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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:6x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
61 -67
The PRODUCT of n consecutive integers is divisible by n!.
The same sign as the base

2. In an evenly spaced set - the mean and median are equal to the _____ of _________.
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime
53 -59

3. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER
FACTOR
31 -37

4. The formula for finding the number of consecutive multiples in a set is _______.
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
Put the coefficient under the radical to get a better approximation

5. Prime Numbers:4x
83 -89
Prime
41 -43 -47
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

6. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE

7. 3n + 3n + 3n = _____ = ______
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}
2.5
The same sign as the base

8. The prime factorization of a perfect square contains only ______ powers of primes.
13
53 -59
EVEN
A MULTIPLE

9. For ODD ROOTS - the root has ______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
31 -37
The same sign as the base
61 -67

10. Prime Numbers:7x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime factorization
71 -73 -79

11. v5˜
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.
2.5
11 -13 -17 -19
ODD

12. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
61 -67
15
2 -3 -5 -7

13. If N is a divisor of x and y - then _______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
97
NEVER CONTRADICT ONE ANOTHER
N is a divisor of x+y

14. v3˜
15
53 -59
1.7
25

15. v169=
13
Prime
2.5
3·3n = 3^{n+1}

16. The average of an ODD number of consecutive integers will ________ be an integer.
[(last - first) / increment] + 1
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The middle number

17. v256=
16
14
41 -43 -47
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

18. Prime Numbers:2x
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
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A non-multiple of N.

19. Positive integers with only two factors must be ___.
25
Prime
13
16

20. Prime Numbers:1x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
11 -13 -17 -19
A PERFECT SQUARE
ODD

21. Prime Numbers:9x
2.5
97
A PERFECT SQUARE
31 -37

22. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Either a multiple of N or a non-multiple of N
The middle number
83 -89
A PERFECT SQUARE

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

24. N! is _____ of all integers from 1 to N.
97
ODD
A MULTIPLE
Never prime

25. Prime factors of _____ must come in pairs of three.
Put the coefficient under the radical to get a better approximation
PERFECT CUBES
A PERFECT SQUARE
31 -37

26. The two statements in a data sufficiency problem will _______________.
41 -43 -47
3·3n = 3^{n+1}
PERFECT CUBES
NEVER CONTRADICT ONE ANOTHER

27. In an evenly spaced set - the average can be found by finding ________.
11 -13 -17 -19
A PERFECT SQUARE
3·3n = 3^{n+1}
The middle number

28. Any integer with an ODD number of total factors must be _______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE

29. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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 SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
2 -3 -5 -7
ODD

30. Positive integers with more than two factors are ____.
Never prime
14
97
Put the coefficient under the radical to get a better approximation

31. v625=
1.7
71 -73 -79
2 -3 -5 -7
25

32. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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
EVEN
2.5
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

33. Prime Numbers:3x
31 -37
97
61 -67
In an evenly spaced set - the average and the median are equal.

34. 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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35. Prime Numbers:5x
53 -59
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

36. v225=
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The average of an ODD number of consecutive integers will ALWAYS be an integer.

37. v196=
97
41 -43 -47
14
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.

38. If the problem states/assumes that a number is an integer - check to see if you can use _______.
FACTOR
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
Prime factorization

39. v2˜
1.4
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
N is a divisor of x+y

40. If estimating a root with a coefficient - _____ .
61 -67
The sum of any two primes will be even - unless one of the two primes is 2.
25
Put the coefficient under the radical to get a better approximation

41. The sum of any two primes will be ____ - unless ______.
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.
13
N is a divisor of x+y

42. Prime Numbers:8x
The average of the set times the number of elements in the set
83 -89
ODD
1.7

43. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
23 -29
FACTOR
Never prime

44. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A PERFECT SQUARE
41 -43 -47
N is a divisor of x+y
A non-multiple of N.

45. 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. The smallest or largest element 2. The increment 3. The number of items in the set
1.7
3·3n = 3^{n+1}

46. 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
14
ODD
Never prime

47. 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?
[(last - first) / increment] + 1
1.4
61 -67
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.

48. If 2 cannot be one of the primes in the sum - the sum must be _____.
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
If 2 cannot be one of the primes in the sum - the sum must be even.

49. Prime Numbers:0x
The average of an EVEN number of consecutive integers will NEVER be an integer.
2 -3 -5 -7
41 -43 -47
3·3n = 3^{n+1}

50. In an evenly spaced set - the sum of the terms is equal to ____.
61 -67
16
The average of the set times the number of elements in the set
A MULTIPLE