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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. Prime Numbers:1x
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
83 -89
11 -13 -17 -19

2. If N is a divisor of x and y - then _______.
A MULTIPLE
PERFECT CUBES
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS be an integer.

3. 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
83 -89
71 -73 -79
15
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

4. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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.
ONLY the nonnegative root of the numberUNLIKE
61 -67
The PRODUCT of n consecutive integers is divisible by n!.

5. v256=
11 -13 -17 -19
16
FACTOR
41 -43 -47

6. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
In an evenly spaced set - the average and the median are equal.
61 -67
[(last - first) / increment] + 1
FACTOR

7. Positive integers with more than two factors are ____.
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
Never prime
97

8. v625=
83 -89
25
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
N is a divisor of x+y

9. 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. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.
15

10. The sum of any two primes will be ____ - unless ______.
15
61 -67
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

11. If 2 cannot be one of the primes in the sum - the sum must be _____.
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
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.

12. In an evenly spaced set - the ____ and the ____ are equal.
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
15
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. Prime Numbers:3x
The PRODUCT of n consecutive integers is divisible by n!.
97
31 -37
83 -89

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

15. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ONLY the nonnegative root of the numberUNLIKE
NEVER CONTRADICT ONE ANOTHER
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

16. Prime Numbers:4x
15
2 -3 -5 -7
41 -43 -47
A PERFECT SQUARE

17. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
14

18. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The same sign as the base
Either a multiple of N or a non-multiple of N
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE

19. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
97
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.
[(last - first) / increment] + 1

20. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
71 -73 -79
14
A non-multiple of N.
1. The smallest or largest element 2. The increment 3. The number of items in the set

21. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Prime
A non-multiple of N.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.

22. 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.
41 -43 -47
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
61 -67

23. v225=
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.
11 -13 -17 -19
15
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

24. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
1.4
The same sign as the base
Either a multiple of N or a non-multiple of N

25. The formula for finding the number of consecutive multiples in a set is _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
3·3n = 3^{n+1}
N is a divisor of x+y
[(last - first) / increment] + 1

26. 3n + 3n + 3n = _____ = ______
Prime
ODD
97
3·3n = 3^{n+1}

27. The two statements in a data sufficiency problem will _______________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
NEVER CONTRADICT ONE ANOTHER
11 -13 -17 -19

28. 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?
71 -73 -79
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.
16
If 2 cannot be one of the primes in the sum - the sum must be even.

29. Prime Numbers:9x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
16
97
Prime

30. How to find the sum of consecutive integers:
1. The smallest or largest element 2. The increment 3. The number of items in the set
11 -13 -17 -19
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.

31. Prime Numbers:6x
2.5
A PERFECT SQUARE
61 -67
The PRODUCT of n consecutive integers is divisible by n!.

32. v3˜
ONLY the nonnegative root of the numberUNLIKE
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
Never prime
1.7

33. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Prime
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. Average the first and last to find the mean. 2. Count the number of terms. 3. Multiply the mean by the number of terms.

34. The average of an EVEN number of consecutive integers will ________ be an integer.
23 -29
The average of an EVEN number of consecutive integers will NEVER be an integer.
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.

35. v2˜
1.4
[(last - first) / increment] + 1
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

36. v5˜
If 2 cannot be one of the primes in the sum - the sum must be 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2.5

37. Prime Numbers:7x
97
71 -73 -79
15
Either a multiple of N or a non-multiple of N

38. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER
3·3n = 3^{n+1}
The average of the set times the number of elements in the set

39. N! is _____ of all integers from 1 to N.
A MULTIPLE
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.
25

40. The prime factorization of __________ contains only EVEN powers of primes.
A non-multiple of N.
A PERFECT SQUARE
16
The average of an ODD number of consecutive integers will ALWAYS be an integer.

41. The prime factorization of a perfect square contains only ______ powers of primes.
83 -89
Prime factorization
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN

42. If estimating a root with a coefficient - _____ .
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.
Put the coefficient under the radical to get a better approximation
71 -73 -79

43. v169=
[(last - first) / increment] + 1
13
EVEN
1. The smallest or largest element 2. The increment 3. The number of items in the set

44. All perfect squares have a(n) _________ number of total factors.
EVEN
ODD
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

45. In an evenly spaced set - the average can be found by finding ________.
The middle number
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.

46. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
23 -29
A PERFECT SQUARE
Prime factorization

47. Prime Numbers:2x
N is a divisor of x+y
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.
A non-multiple of N.

48. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Never prime
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime factorization
31 -37

49. Prime Numbers:5x
13
2.5
53 -59
EVEN

50. 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