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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. The average of an EVEN number of consecutive integers will ________ be an integer.
A non-multiple of N.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Either a multiple of N or a non-multiple of N
Never prime

3. If estimating a root with a coefficient - _____ .
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
3·3n = 3^{n+1}
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

4. If 2 cannot be one of the primes in the sum - the sum must be _____.
2 -3 -5 -7
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.
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.

5. If the problem states/assumes that a number is an integer - check to see if you can use _______.
16
ODD
Prime factorization
PERFECT CUBES

6. Prime Numbers:9x
97
16
Prime factorization
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. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The sum of any two primes will be even - unless one of the two primes is 2.
A non-multiple of N.
11 -13 -17 -19
FACTOR

8. v256=
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
A non-multiple of N.
16

9. 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?
3·3n = 3^{n+1}
97
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.
41 -43 -47

10. The prime factorization of __________ contains only EVEN powers of primes.
The middle number
A PERFECT SQUARE
A MULTIPLE
NEVER CONTRADICT ONE ANOTHER

11. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
Put the coefficient under the radical to get a better approximation
The average of an EVEN number of consecutive integers will NEVER be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

12. Any integer with an ODD number of total factors must be _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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
Either a multiple of N or a non-multiple of N

13. The average of an ODD number of consecutive integers will ________ be an integer.
2.5
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

14. v169=
Put the coefficient under the radical to get a better approximation
13
1.7
If 2 cannot be one of the primes in the sum - the sum must be even.

15. ³v216 =
The PRODUCT of n consecutive integers is divisible by n!.
PERFECT CUBES
53 -59
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

16. In an evenly spaced set - the ____ and the ____ are equal.
13
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the average and the median are equal.
The average of the set times the number of elements in the set

17. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
In an evenly spaced set - the average and the median are equal.
41 -43 -47
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER

18. The prime factorization of a perfect square contains only ______ powers of primes.
Prime
A non-multiple of N.
EVEN
The average of the set times the number of elements in the set

19. Positive integers with only two factors must be ___.
Prime
11 -13 -17 -19
53 -59
[(last - first) / increment] + 1

20. Prime Numbers:5x
In an evenly spaced set - the average and the median are equal.
53 -59
PERFECT CUBES
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

21. How to find the sum of consecutive integers:
PERFECT CUBES
A non-multiple of N.
Prime factorization
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.

22. 3n + 3n + 3n = _____ = ______
The same sign as the base
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 average of an EVEN number of consecutive integers will NEVER be an integer.
3·3n = 3^{n+1}

23. Prime Numbers:3x
Never prime
31 -37
Either a multiple of N or a non-multiple of N
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.

24. The PRODUCT of n consecutive integers is divisible by ____.
14
The PRODUCT of n consecutive integers is divisible by n!.
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
53 -59

25. All perfect squares have a(n) _________ number of total factors.
ODD
11 -13 -17 -19
Never prime
14

26. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Either a multiple of N or a non-multiple of N
97
3·3n = 3^{n+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.

27. Prime Numbers:2x
1.4
23 -29
A PERFECT SQUARE
FACTOR

28. N! is _____ of all integers from 1 to N.
Either a multiple of N or a non-multiple of N
A MULTIPLE
23 -29
PERFECT CUBES

29. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
11 -13 -17 -19
97
14

30. 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
53 -59
A non-multiple of N.

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
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.
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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

32. v625=
A PERFECT SQUARE
61 -67
25
83 -89

33. In an evenly spaced set - the average can be found by finding ________.
A PERFECT SQUARE
The middle number
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.
Put the coefficient under the radical to get a better approximation

34. v196=
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
The sum of any two primes will be even - unless one of the two primes is 2.
14
25

35. Prime Numbers:1x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Either a multiple of N or a non-multiple of N
11 -13 -17 -19
EVEN

36. Prime Numbers:6x
PERFECT CUBES
11 -13 -17 -19
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.

37. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
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.
ONLY the nonnegative root of the numberUNLIKE
FACTOR

38. Positive integers with more than two factors are ____.
13
14
1. The smallest or largest element 2. The increment 3. The number of items in the set
Never prime

39. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
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.
ONLY the nonnegative root of the numberUNLIKE
61 -67

40. In an evenly spaced set - the sum of the terms is equal to ____.
2.5
23 -29
A PERFECT SQUARE
The average of the set times the number of elements in the set

41. Prime Numbers:4x
13
41 -43 -47
1.4
[(last - first) / increment] + 1

42. The two statements in a data sufficiency problem will _______________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
16

43. Prime Numbers:8x
83 -89
2.5
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.
1.7

44. For ODD ROOTS - the root has ______.
The same sign as the base
13
A MULTIPLE
ODD

45. v3˜
61 -67
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.7
3·3n = 3^{n+1}

46. Any integer with an EVEN number of total factors cannot be ______.
3·3n = 3^{n+1}
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 sum of any two primes will be even - unless one of the two primes is 2.

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

48. In an evenly spaced set - the mean and median are equal to the _____ of _________.
2 -3 -5 -7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
14
A PERFECT SQUARE

49. The formula for finding the number of consecutive multiples in a set is _______.
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.
[(last - first) / increment] + 1
Put the coefficient under the radical to get a better approximation

50. Prime Numbers:7x
71 -73 -79
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
14
Prime