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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. 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

2. If estimating a root with a coefficient - _____ .
41 -43 -47
Put the coefficient under the radical to get a better approximation
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.

3. Prime Numbers:1x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
11 -13 -17 -19
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE

4. v5˜
2.5
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
23 -29

5. Prime Numbers:7x
A PERFECT SQUARE
11 -13 -17 -19
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
71 -73 -79

6. The prime factorization of a perfect square contains only ______ powers of primes.
13
2.5
EVEN
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

7. In an evenly spaced set - the sum of the terms is equal to ____.
EVEN
A PERFECT SQUARE
The average of the set times the number of elements in the set
Never prime

8. The sum of any two primes will be ____ - unless ______.
Prime
The sum of any two primes will be even - unless one of the two primes is 2.
[(last - first) / increment] + 1
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 ________.
71 -73 -79
25
A non-multiple of N.
23 -29

10. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A MULTIPLE
ODD

11. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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.
2.5
Either a multiple of N or a non-multiple of N

12. For ODD ROOTS - the root has ______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The same sign as the base
A non-multiple of N.
41 -43 -47

13. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
2 -3 -5 -7
A MULTIPLE
2.5

14. Let N be an integer. If you add two non-multiples of N - the result could be _______.
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.
PERFECT CUBES
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

15. The PRODUCT of n consecutive integers is divisible by ____.
The average of an EVEN number of consecutive integers will NEVER be an integer.
2.5
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE

16. 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
NEVER CONTRADICT ONE ANOTHER
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
1.7

17. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.
13

18. 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.
31 -37
Never prime
71 -73 -79

19. 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
2 -3 -5 -7
53 -59
41 -43 -47

20. If 2 cannot be one of the primes in the sum - the sum must be _____.
The same sign as the base
15
If 2 cannot be one of the primes in the sum - the sum must be even.
A MULTIPLE

21. In an evenly spaced set - the average can be found by finding ________.
A PERFECT SQUARE
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.
The middle number

22. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
14
FACTOR
The same sign as the base
25

23. Prime Numbers:5x
53 -59
71 -73 -79
PERFECT CUBES
The average of an ODD number of consecutive integers will ALWAYS be an integer.

24. Prime Numbers:8x
25
Put the coefficient under the radical to get a better approximation
2.5
83 -89

25. Prime Numbers:2x
Either a multiple of N or a non-multiple of N
1.4
The same sign as the base
23 -29

26. 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.
15
A PERFECT SQUARE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

27. In an evenly spaced set - the mean and median are equal to the _____ of _________.
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE

28. Prime Numbers:4x
15
N is a divisor of x+y
The average of an EVEN number of consecutive integers will NEVER be an integer.
41 -43 -47

29. v256=
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
41 -43 -47
16
Prime factorization

30. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
ODD
The same sign as the base
25

31. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

32. ³v216 =
[(last - first) / increment] + 1
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
16
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

33. Positive integers with only two factors must be ___.
Prime
NEVER CONTRADICT ONE ANOTHER
PERFECT CUBES
3·3n = 3^{n+1}

34. v196=
14
1.4
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.

35. Positive integers with more than two factors are ____.
Never prime
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.
A PERFECT SQUARE

36. Any integer with an EVEN number of total factors cannot be ______.
PERFECT CUBES
25
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE

37. Prime Numbers:0x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2 -3 -5 -7
1.4
EVEN

38. How to find the sum of consecutive integers:
FACTOR
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.
1.4

39. Any integer with an ODD number of total factors must be _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
3·3n = 3^{n+1}

40. v2˜
1.4
The average of an ODD number of consecutive integers will ALWAYS be an integer.
FACTOR
53 -59

41. The two statements in a data sufficiency problem will _______________.
The same sign as the base
N is a divisor of x+y
41 -43 -47
NEVER CONTRADICT ONE ANOTHER

42. Prime Numbers:6x
71 -73 -79
In an evenly spaced set - the average and the median are equal.
61 -67
13

43. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
A MULTIPLE
A non-multiple of N.
FACTOR

44. Prime Numbers:9x
97
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
FACTOR

45. 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 factorization
2.5
A MULTIPLE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

46. 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.
EVEN
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

47. v3˜
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.7
2.5
14

48. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.
Put the coefficient under the radical to get a better approximation
N is a divisor of x+y

49. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The average of the set times the number of elements in the set
PERFECT CUBES
11 -13 -17 -19
ONLY the nonnegative root of the numberUNLIKE

50. v225=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
14
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
15