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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. v2˜
PERFECT CUBES
1.4
14
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.

2. Any integer with an EVEN number of total factors cannot be ______.
71 -73 -79
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE
Never prime

3. v225=
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
[(last - first) / increment] + 1
Never prime
15

4. The prime factorization of a perfect square contains only ______ powers of primes.
23 -29
Either a multiple of N or a non-multiple of N
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN

5. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
The PRODUCT of n consecutive integers is divisible by n!.
2 -3 -5 -7
A PERFECT SQUARE

6. Prime Numbers:2x
If 2 cannot be one of the primes in the sum - the sum must be even.
23 -29
The sum of any two primes will be even - unless one of the two primes is 2.
41 -43 -47

7. Prime Numbers:4x
16
ODD
Put the coefficient under the radical to get a better approximation
41 -43 -47

8. Prime Numbers:7x
Never prime
61 -67
71 -73 -79
In an evenly spaced set - the average and the median are equal.

9. Prime Numbers:9x
The middle number
1. The smallest or largest element 2. The increment 3. The number of items in the set
97
FACTOR

10. The PRODUCT of n consecutive integers is divisible by ____.
A PERFECT SQUARE
15
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the average and the median are equal.

11. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
25

12. v5˜
FACTOR
2.5
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!.

13. In an evenly spaced set - the average can be found by finding ________.
The middle number
Never prime
A PERFECT SQUARE
25

14. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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.
3·3n = 3^{n+1}
1.7

15. In an evenly spaced set - the ____ and the ____ are equal.
ODD
In an evenly spaced set - the average and the median are equal.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
61 -67

16. All perfect squares have a(n) _________ number of total factors.
3·3n = 3^{n+1}
ODD
1.7
A non-multiple of N.

17. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE

18. The average of an ODD number of consecutive integers will ________ be an integer.
13
The average of an ODD number of consecutive integers will ALWAYS be an integer.
16
EVEN

19. ³v216 =
16
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
1.7

20. Positive integers with only two factors must be ___.
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.
ODD
3·3n = 3^{n+1}
Prime

21. The two statements in a data sufficiency problem will _______________.
Put the coefficient under the radical to get a better approximation
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER
The sum of any two primes will be even - unless one of the two primes is 2.

22. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
16
The sum of any two primes will be even - unless one of the two primes is 2.
The average of the set times the number of elements in the set

23. Prime Numbers:5x
61 -67
The PRODUCT of n consecutive integers is divisible by n!.
The same sign as the base
53 -59

24. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A PERFECT SQUARE
31 -37
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.

25. v169=
83 -89
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.
13

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
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
A MULTIPLE
A non-multiple of N.

27. Prime factors of _____ must come in pairs of three.
The middle number
Prime factorization
A MULTIPLE
PERFECT CUBES

28. 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
13
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
[(last - first) / increment] + 1
A PERFECT SQUARE

29. v196=
13
14
11 -13 -17 -19
1.4

30. Prime Numbers:8x
In an evenly spaced set - the average and the median are equal.
83 -89
FACTOR
Never prime

31. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE
The middle number
Prime

32. Prime Numbers:1x
11 -13 -17 -19
EVEN
53 -59
The average of an ODD number of consecutive integers will ALWAYS be an integer.

33. Prime Numbers:0x
15
2 -3 -5 -7
A non-multiple of N.
Prime factorization

34. 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 average of the set times the number of elements in the set
In an evenly spaced set - the average and the median are equal.
N is a divisor of x+y

35. In an evenly spaced set - the sum of the terms is equal to ____.
EVEN
PERFECT CUBES
A MULTIPLE
The average of the set times the number of elements in the set

36. 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.
If 2 cannot be one of the primes in the sum - the sum must be even.
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.
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.

37. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
53 -59
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
Never prime

38. How to find the sum of consecutive integers:
31 -37
The same sign as the base
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.
Either a multiple of N or a non-multiple of N

39. Prime Numbers:6x
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
Never prime
61 -67

40. Prime Numbers:3x
31 -37
A MULTIPLE
23 -29
EVEN

41. If estimating a root with a coefficient - _____ .
41 -43 -47
1. The smallest or largest element 2. The increment 3. The number of items in the set
61 -67
Put the coefficient under the radical to get a better approximation

42. Positive integers with more than two factors are ____.
Either a multiple of N or a non-multiple of 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.
Never prime
97

43. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
83 -89
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37
1.4

44. v625=
14
13
41 -43 -47
25

45. If the problem states/assumes that a number is an integer - check to see if you can use _______.
FACTOR
A PERFECT SQUARE
Prime factorization
61 -67

46. v256=
23 -29
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
16
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.

47. 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 sum of any two primes will be even - unless one of the two primes is 2.
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 average of the set times the number of elements in the set

48. 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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49. N! is _____ of all integers from 1 to N.
1.4
15
53 -59
A MULTIPLE

50. v3˜
23 -29
1.7
A non-multiple of N.
EVEN

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GMAT Number Properties

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