. v2˜
1.4
14
2.5
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

20. All perfect squares have a(n) _________ number of total factors.
In an evenly spaced set - the average and the median are equal.
ODD
EVEN
16

21. The average of an EVEN number of consecutive integers will ________ be an integer.
A MULTIPLE
The average of an EVEN number of consecutive integers will NEVER be an integer.
2.5
PERFECT CUBES

22. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The average of the set times the number of elements in the set
3·3n = 3^{n+1}
25
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

23. Prime Numbers:7x
The average of an EVEN number of consecutive integers will NEVER be an integer.
71 -73 -79
EVEN
Put the coefficient under the radical to get a better approximation

24. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
31 -37
FACTOR
16
A MULTIPLE

25. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
1.4
2 -3 -5 -7
A non-multiple of N.
The average of an EVEN number of consecutive integers will NEVER be an integer.

26. v169=
EVEN
3·3n = 3^{n+1}
The average of the set times the number of elements in the set
13

27. 3n + 3n + 3n = _____ = ______
83 -89
2.5
ODD
3·3n = 3^{n+1}

28. How to find the sum of consecutive integers:
41 -43 -47
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
NEVER CONTRADICT ONE ANOTHER
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.

29. v625=
[(last - first) / increment] + 1
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25
FACTOR

30. Prime Numbers:3x
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37
The middle number
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

31. The PRODUCT of n consecutive integers is divisible by ____.
The middle number
Prime
The PRODUCT of n consecutive integers is divisible by n!.
Either a multiple of N or a non-multiple of N

32. Positive integers with more than two factors are ____.
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
1.7
Never prime

33. Prime Numbers:0x
2 -3 -5 -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
Prime factorization
FACTOR

34. If estimating a root with a coefficient - _____ .
83 -89
Never prime
Put the coefficient under the radical to get a better approximation
16

35. 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 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
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
[(last - first) / increment] + 1

36. If 2 cannot be one of the primes in the sum - the sum must be _____.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
If 2 cannot be one of the primes in the sum - the sum must be even.
25
Either a multiple of N or a non-multiple of N

37. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
41 -43 -47
Either a multiple of N or a non-multiple of N
71 -73 -79

38. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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.
97
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
71 -73 -79

39. Any integer with an ODD number of total factors must be _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN
A PERFECT SQUARE
2 -3 -5 -7

40. Let N be an integer. If you add two non-multiples of N - the result could be _______.
A non-multiple of N.
97
2.5
Either a multiple of N or a non-multiple of N

41. v5˜
31 -37
Prime
83 -89
2.5

42. 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?
In an evenly spaced set - the average and the median are equal.
13
If 2 cannot be one of the primes in the sum - the sum must be even.
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.

43. v225=
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.
83 -89
15

44. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
11 -13 -17 -19
A PERFECT SQUARE
Never prime

45. In an evenly spaced set - the sum of the terms is equal to ____.
61 -67
The average of the set times the number of elements in the set
Prime
A PERFECT SQUARE

46. Prime Numbers:2x
31 -37
23 -29
61 -67
A PERFECT SQUARE

47. 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 sum of any two primes will be even - unless one of the two primes is 2.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
16
The average of the set times the number of elements in the set

48. Prime Numbers:9x
A PERFECT SQUARE
The average of the set times the number of elements in the set
1.4
97

49. In an evenly spaced set - the average can be found by finding ________.
The same sign as the base
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The middle number
FACTOR

50. The two statements in a data sufficiency problem will _______________.
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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1. The smallest or largest element 2. The increment 3. The number of items in the set