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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. Prime Numbers:3x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
31 -37
97
2.5

2. v2˜
1.4
83 -89
Either a multiple of N or a non-multiple of N
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

3. Positive integers with only two factors must be ___.
14
Prime
EVEN
The average of the set times the number of elements in the set

4. In an evenly spaced set - the average can be found by finding ________.
The PRODUCT of n consecutive integers is divisible by n!.
A non-multiple of N.
The middle number
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

5. v5˜
1. The smallest or largest element 2. The increment 3. The number of items in the set
The same sign as the base
2.5
13

6. v169=
[(last - first) / increment] + 1
13
16
3·3n = 3^{n+1}

7. If the problem states/assumes that a number is an integer - check to see if you can use _______.
ODD
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.
Prime factorization

8. In an evenly spaced set - the sum of the terms is equal to ____.
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
The PRODUCT of n consecutive integers is divisible by n!.

9. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
Never prime
A non-multiple of N.
The middle number
EVEN

10. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.
Prime factorization

11. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
23 -29
83 -89
1.7

12. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
25
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.

13. v625=
1. The smallest or largest element 2. The increment 3. The number of items in the set
2 -3 -5 -7
23 -29
25

14. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
Prime
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 same sign as the base

15. Any integer with an EVEN number of total factors cannot be ______.
The average of the set times the number of elements in the set
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
97

16. Prime Numbers:9x
A non-multiple of N.
97
14
1.7

17. v196=
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Either a multiple of N or a non-multiple of N
14
EVEN

18. For ODD ROOTS - the root has ______.
3·3n = 3^{n+1}
The same sign as the base
Prime factorization
2 -3 -5 -7

19. Prime factors of _____ must come in pairs of three.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ONLY the nonnegative root of the numberUNLIKE
PERFECT CUBES

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. If N is a divisor of x and y - then _______.
97
Put the coefficient under the radical to get a better approximation
Prime factorization
N is a divisor of x+y

22. Prime Numbers:5x
53 -59
A PERFECT SQUARE
23 -29
1.7

23. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Put the coefficient under the radical to get a better approximation
A MULTIPLE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER

24. Prime Numbers:6x
A PERFECT SQUARE
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
61 -67

25. Prime Numbers:1x
13
ODD
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER

26. 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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
71 -73 -79
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 gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

27. v3˜
N is a divisor of x+y
In an evenly spaced set - the average and the median are equal.
15
1.7

28. If 2 cannot be one of the primes in the sum - the sum must be _____.
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1. The smallest or largest element 2. The increment 3. The number of items in the set

29. Prime Numbers:4x
PERFECT CUBES
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.
41 -43 -47
53 -59

30. How to find the sum of consecutive integers:
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
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.
97

31. 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
A non-multiple of N.
11 -13 -17 -19
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the average and the median are equal.

32. The sum of any two primes will be ____ - unless ______.
Put the coefficient under the radical to get a better approximation
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.
The sum of any two primes will be even - unless one of the two primes is 2.

33. The prime factorization of a perfect square contains only ______ powers of primes.
83 -89
53 -59
3·3n = 3^{n+1}
EVEN

34. 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
Prime factorization
NEVER CONTRADICT ONE ANOTHER
23 -29

35. Positive integers with more than two factors are ____.
PERFECT CUBES
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime

36. All perfect squares have a(n) _________ number of total factors.
ODD
If 2 cannot be one of the primes in the sum - the sum must be even.
53 -59
Prime

37. The average of an ODD number of consecutive integers will ________ be an integer.
53 -59
97
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A MULTIPLE

38. Prime Numbers:8x
Prime
Put the coefficient under the radical to get a better approximation
A non-multiple of N.
83 -89

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

40. ³v216 =
N is a divisor of x+y
The average of the set times the number of elements in the set
The same sign as the base
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

41. Prime Numbers:0x
15
2 -3 -5 -7
PERFECT CUBES
The sum of any two primes will be even - unless one of the two primes is 2.

42. N! is _____ of all integers from 1 to N.
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.
3·3n = 3^{n+1}
A MULTIPLE

43. Prime Numbers:7x
71 -73 -79
15
A non-multiple of N.
N is a divisor of x+y

44. v256=
16
3·3n = 3^{n+1}
PERFECT CUBES
NEVER CONTRADICT ONE ANOTHER

45. In an evenly spaced set - the ____ and the ____ are equal.
16
NEVER CONTRADICT ONE ANOTHER
In an evenly spaced set - the average and the median are equal.
EVEN

46. The average of an EVEN number of consecutive integers will ________ 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.
Never prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.

47. If estimating a root with a coefficient - _____ .
In an evenly spaced set - the average and the median are equal.
Put the coefficient under the radical to get a better approximation
31 -37
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.

48. Any integer with an ODD number of total factors must be _______.
61 -67
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
Never prime

49. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
EVEN
ONLY the nonnegative root of the numberUNLIKE
23 -29
A PERFECT SQUARE

50. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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.
Put the coefficient under the radical to get a better approximation
[(last - first) / increment] + 1