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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. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The sum of any two primes will be even - unless one of the two primes is 2.
ONLY the nonnegative root of the numberUNLIKE
NEVER CONTRADICT ONE ANOTHER
FACTOR

2. Any integer with an EVEN number of total factors cannot be ______.
53 -59
The average of the set times the number of elements in the set
A PERFECT SQUARE
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.

3. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
N is a divisor of x+y
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.
ONLY the nonnegative root of the numberUNLIKE

4. In an evenly spaced set - the sum of the terms is equal to ____.
1.7
A PERFECT SQUARE
The average of the set times the number of elements in the set
1.4

5. 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
14
31 -37
The PRODUCT of n consecutive integers is divisible by n!.

6. 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
41 -43 -47
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.

7. The PRODUCT of n consecutive integers is divisible by ____.
13
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.
The same sign as the base

8. v2˜
1.4
The average of the set times the number of elements in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

9. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
A MULTIPLE
2 -3 -5 -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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

10. If N is a divisor of x and y - then _______.
N is a divisor of x+y
1.4
41 -43 -47
71 -73 -79

11. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
1.4
1. The smallest or largest element 2. The increment 3. The number of items in the set
61 -67
71 -73 -79

12. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
97
31 -37
15

13. 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
23 -29
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
In an evenly spaced set - the average and the median are equal.
Never prime

14. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
41 -43 -47
A PERFECT SQUARE
N is a divisor of x+y

15. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Prime factorization
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.
ODD

16. All perfect squares have a(n) _________ number of total factors.
ODD
The average of an ODD number of consecutive integers will ALWAYS be an integer.
FACTOR
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

17. ³v216 =
A PERFECT SQUARE
25
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Prime

18. Prime Numbers:8x
The average of an EVEN number of consecutive integers will NEVER 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.
83 -89
A PERFECT SQUARE

19. Positive integers with only two factors must be ___.
53 -59
Put the coefficient under the radical to get a better approximation
16
Prime

20. Prime Numbers:6x
Either a multiple of N or a non-multiple of N
A MULTIPLE
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.

21. The prime factorization of a perfect square contains only ______ powers of primes.
41 -43 -47
EVEN
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
25

22. In an evenly spaced set - the average can be found by finding ________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER
[(last - first) / increment] + 1
The middle number

23. v5˜
2.5
NEVER CONTRADICT ONE ANOTHER
The average of an ODD number of consecutive integers will ALWAYS be an integer.
13

24. N! is _____ of all integers from 1 to N.
A MULTIPLE
Prime factorization
71 -73 -79
Either a multiple of N or a non-multiple of N

25. Prime Numbers:4x
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
61 -67
41 -43 -47

26. Prime Numbers:3x
71 -73 -79
NEVER CONTRADICT ONE ANOTHER
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

27. The two statements in a data sufficiency problem will _______________.
31 -37
NEVER CONTRADICT ONE ANOTHER
EVEN
41 -43 -47

28. Prime Numbers:7x
71 -73 -79
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N
16

29. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The average of the set times the number of elements in the set
A non-multiple of N.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE

30. 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.
A PERFECT SQUARE
11 -13 -17 -19
The PRODUCT of n consecutive integers is divisible by n!.

31. 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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32. 3n + 3n + 3n = _____ = ______
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
3·3n = 3^{n+1}
1. The smallest or largest element 2. The increment 3. The number of items in the set
16

33. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
[(last - first) / increment] + 1
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
71 -73 -79

34. 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
Prime
71 -73 -79
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
97

35. v169=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
13
41 -43 -47

36. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
Prime
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.

37. v256=
16
In an evenly spaced set - the average and the median are equal.
2.5
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

38. The formula for finding the number of consecutive multiples in a set is _______.
In an evenly spaced set - the average and the median are equal.
11 -13 -17 -19
[(last - first) / increment] + 1
The average of the set times the number of elements in the set

39. For ODD ROOTS - the root has ______.
53 -59
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.

40. v196=
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.
11 -13 -17 -19
The same sign as the base

41. Let N be an integer. If you add two non-multiples of N - the result could be _______.
ODD
Either a multiple of N or a non-multiple of N
97
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

42. Prime Numbers:5x
[(last - first) / increment] + 1
ONLY the nonnegative root of the numberUNLIKE
53 -59
A PERFECT SQUARE

43. Prime Numbers:1x
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
11 -13 -17 -19
16

44. v225=
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ODD
1.4
15

45. v3˜
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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.7

46. The average of an EVEN number of consecutive integers will ________ be an integer.
16
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime factorization
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

47. Prime factors of _____ must come in pairs of three.
Either a multiple of N or a non-multiple of N
PERFECT CUBES
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.

48. Prime Numbers:0x
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
2 -3 -5 -7
Never prime

49. Positive integers with more than two factors are ____.
13
Never prime
2.5
In an evenly spaced set - the average and the median are equal.

50. v625=
83 -89
25
13
71 -73 -79