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GMAT Number Properties

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
The average of an EVEN number of consecutive integers will NEVER be an integer.
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.

2. v3˜
61 -67
1.7
Prime
The average of the set times the number of elements in the set

3. v5˜
16
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The average of the set times the number of elements in the set

4. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The middle number
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

5. Prime Numbers:0x
71 -73 -79
25
Either a multiple of N or a non-multiple of N
2 -3 -5 -7

6. If estimating a root with a coefficient - _____ .
A MULTIPLE
61 -67
Put the coefficient under the radical to get a better approximation
1.7

7. Prime Numbers:8x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
83 -89
The sum of any two primes will be even - unless one of the two primes is 2.
2 -3 -5 -7

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

9. The sum of any two primes will be ____ - unless ______.
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.
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.
FACTOR

10. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
41 -43 -47
ONLY the nonnegative root of the numberUNLIKE
11 -13 -17 -19
Never prime

11. 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
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set
2 -3 -5 -7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

12. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime factorization
11 -13 -17 -19

13. If N is a divisor of x and y - then _______.
97
A MULTIPLE
31 -37
N is a divisor of x+y

14. Any integer with an EVEN number of total factors cannot be ______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
41 -43 -47
ODD
A PERFECT SQUARE

15. Any integer with an ODD number of total factors must be _______.
1.7
1. The smallest or largest element 2. The increment 3. The number of items in the set
A non-multiple of N.
A PERFECT SQUARE

16. 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.
The middle number
The average of the set times the number of elements in the set

17. N! is _____ of all integers from 1 to N.
1.7
EVEN
A MULTIPLE
If 2 cannot be one of the primes in the sum - the sum must be even.

18. v169=
13
Prime factorization
Prime
ODD

19. Prime Numbers:2x
23 -29
The same sign as the base
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 PERFECT SQUARE

20. How to find the sum of consecutive integers:
97
23 -29
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

21. In an evenly spaced set - the average can be found by finding ________.
The middle number
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

22. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
ODD
FACTOR
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE

23. Positive integers with more than two factors are ____.
Never prime
2.5
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

24. Positive integers with only two factors must be ___.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25
Prime
In an evenly spaced set - the average and the median are equal.

25. 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.
31 -37
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
16

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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
3·3n = 3^{n+1}
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 mean and median are equal to the average of the first and the last number.

27. v2˜
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
1.4
The PRODUCT of n consecutive integers is divisible by n!.

28. 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?
If 2 cannot be one of the primes in the sum - the sum must be even.
The same sign as the base
Prime
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.

29. ³v216 =
25
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ODD
EVEN

30. The prime factorization of a perfect square contains only ______ powers of primes.
1.7
83 -89
71 -73 -79
EVEN

31. The average of an EVEN number of consecutive integers will ________ be an integer.
71 -73 -79
31 -37
61 -67
The average of an EVEN number of consecutive integers will NEVER be an integer.

32. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
71 -73 -79
The average of an EVEN number of consecutive integers will NEVER be an integer.
The average of the set times the number of elements in the set

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

34. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Never prime

35. The PRODUCT of n consecutive integers is divisible by ____.
41 -43 -47
N is a divisor of x+y
The PRODUCT of n consecutive integers is divisible by n!.
1.4

36. Prime Numbers:5x
53 -59
23 -29
1.4
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

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. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
71 -73 -79
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The middle number

39. v256=
Prime
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.
16
Either a multiple of N or a non-multiple of N

40. In an evenly spaced set - the ____ and the ____ are equal.
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

41. Prime Numbers:3x
If 2 cannot be one of the primes in the sum - the sum must be even.
N is a divisor of x+y
31 -37
ODD

42. In an evenly spaced set - the sum of the terms is equal to ____.
97
The average of the set times the number of elements in the set
Never prime
11 -13 -17 -19

43. The average of an ODD number of consecutive integers will ________ be an integer.
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.
61 -67
25

44. v625=
The PRODUCT of n consecutive integers is divisible by n!.
A MULTIPLE
25
The average of an ODD number of consecutive integers will ALWAYS be an integer.

45. v225=
15
EVEN
14
71 -73 -79

46. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
The average of an ODD number of consecutive integers will ALWAYS be an integer.
97
A PERFECT SQUARE

47. v196=
NEVER CONTRADICT ONE ANOTHER
53 -59
13
14

48. If 2 cannot be one of the primes in the sum - the sum must be _____.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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.
A PERFECT SQUARE

49. 3n + 3n + 3n = _____ = ______
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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
11 -13 -17 -19
3·3n = 3^{n+1}

50. Prime Numbers:9x
A PERFECT SQUARE
Prime
97
If 2 cannot be one of the primes in the sum - the sum must be even.

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GMAT Number Properties

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