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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. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
A MULTIPLE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
PERFECT CUBES
53 -59

2. 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.
Put the coefficient under the radical to get a better approximation
13
NEVER CONTRADICT ONE ANOTHER

3. All perfect squares have a(n) _________ number of total factors.
83 -89
The average of the set times the number of elements in the set
16
ODD

4. Prime Numbers:2x
A MULTIPLE
2 -3 -5 -7
23 -29
Prime factorization

5. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2.5
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

6. In an evenly spaced set - the average can be found by finding ________.
1.7
The middle number
16
2 -3 -5 -7

7. 3n + 3n + 3n = _____ = ______
Prime factorization
[(last - first) / increment] + 1
23 -29
3·3n = 3^{n+1}

8. In an evenly spaced set - the ____ and the ____ are equal.
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
PERFECT CUBES
In an evenly spaced set - the average and the median are equal.
2 -3 -5 -7

9. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
N is a divisor of x+y
ONLY the nonnegative root of the numberUNLIKE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The PRODUCT of n consecutive integers is divisible by n!.

10. v196=
14
1.4
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Never prime

11. 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.
In an evenly spaced set - the average and the median are equal.
1.7
PERFECT CUBES

12. The average of an EVEN number of consecutive integers will ________ be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}
1.4
The average of an EVEN number of consecutive integers will NEVER be an integer.

13. The prime factorization of __________ contains only EVEN powers of primes.
The sum of any two primes will be even - unless one of the two primes is 2.
3·3n = 3^{n+1}
41 -43 -47
A PERFECT SQUARE

14. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
13
16
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1. The smallest or largest element 2. The increment 3. The number of items in the set

15. v625=
14
1.7
25
11 -13 -17 -19

16. 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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17. The prime factorization of a perfect square contains only ______ powers of primes.
Never prime
A MULTIPLE
2.5
EVEN

18. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
EVEN
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.
31 -37

19. If the problem states/assumes that a number is an integer - check to see if you can use _______.
ONLY the nonnegative root of the numberUNLIKE
Prime factorization
53 -59
The average of an EVEN number of consecutive integers will NEVER be an integer.

20. The formula for finding the number of consecutive multiples in a set is _______.
53 -59
FACTOR
41 -43 -47
[(last - first) / increment] + 1

21. Prime factors of _____ must come in pairs of three.
2 -3 -5 -7
1. The smallest or largest element 2. The increment 3. The number of items in the set
PERFECT CUBES
FACTOR

22. The two statements in a data sufficiency problem will _______________.
FACTOR
1.7
1.4
NEVER CONTRADICT ONE ANOTHER

23. 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.
71 -73 -79
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

24. Prime Numbers:6x
61 -67
15
1.7
Prime

25. Prime Numbers:9x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number
25
97

26. Prime Numbers:1x
23 -29
11 -13 -17 -19
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.4

27. Prime Numbers:3x
N is a divisor of x+y
31 -37
[(last - first) / increment] + 1
23 -29

28. v5˜
A PERFECT SQUARE
[(last - first) / increment] + 1
2.5
A MULTIPLE

29. If estimating a root with a coefficient - _____ .
83 -89
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
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER

30. Positive integers with only two factors must be ___.
The same sign as the base
[(last - first) / increment] + 1
A PERFECT SQUARE
Prime

31. For ODD ROOTS - the root has ______.
Prime factorization
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The same sign as the base
2 -3 -5 -7

32. v3˜
A PERFECT SQUARE
23 -29
1.7
A MULTIPLE

33. The sum of any two primes will be ____ - unless ______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The sum of any two primes will be even - unless one of the two primes is 2.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
83 -89

34. The average of an ODD number of consecutive integers will ________ be an integer.
11 -13 -17 -19
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ODD
16

35. ³v216 =
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.
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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

36. Prime Numbers:4x
41 -43 -47
14
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

37. Prime Numbers:0x
EVEN
2 -3 -5 -7
A MULTIPLE
97

38. In an evenly spaced set - the sum of the terms is equal to ____.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE
53 -59
The average of the set times the number of elements in the set

39. Prime Numbers:5x
EVEN
31 -37
53 -59
2.5

40. If N is a divisor of x and y - then _______.
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
The same sign as the base
25

41. How to find the sum of consecutive integers:
61 -67
A PERFECT SQUARE
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

42. v169=
1.4
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
13

43. The PRODUCT of n consecutive integers is divisible by ____.
FACTOR
The average of the set times the number of elements in the set
1. The smallest or largest element 2. The increment 3. The number of items in the set
The PRODUCT of n consecutive integers is divisible by n!.

44. Let N be an integer. If you add two non-multiples of N - the result could be _______.
41 -43 -47
2 -3 -5 -7
Either a multiple of N or a non-multiple of N
N is a divisor of x+y

45. Prime Numbers:7x
25
71 -73 -79
83 -89
97

46. N! is _____ of all integers from 1 to N.
A MULTIPLE
FACTOR
EVEN
The average of an ODD number of consecutive integers will ALWAYS be an integer.

47. Positive integers with more than two factors are ____.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25
A PERFECT SQUARE
Never prime

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

49. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
2 -3 -5 -7
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of the set times the number of elements in the set
1.7

50. 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
41 -43 -47
If 2 cannot be one of the primes in the sum - the sum must be even.
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 average of an EVEN number of consecutive integers will NEVER be an integer.