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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 a perfect square contains only ______ powers of primes.
EVEN
13
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE

2. Prime Numbers:0x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
83 -89
1. The smallest or largest element 2. The increment 3. The number of items in the set
2 -3 -5 -7

3. 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
A MULTIPLE
1. The smallest or largest element 2. The increment 3. The number of items in the set
ODD

4. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
3·3n = 3^{n+1}
The PRODUCT of n consecutive integers is divisible by n!.
N is a divisor of x+y

5. Prime Numbers:5x
53 -59
The same sign as the base
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 an ODD number of consecutive integers will ALWAYS be an integer.

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

7. If N is a divisor of x and y - then _______.
PERFECT CUBES
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
N is a divisor of x+y
71 -73 -79

8. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
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 CONTRADICT ONE ANOTHER
A PERFECT SQUARE

9. N! is _____ of all integers from 1 to N.
A PERFECT SQUARE
A MULTIPLE
The sum of any two primes will be even - unless one of the two primes is 2.
2 -3 -5 -7

10. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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.
97
61 -67

11. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
71 -73 -79
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.
A MULTIPLE

12. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
ODD
PERFECT CUBES
A PERFECT SQUARE
A non-multiple of N.

13. v5˜
Prime
ODD
2.5
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

14. Prime Numbers:8x
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
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The sum of any two primes will be even - unless one of the two primes is 2.

15. Positive integers with only two factors must be ___.
A PERFECT SQUARE
Never prime
Prime
83 -89

16. How to find the sum of consecutive integers:
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A MULTIPLE
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.
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.

17. The average of an ODD number of consecutive integers will ________ be an integer.
23 -29
The average of an ODD number of consecutive integers will ALWAYS be an integer.
14
If 2 cannot be one of the primes in the sum - the sum must be even.

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?
83 -89
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.
53 -59
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. v256=
Either a multiple of N or a non-multiple of N
16
11 -13 -17 -19
15

20. 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

21. The PRODUCT of n consecutive integers is divisible by ____.
2.5
EVEN
A non-multiple of N.
The PRODUCT of n consecutive integers is divisible by n!.

22. In an evenly spaced set - the average can be found by finding ________.
25
The middle number
Prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.

23. Prime Numbers:1x
3·3n = 3^{n+1}
The average of an EVEN number of consecutive integers will NEVER be an integer.
The same sign as the base
11 -13 -17 -19

24. Any integer with an EVEN number of total factors cannot be ______.
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
31 -37
1.4

25. 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
FACTOR
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
83 -89
1.4

26. Prime Numbers:7x
A PERFECT SQUARE
71 -73 -79
Never prime
In an evenly spaced set - the average and the median are equal.

27. In an evenly spaced set - the mean and median are equal to the _____ of _________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
61 -67
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13

28. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
97
PERFECT CUBES
FACTOR
A non-multiple of N.

29. Prime Numbers:3x
31 -37
The sum of any two primes will be even - unless one of the two primes is 2.
97
The same sign as the base

30. In an evenly spaced set - the ____ and the ____ are equal.
Prime factorization
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.

31. v196=
61 -67
In an evenly spaced set - the average and the median are equal.
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.
14

32. 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.
71 -73 -79
A MULTIPLE
The middle number

33. If 2 cannot be one of the primes in the sum - the sum must be _____.
A PERFECT SQUARE
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.
If 2 cannot be one of the primes in the sum - the sum must be even.

34. Prime Numbers:4x
A PERFECT SQUARE
Prime
41 -43 -47
PERFECT CUBES

35. If estimating a root with a coefficient - _____ .
A PERFECT SQUARE
A MULTIPLE
1.7
Put the coefficient under the radical to get a better approximation

36. v225=
15
In an evenly spaced set - the average and the median are equal.
Prime factorization
The average of an ODD number of consecutive integers will ALWAYS be an integer.

37. Positive integers with more than two factors are ____.
3·3n = 3^{n+1}
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.
Never prime

38. v169=
41 -43 -47
ODD
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13

39. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ONLY the nonnegative root of the numberUNLIKE
The average of an EVEN number of consecutive integers will NEVER be an integer.
Either a multiple of N or a non-multiple of N

40. The formula for finding the number of consecutive multiples in a set is _______.
In an evenly spaced set - the average and the median are equal.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If 2 cannot be one of the primes in the sum - the sum must be even.
[(last - first) / increment] + 1

41. Any integer with an ODD number of total factors must be _______.
1.4
71 -73 -79
A PERFECT SQUARE
The same sign as the base

42. 3n + 3n + 3n = _____ = ______
NEVER CONTRADICT ONE ANOTHER
The average of an EVEN number of consecutive integers will NEVER be an integer.
EVEN
3·3n = 3^{n+1}

43. For ODD ROOTS - the root has ______.
The same sign as the base
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
53 -59

44. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.4
A non-multiple of N.
71 -73 -79

45. v3˜
1.7
The same sign as the base
The PRODUCT of n consecutive integers is divisible by n!.
41 -43 -47

46. The prime factorization of __________ contains only EVEN powers of primes.
41 -43 -47
FACTOR
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

47. v625=
25
Prime factorization
A PERFECT SQUARE
71 -73 -79

48. The two statements in a data sufficiency problem will _______________.
N is a divisor of x+y
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.
83 -89
NEVER CONTRADICT ONE ANOTHER

49. v2˜
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.
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

50. Prime Numbers:9x
N is a divisor of x+y
A PERFECT SQUARE
97
61 -67