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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=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1. The smallest or largest element 2. The increment 3. The number of items in the set
14
NEVER CONTRADICT ONE ANOTHER

2. 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

3. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
53 -59
11 -13 -17 -19
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

4. Let N be an integer. If you add two non-multiples of N - the result could be _______.
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
83 -89

5. Prime Numbers:0x
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.
2 -3 -5 -7
53 -59
71 -73 -79

6. v169=
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
13

7. N! is _____ of all integers from 1 to N.
A MULTIPLE
71 -73 -79
A non-multiple of N.
13

8. For ODD ROOTS - the root has ______.
ONLY the nonnegative root of the numberUNLIKE
15
1.4
The same sign as the base

9. Positive integers with only two factors must be ___.
Prime
The average of the set times the number of elements in the set
The same sign as the base
NEVER CONTRADICT ONE ANOTHER

10. Prime Numbers:9x
2 -3 -5 -7
97
14
11 -13 -17 -19

11. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
N is a divisor of x+y
1.7
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.

12. Prime Numbers:3x
13
N is a divisor of x+y
83 -89
31 -37

13. 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
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.
EVEN
15
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

14. Prime Numbers:4x
41 -43 -47
2 -3 -5 -7
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

15. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
1.4
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER

16. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Never prime
Prime factorization
71 -73 -79
2 -3 -5 -7

17. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
If 2 cannot be one of the primes in the sum - the sum must be even.
FACTOR
3·3n = 3^{n+1}
The average of the set times the number of elements in the set

18. v256=
16
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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

19. The sum of any two primes will be ____ - unless ______.
Never prime
25
The sum of any two primes will be even - unless one of the two primes is 2.
61 -67

20. If N is a divisor of x and y - then _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
N is a divisor of x+y
3·3n = 3^{n+1}
A PERFECT SQUARE

21. v2˜
1.4
The sum of any two primes will be even - unless one of the two primes is 2.
83 -89
61 -67

22. 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?
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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.
Prime factorization
ONLY the nonnegative root of the numberUNLIKE

23. v3˜
The sum of any two primes will be even - unless one of the two primes is 2.
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
1.7
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.

24. If estimating a root with a coefficient - _____ .
Either a multiple of N or a non-multiple of N
Prime
97
Put the coefficient under the radical to get a better approximation

25. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
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.
31 -37
The average of an EVEN number of consecutive integers will NEVER be an integer.

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.
ODD
[(last - first) / increment] + 1
83 -89

27. Prime Numbers:6x
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.
15
2.5

28. In an evenly spaced set - the average can be found by finding ________.
N is a divisor of x+y
The middle number
ONLY the nonnegative root of the numberUNLIKE
31 -37

29. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime
ONLY the nonnegative root of the numberUNLIKE
16

30. 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 non-multiple of N.
53 -59
The average of the set times the number of elements in the set

31. 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
If 2 cannot be one of the primes in the sum - the sum must be even.
The middle number
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.

32. v625=
A PERFECT SQUARE
25
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.

33. All perfect squares have a(n) _________ number of total factors.
23 -29
ODD
If 2 cannot be one of the primes in the sum - the sum must be even.
1. The smallest or largest element 2. The increment 3. The number of items in the set

34. Prime Numbers:5x
Either a multiple of N or a non-multiple of N
53 -59
83 -89
13

35. The average of an ODD number of consecutive integers will ________ be an integer.
The average of the set times the number of elements in the set
41 -43 -47
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE

36. v225=
Put the coefficient under the radical to get a better approximation
15
A MULTIPLE
EVEN

37. Positive integers with more than two factors are ____.
97
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime
FACTOR

38. Prime Numbers:7x
71 -73 -79
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97
A non-multiple of N.

39. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Prime factorization
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE

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

41. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
11 -13 -17 -19
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.

42. 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
15
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

43. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
83 -89
The same sign as the base
The sum of any two primes will be even - unless one of the two primes is 2.

44. In an evenly spaced set - the sum of the terms is equal to ____.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29
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

45. The formula for finding the number of consecutive multiples in a set is _______.
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.
97
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.
[(last - first) / increment] + 1

46. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
N is a divisor of x+y
Either a multiple of N or 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
A non-multiple of N.

47. Prime Numbers:1x
11 -13 -17 -19
1.7
If 2 cannot be one of the primes in the sum - the sum must be even.
The average of an EVEN number of consecutive integers will NEVER be an integer.

48. Prime Numbers:8x
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
61 -67
83 -89

49. 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.
NEVER CONTRADICT ONE ANOTHER
A MULTIPLE
A PERFECT SQUARE

50. v5˜
61 -67
53 -59
The sum of any two primes will be even - unless one of the two primes is 2.
2.5