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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. The formula for finding the number of consecutive multiples in a set is _______.
The sum of any two primes will be even - unless one of the two primes is 2.
[(last - first) / increment] + 1
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
If 2 cannot be one of the primes in the sum - the sum must be even.

2. Prime Numbers:8x
ODD
A PERFECT SQUARE
16
83 -89

3. In an evenly spaced set - the ____ and the ____ are equal.
61 -67
In an evenly spaced set - the average and the median are equal.
16
A MULTIPLE

4. Any integer with an ODD number of total factors must be _______.
The PRODUCT of n consecutive integers is divisible by n!.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
1.7

5. 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?
14
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.
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

6. v196=
14
N is a divisor of x+y
53 -59
A PERFECT SQUARE

7. Any integer with an EVEN number of total factors cannot be ______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.

8. 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

9. 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
2.5

10. 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
The PRODUCT of n consecutive integers is divisible by n!.
N is a divisor of x+y
3·3n = 3^{n+1}
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

11. ³v216 =
The same sign as the base
83 -89
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

12. Prime Numbers:2x
61 -67
A PERFECT SQUARE
23 -29
83 -89

13. Prime Numbers:6x
97
N is a divisor of x+y
61 -67
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

14. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
N is a divisor of x+y
97
FACTOR
PERFECT CUBES

15. Prime Numbers:4x
25
41 -43 -47
Prime
A MULTIPLE

16. Prime Numbers:9x
97
1.7
23 -29
2 -3 -5 -7

17. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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.
If 2 cannot be one of the primes in the sum - the sum must be even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

18. Positive integers with only two factors must be ___.
41 -43 -47
Prime
A PERFECT SQUARE
14

19. The average of an EVEN number of consecutive integers will ________ be an integer.
The middle number
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE

20. All perfect squares have a(n) _________ number of total factors.
ODD
71 -73 -79
1.7
In an evenly spaced set - the average and the median are equal.

21. v2˜
N is a divisor of x+y
The PRODUCT of n consecutive integers is divisible by n!.
1.4
NEVER CONTRADICT ONE ANOTHER

22. In an evenly spaced set - the sum of the terms is equal to ____.
ONLY the nonnegative root of the numberUNLIKE
The average of the set times the number of elements in the set
NEVER CONTRADICT ONE ANOTHER
15

23. 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
A MULTIPLE
ODD
61 -67

24. The prime factorization of a perfect square contains only ______ powers of primes.
2 -3 -5 -7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
[(last - first) / increment] + 1
EVEN

25. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
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
13
1.4

26. Prime Numbers:5x
ODD
53 -59
The PRODUCT of n consecutive integers is divisible by n!.
EVEN

27. Prime Numbers:0x
11 -13 -17 -19
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
2 -3 -5 -7
Prime factorization

28. v256=
41 -43 -47
A non-multiple of N.
16
[(last - first) / increment] + 1

29. If N is a divisor of x and y - then _______.
PERFECT CUBES
A non-multiple of N.
N is a divisor of x+y
3·3n = 3^{n+1}

30. v225=
61 -67
ODD
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
15

31. The average of an ODD number of consecutive integers will ________ be an integer.
31 -37
1.4
In an evenly spaced set - the average and the median are equal.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

32. v169=
13
2 -3 -5 -7
The same sign as the base
16

33. In an evenly spaced set - the mean and median are equal to the _____ of _________.
83 -89
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.

34. For ODD ROOTS - the root has ______.
The same sign as the base
1.4
[(last - first) / increment] + 1
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

35. If 2 cannot be one of the primes in the sum - the sum must be _____.
11 -13 -17 -19
In an evenly spaced set - the average and the median 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
If 2 cannot be one of the primes in the sum - the sum must be even.

36. The two statements in a data sufficiency problem will _______________.
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
97
NEVER CONTRADICT ONE ANOTHER

37. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
1.4
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The average of the set times the number of elements in the set

38. 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2.5
FACTOR

39. If the problem states/assumes that a number is an integer - check to see if you can use _______.
N is a divisor of x+y
Prime factorization
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1. The smallest or largest element 2. The increment 3. The number of items in the set

40. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
41 -43 -47
Put the coefficient under the radical to get a better approximation
Never prime

41. Prime Numbers:1x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1.4
11 -13 -17 -19
61 -67

42. 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
Put the coefficient under the radical to get a better approximation
A MULTIPLE
1. The smallest or largest element 2. The increment 3. The number of items in the set

43. N! is _____ of all integers from 1 to N.
PERFECT CUBES
2.5
A MULTIPLE
[(last - first) / increment] + 1

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

45. 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
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime
1. The smallest or largest element 2. The increment 3. The number of items in the set
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

46. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
NEVER CONTRADICT ONE ANOTHER
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
16

47. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
53 -59
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
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. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
2 -3 -5 -7
14
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.

49. How to find the sum of consecutive integers:
16
If 2 cannot be one of the primes in the sum - the sum must be even.
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

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