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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. v196=
15
23 -29
14
2.5

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

3. v225=
If 2 cannot be one of the primes in the sum - the sum must be even.
Either a multiple of N or a non-multiple of N
The average of an EVEN number of consecutive integers will NEVER be an integer.
15

4. For ODD ROOTS - the root has ______.
97
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The same sign as the base
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

5. v5˜
3·3n = 3^{n+1}
2.5
61 -67
14

6. Prime Numbers:5x
53 -59
ONLY the nonnegative root of the numberUNLIKE
ODD
Never prime

7. In an evenly spaced set - the sum of the terms is equal to ____.
31 -37
The average of the set times the number of elements in the set
11 -13 -17 -19
Either a multiple of N or a non-multiple of N

8. If estimating a root with a coefficient - _____ .
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
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.
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER

9. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
1. The smallest or largest element 2. The increment 3. The number of items in the set
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.7
FACTOR

10. Prime factors of _____ must come in pairs of three.
ONLY the nonnegative root of the numberUNLIKE
If 2 cannot be one of the primes in the sum - the sum must be even.
PERFECT CUBES
A PERFECT SQUARE

11. The average of an ODD number of consecutive integers will ________ be an integer.
In an evenly spaced set - the average and the median are equal.
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.
97

12. Prime Numbers:1x
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.
FACTOR
A PERFECT SQUARE
11 -13 -17 -19

13. How to find the sum of consecutive integers:
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.
A PERFECT SQUARE
41 -43 -47
23 -29

14. The prime factorization of __________ contains only EVEN powers of primes.
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.
71 -73 -79
A PERFECT SQUARE
11 -13 -17 -19

15. Prime Numbers:8x
83 -89
A PERFECT SQUARE
3·3n = 3^{n+1}
A PERFECT SQUARE

16. v3˜
N is a divisor of x+y
41 -43 -47
The middle number
1.7

17. N! is _____ of all integers from 1 to N.
A MULTIPLE
A PERFECT SQUARE
97
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

18. The two statements in a data sufficiency problem will _______________.
14
NEVER CONTRADICT ONE ANOTHER
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.

19. In an evenly spaced set - the average can be found by finding ________.
16
The middle number
2 -3 -5 -7
23 -29

20. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The PRODUCT of n consecutive integers is divisible by n!.
The sum of any two primes will be even - unless one of the two primes is 2.
N is a divisor of x+y

21. Prime Numbers:4x
ONLY the nonnegative root of the numberUNLIKE
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
41 -43 -47
A MULTIPLE

22. The formula for finding the number of consecutive multiples in a set is _______.
FACTOR
[(last - first) / increment] + 1
2.5
The average of an EVEN number of consecutive integers will NEVER be an integer.

23. 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.
3·3n = 3^{n+1}
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

24. v256=
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
14
16
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

25. Positive integers with more than two factors are ____.
2.5
Never prime
If 2 cannot be one of the primes in the sum - the sum must be even.
71 -73 -79

26. 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
A MULTIPLE
1.4
1.7

27. Prime Numbers:9x
FACTOR
97
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Put the coefficient under the radical to get a better approximation

28. v625=
1.4
53 -59
25
In an evenly spaced set - the average and the median are equal.

29. 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.
2.5
1.7
13

30. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
16
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.
Prime factorization

31. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Put the coefficient under the radical to get a better approximation
The same sign as the base
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A MULTIPLE

32. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
Prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the average and the median are equal.

33. Prime Numbers:0x
2 -3 -5 -7
ODD
71 -73 -79
Prime factorization

34. All perfect squares have a(n) _________ number of total factors.
The same sign as the base
A non-multiple of N.
16
ODD

35. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
16
ONLY the nonnegative root of the numberUNLIKE
1. The smallest or largest element 2. The increment 3. The number of items in the set

36. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The middle number
15
Prime
Either a multiple of N or a non-multiple of N

37. 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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38. Prime Numbers:6x
61 -67
71 -73 -79
1.4
PERFECT CUBES

39. Prime Numbers:7x
97
71 -73 -79
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

40. v169=
A non-multiple of N.
ODD
83 -89
13

41. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
NEVER CONTRADICT ONE ANOTHER
97

42. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A non-multiple of N.
Prime factorization
53 -59
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

43. 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.
53 -59
Prime factorization
ODD

44. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
31 -37
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

45. 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.
97
2 -3 -5 -7
13

46. Prime Numbers:3x
The same sign as the base
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
31 -37

47. Any integer with an ODD number of total factors must be _______.
25
13
31 -37
A PERFECT SQUARE

48. If N is a divisor of x and y - then _______.
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
The sum of any two primes will be even - unless one of the two primes is 2.
N is a divisor of x+y

49. 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
15
A MULTIPLE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
97

50. Prime Numbers:2x
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.
23 -29
EVEN