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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. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
[(last - first) / increment] + 1
3·3n = 3^{n+1}
The middle number

2. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
16
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The sum of any two primes will be even - unless one of the two primes is 2.
The same sign as the base

3. v625=
A PERFECT SQUARE
25
61 -67
53 -59

4. 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

5. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
2.5
11 -13 -17 -19
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

6. The two statements in a data sufficiency problem will _______________.
ODD
NEVER CONTRADICT ONE ANOTHER
ONLY the nonnegative root of the numberUNLIKE
53 -59

7. Prime Numbers:3x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The middle number
Prime
31 -37

8. v2˜
The sum of any two primes will be even - unless one of the two primes is 2.
31 -37
1.7
1.4

9. v196=
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
N is a divisor of x+y
ODD
14

10. N! is _____ of all integers from 1 to N.
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE
The average of the set times the number of elements in the set
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. Prime Numbers:6x
3·3n = 3^{n+1}
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97
61 -67

12. 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?
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
A PERFECT SQUARE
Never prime

13. The average of an ODD number of consecutive integers will ________ be an integer.
FACTOR
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
The average of an ODD number of consecutive integers will ALWAYS be an integer.

14. If the problem states/assumes that a number is an integer - check to see if you can use _______.
41 -43 -47
Prime factorization
1.7
53 -59

15. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
Never prime

16. 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.
The same sign as the base
2 -3 -5 -7
N is a divisor of x+y

17. Prime Numbers:1x
71 -73 -79
A PERFECT SQUARE
11 -13 -17 -19
A non-multiple of N.

18. Prime Numbers:8x
1. The smallest or largest element 2. The increment 3. The number of items in the set
3·3n = 3^{n+1}
2 -3 -5 -7
83 -89

19. v256=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.
16

20. Positive integers with only two factors must be ___.
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime
A PERFECT SQUARE
[(last - first) / increment] + 1

21. Prime Numbers:2x
A MULTIPLE
23 -29
83 -89
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

22. Prime Numbers:4x
11 -13 -17 -19
41 -43 -47
Prime
2.5

23. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number
If 2 cannot be one of the primes in the sum - the sum must be even.

24. The prime factorization of __________ contains only EVEN powers of primes.
[(last - first) / increment] + 1
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.
N is a divisor of x+y

25. The sum of any two primes will be ____ - unless ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The sum of any two primes will be even - unless one of the two primes is 2.
Put the coefficient under the radical to get a better approximation
61 -67

26. 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.
23 -29
53 -59
The PRODUCT of n consecutive integers is divisible by n!.

27. Any integer with an EVEN number of total factors cannot be ______.
Prime factorization
A PERFECT SQUARE
71 -73 -79
3·3n = 3^{n+1}

28. 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
EVEN
A non-multiple of N.
1.7

29. Positive integers with more than two factors are ____.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ODD
Prime factorization
Never prime

30. The formula for finding the number of consecutive multiples in a set is _______.
14
61 -67
NEVER CONTRADICT ONE ANOTHER
[(last - first) / increment] + 1

31. ³v216 =
1.7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
In an evenly spaced set - the average and the median are equal.

32. 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
EVEN
The same sign as the base
A non-multiple of N.
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

33. Any integer with an ODD number of total factors must be _______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

34. v225=
15
If 2 cannot be one of the primes in the sum - the sum must be even.
ODD
23 -29

35. How to find the sum of consecutive integers:
A non-multiple of N.
41 -43 -47
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.

36. In an evenly spaced set - the ____ and the ____ are equal.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
NEVER CONTRADICT ONE ANOTHER
In an evenly spaced set - the average and the median are equal.

37. Prime Numbers:9x
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
53 -59
97

38. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
16
61 -67
2.5

39. In an evenly spaced set - the mean and median are equal to the _____ of _________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
[(last - first) / increment] + 1

40. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER
The middle number
The average of an ODD number of consecutive integers will ALWAYS be an integer.

41. Prime Numbers:5x
53 -59
Prime
2.5
A PERFECT SQUARE

42. The PRODUCT of n consecutive integers is divisible by ____.
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
The same sign as the base
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.

43. In an evenly spaced set - the sum of the terms is equal to ____.
The middle number
1.7
The average of the set times the number of elements in the set
ODD

44. Prime Numbers:0x
Prime
2.5
2 -3 -5 -7
1. The smallest or largest element 2. The increment 3. The number of items in the set

45. v169=
A PERFECT SQUARE
53 -59
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
13

46. All perfect squares have a(n) _________ number of total factors.
1.7
Prime
A non-multiple of N.
ODD

47. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
14
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.
FACTOR

48. If estimating a root with a coefficient - _____ .
The same sign as the base
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
83 -89

49. v3˜
A PERFECT SQUARE
[(last - first) / increment] + 1
1.7
EVEN

50. v5˜
71 -73 -79
The sum of any two primes will be even - unless one of the two primes is 2.
2.5
83 -89