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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. v3˜
1.7
71 -73 -79
A MULTIPLE
2 -3 -5 -7

2. Positive integers with only two factors must be ___.
1. The smallest or largest element 2. The increment 3. The number of items in the set
53 -59
In an evenly spaced set - the average and the median are equal.
Prime

3. v2˜
2 -3 -5 -7
The same sign as the base
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
1.4

4. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
[(last - first) / increment] + 1
13
N is a divisor of x+y

5. The prime factorization of __________ contains only EVEN powers of primes.
The PRODUCT of n consecutive integers is divisible by n!.
71 -73 -79
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation

6. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
25
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.
2 -3 -5 -7

7. Prime Numbers:1x
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.
In an evenly spaced set - the average and the median are equal.
2.5
11 -13 -17 -19

8. Prime Numbers:0x
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 -3 -5 -7
Prime factorization
The same sign as the base

9. Prime Numbers:4x
13
41 -43 -47
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.

10. Prime Numbers:2x
Either a multiple of N or a non-multiple of N
23 -29
41 -43 -47
11 -13 -17 -19

11. Prime factors of _____ must come in pairs of three.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
PERFECT CUBES
61 -67
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.

12. ³v216 =
ONLY the nonnegative root of the numberUNLIKE
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
16

13. In an evenly spaced set - the ____ and the ____ are equal.
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 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.
In an evenly spaced set - the average and the median are equal.

14. Prime Numbers:5x
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
53 -59
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.

15. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
14

16. Let N be an integer. If you add two non-multiples of N - the result could be _______.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The same sign as the base
Either a multiple of N or a non-multiple of N
The sum of any two primes will be even - unless one of the two primes is 2.

17. In an evenly spaced set - the sum of the terms is equal to ____.
71 -73 -79
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
The average of the set times the number of elements in the set

18. If estimating a root with a coefficient - _____ .
In an evenly spaced set - the average and the median are equal.
The same sign as the base
Put the coefficient under the radical to get a better approximation
14

19. In an evenly spaced set - the mean and median are equal to the _____ of _________.
A non-multiple of N.
13
FACTOR
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

20. Prime Numbers:9x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
97
31 -37
The sum of any two primes will be even - unless one of the two primes is 2.

21. If 2 cannot be one of the primes in the sum - the sum must be _____.
16
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.
Prime
If 2 cannot be one of the primes in the sum - the sum must be even.

22. The PRODUCT of n consecutive integers is divisible by ____.
NEVER CONTRADICT ONE ANOTHER
14
ODD
The PRODUCT of n consecutive integers is divisible by n!.

23. All perfect squares have a(n) _________ number of total factors.
ODD
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

24. 3n + 3n + 3n = _____ = ______
ODD
41 -43 -47
N is a divisor of x+y
3·3n = 3^{n+1}

25. v169=
Never prime
3·3n = 3^{n+1}
The average of an EVEN number of consecutive integers will NEVER be an integer.
13

26. The two statements in a data sufficiency problem will _______________.
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
15
NEVER CONTRADICT ONE ANOTHER

27. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set
97
15

28. Prime Numbers:7x
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE
15

29. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
[(last - first) / increment] + 1
2 -3 -5 -7
ONLY the nonnegative root of the numberUNLIKE

30. The formula for finding the number of consecutive multiples in a set is _______.
13
[(last - first) / increment] + 1
97
71 -73 -79

31. Prime Numbers:3x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
31 -37
In an evenly spaced set - the average and the median are equal.
If 2 cannot be one of the primes in the sum - the sum must be even.

32. If N is a divisor of x and y - then _______.
NEVER CONTRADICT ONE ANOTHER
15
N is a divisor of x+y
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

33. 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
41 -43 -47
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
83 -89

34. 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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35. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
83 -89
23 -29
FACTOR
[(last - first) / increment] + 1

36. 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
Either a multiple of N or a non-multiple of N
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 PERFECT SQUARE

37. The average of an EVEN number of consecutive integers will ________ be an integer.
61 -67
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.
EVEN

38. v196=
1. The smallest or largest element 2. The increment 3. The number of items in the set
14
25
The average of the set times the number of elements in the set

39. How to find the sum of consecutive integers:
Never prime
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 ODD number of consecutive integers will ALWAYS be an integer.
FACTOR

40. v256=
The average of an EVEN number of consecutive integers will NEVER be an integer.
16
1.7
41 -43 -47

41. The prime factorization of a perfect square contains only ______ powers of primes.
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.
EVEN
25
A non-multiple of N.

42. v625=
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the average and the median are equal.
25
A MULTIPLE

43. In an evenly spaced set - the average can be found by finding ________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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
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.

44. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
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
A non-multiple of N.
PERFECT CUBES

45. 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.
The PRODUCT of n consecutive integers is divisible by n!.
Put the coefficient under the radical to get a better approximation
13

46. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
15
A MULTIPLE
ONLY the nonnegative root of the numberUNLIKE
16

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 middle number
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.
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.

48. Prime Numbers:6x
13
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
61 -67

49. v5˜
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.
61 -67
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.

50. N! is _____ of all integers from 1 to N.
The average of the set times the number of elements in the set
A MULTIPLE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
13