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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.
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. For ODD ROOTS - the root has ______.
2.5
14
The middle number
The same sign as the base

2. 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.
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
FACTOR
61 -67

3. Prime Numbers:2x
NEVER CONTRADICT ONE ANOTHER
61 -67
53 -59
23 -29

4. v256=
15
2 -3 -5 -7
16
EVEN

5. 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.
The average of the set times the number of elements in the set
97
N is a divisor of x+y

6. v169=
13
11 -13 -17 -19
PERFECT CUBES
23 -29

7. 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
53 -59
1.7
ONLY the nonnegative root of the numberUNLIKE

8. v225=
15
A PERFECT SQUARE
FACTOR
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

9. ³v216 =
61 -67
Put the coefficient under the radical to get a better approximation
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}

10. Any integer with an ODD number of total factors must be _______.
71 -73 -79
53 -59
A PERFECT SQUARE
11 -13 -17 -19

11. N! is _____ of all integers from 1 to N.
ODD
The middle number
A MULTIPLE
71 -73 -79

12. Prime Numbers:5x
In an evenly spaced set - the average and the median are equal.
2.5
ODD
53 -59

13. v5˜
2.5
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
23 -29

14. Prime Numbers:1x
A MULTIPLE
31 -37
11 -13 -17 -19
83 -89

15. The sum of any two primes will be ____ - unless ______.
15
ONLY the nonnegative root of the numberUNLIKE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The sum of any two primes will be even - unless one of the two primes is 2.

16. Prime Numbers:8x
In an evenly spaced set - the average and the median are equal.
FACTOR
A PERFECT SQUARE
83 -89

17. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
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!.
A PERFECT SQUARE

18. 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
14
A non-multiple of N.

19. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
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 PERFECT SQUARE
61 -67
1. The smallest or largest element 2. The increment 3. The number of items in the set

20. Let N be an integer. If you add two non-multiples of N - the result could be _______.
11 -13 -17 -19
Either a multiple of N or a non-multiple of N
N is a divisor of x+y
[(last - first) / increment] + 1

21. In an evenly spaced set - the mean and median are equal to the _____ of _________.
The sum of any two primes will be even - unless one of the two primes is 2.
71 -73 -79
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.

22. In an evenly spaced set - the ____ and the ____ are equal.
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.
PERFECT CUBES
N is a divisor of x+y

23. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
The average of an ODD number of consecutive integers will ALWAYS be an integer.
11 -13 -17 -19
PERFECT CUBES

24. 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.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
PERFECT CUBES

25. 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.
53 -59
PERFECT CUBES
A PERFECT SQUARE

26. Any integer with an EVEN number of total factors cannot be ______.
13
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
31 -37

27. All perfect squares have a(n) _________ number of total factors.
Put the coefficient under the radical to get a better approximation
11 -13 -17 -19
ODD
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

28. Prime Numbers:9x
13
Prime
97
Prime factorization

29. Prime Numbers:6x
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime
15
61 -67

30. Prime Numbers:3x
ODD
NEVER CONTRADICT ONE ANOTHER
Prime factorization
31 -37

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 average of an ODD number of consecutive integers will ALWAYS be an integer.
ONLY the nonnegative root of the numberUNLIKE
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

32. v3˜
1.7
61 -67
16
Either a multiple of N or a non-multiple of N

33. v2˜
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1.4
A MULTIPLE

34. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
PERFECT CUBES
97
FACTOR
N is a divisor of x+y

35. The prime factorization of a perfect square contains only ______ powers of primes.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Never prime
EVEN
The middle number

36. Prime Numbers:0x
41 -43 -47
11 -13 -17 -19
97
2 -3 -5 -7

37. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER
2.5

38. 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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39. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A non-multiple of N.
PERFECT CUBES
The sum of any two primes will be even - unless one of the two primes is 2.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

40. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
1. The smallest or largest element 2. The increment 3. The number of items in the set
ODD
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

41. Positive integers with more than two factors are ____.
Prime
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime
The average of an EVEN number of consecutive integers will NEVER be an integer.

42. The two statements in a data sufficiency problem will _______________.
Either a multiple of N or a non-multiple of N
NEVER CONTRADICT ONE ANOTHER
Never prime
53 -59

43. Prime Numbers:4x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
[(last - first) / increment] + 1
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.
41 -43 -47

44. v625=
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.
A MULTIPLE
FACTOR
25

45. If 2 cannot be one of the primes in the sum - the sum must be _____.
Either a multiple of N or a non-multiple of N
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

46. 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
61 -67
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the average and the median are equal.

47. Prime factors of _____ must come in pairs of three.
97
The average of the set times the number of elements in the set
PERFECT CUBES
2.5

48. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
71 -73 -79
1. The smallest or largest element 2. The increment 3. The number of items in the set
Put the coefficient under the radical to get a better approximation

49. v196=
[(last - first) / increment] + 1
14
97
A PERFECT SQUARE

50. In an evenly spaced set - the average can be found by finding ________.
The middle number
The PRODUCT of n consecutive integers is divisible by n!.
16
NEVER CONTRADICT ONE ANOTHER

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GMAT Number Properties

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