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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. 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 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
[(last - first) / increment] + 1
Prime factorization
53 -59

3. v2˜
Prime factorization
1.4
14
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

4. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Put the coefficient under the radical to get a better approximation
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

5. Prime Numbers:4x
97
53 -59
ONLY the nonnegative root of the numberUNLIKE
41 -43 -47

6. Prime Numbers:1x
13
11 -13 -17 -19
Prime
53 -59

7. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
61 -67
14
Never prime

8. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
PERFECT CUBES
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime factorization
23 -29

9. Prime Numbers:3x
13
EVEN
31 -37
71 -73 -79

10. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The PRODUCT of n consecutive integers is divisible by n!.
If 2 cannot be one of the primes in the sum - the sum must be even.
Either a multiple of N or a non-multiple of N
N is a divisor of x+y

11. v169=
ONLY the nonnegative root of the numberUNLIKE
13
N is a divisor of x+y
Prime

12. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
97
A PERFECT SQUARE

13. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.
N is a divisor of x+y
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.

14. The prime factorization of a perfect square contains only ______ powers of primes.
15
EVEN
53 -59
1.4

15. Any integer with an ODD number of total factors must be _______.
The average of the set times the number of elements in the set
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE

16. Prime Numbers:7x
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
71 -73 -79
Never prime

17. N! is _____ of all integers from 1 to N.
ODD
The average of an ODD number of consecutive integers will ALWAYS be an integer.
2 -3 -5 -7
A MULTIPLE

18. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
If 2 cannot be one of the primes in the sum - the sum must be even.
The middle number
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER

19. In an evenly spaced set - the mean and median are equal to the _____ of _________.
83 -89
Prime factorization
71 -73 -79
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

20. The average of an EVEN number of consecutive integers will ________ be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
53 -59

21. The two statements in a data sufficiency problem will _______________.
53 -59
NEVER CONTRADICT ONE ANOTHER
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

22. Prime Numbers:0x
PERFECT CUBES
2 -3 -5 -7
EVEN
FACTOR

23. The average of an ODD number of consecutive integers will ________ be an integer.
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime

24. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
14
1.4
The sum of any two primes will be even - unless one of the two primes is 2.

25. If 2 cannot be one of the primes in the sum - the sum must be _____.
14
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If 2 cannot be one of the primes in the sum - the sum must be even.
3·3n = 3^{n+1}

26. 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
25
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

27. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
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.
3·3n = 3^{n+1}
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

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

29. v3˜
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.
FACTOR
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1.7

30. The PRODUCT of n consecutive integers is divisible by ____.
A non-multiple of N.
The PRODUCT of n consecutive integers is divisible by n!.
Prime factorization
Prime

31. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.7
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 MULTIPLE

32. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
53 -59
23 -29
EVEN

33. In an evenly spaced set - the average can be found by finding ________.
97
PERFECT CUBES
The middle number
3·3n = 3^{n+1}

34. Prime Numbers:2x
The average of the set times the number of elements in the set
A PERFECT SQUARE
23 -29
If 2 cannot be one of the primes in the sum - the sum must be even.

35. The sum of any two primes will be ____ - unless ______.
EVEN
The same sign as the base
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.

36. In an evenly spaced set - the sum of the terms is equal to ____.
The same sign as the base
The PRODUCT of n consecutive integers is divisible by n!.
2 -3 -5 -7
The average of the set times the number of elements in the set

37. v256=
Prime factorization
ODD
The same sign as the base
16

38. Positive integers with only two factors must be ___.
Prime
If 2 cannot be one of the primes in the sum - the sum must be even.
13
23 -29

39. For ODD ROOTS - the root has ______.
The same sign as the base
Prime
31 -37
Put the coefficient under the radical to get a better approximation

40. Positive integers with more than two factors are ____.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

41. v625=
1.7
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
25

42. v196=
ODD
1.7
14
N is a divisor of x+y

43. Prime Numbers:6x
53 -59
61 -67
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 CONTRADICT ONE ANOTHER

44. v5˜
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.
2.5
83 -89
The average of an ODD number of consecutive integers will ALWAYS be an integer.

45. v225=
15
2 -3 -5 -7
A MULTIPLE
13

46. How to find the sum of consecutive integers:
41 -43 -47
97
2.5
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.

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 n consecutive integers is divisible by n if n is odd - but not if n is even.
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.
The average of an EVEN number of consecutive integers will NEVER be an integer.
[(last - first) / increment] + 1

48. If N is a divisor of x and y - then _______.
N is a divisor of x+y
41 -43 -47
EVEN
ONLY the nonnegative root of the numberUNLIKE

49. If the problem states/assumes that a number is an integer - check to see if you can use _______.
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.
25
Prime factorization

50. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
13
15
A PERFECT SQUARE