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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. All perfect squares have a(n) _________ number of total factors.
2 -3 -5 -7
53 -59
ODD
25

2. v2˜
2.5
The middle number
1.4
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. The sum of any two primes will be ____ - unless ______.
A MULTIPLE
The sum of any two primes will be even - unless one of the two primes is 2.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime factorization

4. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
16
97
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1. The smallest or largest element 2. The increment 3. The number of items in the set

5. v5˜
2.5
ONLY the nonnegative root of the numberUNLIKE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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

6. Positive integers with more than two factors are ____.
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.
Never prime
61 -67
The average of the set times the number of elements in the set

7. v196=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
14
In an evenly spaced set - the average and the median are equal.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

8. 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
71 -73 -79
61 -67
83 -89

9. 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.
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.
PERFECT CUBES
A PERFECT SQUARE

10. In an evenly spaced set - the mean and median are equal to the _____ of _________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
16
53 -59
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

11. Prime Numbers:8x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29
83 -89
In an evenly spaced set - the average and the median are equal.

12. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
11 -13 -17 -19
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.

13. v225=
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.
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.
NEVER CONTRADICT ONE ANOTHER

14. The average of an ODD number of consecutive integers will ________ be an integer.
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
16
53 -59

15. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
25
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

16. Positive integers with only two factors must be ___.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The same sign as the base
Prime
NEVER CONTRADICT ONE ANOTHER

17. Prime Numbers:1x
11 -13 -17 -19
A PERFECT SQUARE
FACTOR
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

18. Prime Numbers:5x
53 -59
A MULTIPLE
The same sign as the base
31 -37

19. Prime Numbers:0x
71 -73 -79
3·3n = 3^{n+1}
2 -3 -5 -7
A PERFECT SQUARE

20. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
23 -29
1. The smallest or largest element 2. The increment 3. The number of items in the set
FACTOR
1.7

21. For ODD ROOTS - the root has ______.
The same sign as the base
97
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

22. In an evenly spaced set - the average can be found by finding ________.
FACTOR
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.
NEVER CONTRADICT ONE ANOTHER

23. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
Prime
A PERFECT SQUARE
2 -3 -5 -7

24. The PRODUCT of n consecutive integers is divisible by ____.
If 2 cannot be one of the primes in the sum - the sum must be even.
97
ONLY the nonnegative root of the numberUNLIKE
The PRODUCT of n consecutive integers is divisible by n!.

25. The prime factorization of a perfect square contains only ______ powers of primes.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD
EVEN
23 -29

26. How to find the sum of consecutive integers:
15
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.

27. 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?
53 -59
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.
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.

28. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
ODD
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.

29. Any integer with an EVEN number of total factors cannot be ______.
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
N is a divisor of x+y
A PERFECT SQUARE

30. 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.
Either a multiple of N or a non-multiple of N
41 -43 -47
16

31. v169=
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
13
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 middle number

32. 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

33. Prime Numbers:9x
97
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
41 -43 -47
53 -59

34. Prime Numbers:2x
[(last - first) / increment] + 1
EVEN
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
23 -29

35. 3n + 3n + 3n = _____ = ______
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.
3·3n = 3^{n+1}
71 -73 -79

36. The formula for finding the number of consecutive multiples in a set is _______.
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
41 -43 -47
[(last - first) / increment] + 1

37. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
[(last - first) / increment] + 1
A PERFECT SQUARE
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

38. Prime factors of _____ must come in pairs of three.
25
PERFECT CUBES
53 -59
2.5

39. Prime Numbers:4x
ODD
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
41 -43 -47
25

40. If N is a divisor of x and y - then _______.
2 -3 -5 -7
N is a divisor of x+y
FACTOR
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. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The middle number
A PERFECT SQUARE
A non-multiple of N.
A PERFECT SQUARE

42. N! is _____ of all integers from 1 to N.
The same sign as the base
53 -59
A MULTIPLE
The sum of any two primes will be even - unless one of the two primes is 2.

43. v3˜
1.7
The sum of any two primes will be even - unless one of the two primes is 2.
Prime factorization
1.4

44. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
3·3n = 3^{n+1}
FACTOR
25
A PERFECT SQUARE

45. The prime factorization of __________ contains only EVEN powers of primes.
NEVER CONTRADICT ONE ANOTHER
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.
A PERFECT SQUARE

46. 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!.
2.5
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N

47. If estimating a root with a coefficient - _____ .
41 -43 -47
Put the coefficient under the radical to get a better approximation
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

48. Prime Numbers:7x
11 -13 -17 -19
71 -73 -79
Put the coefficient under the radical to get a better approximation
ONLY the nonnegative root of the numberUNLIKE

49. In an evenly spaced set - the sum of the terms is equal to ____.
3·3n = 3^{n+1}
The same sign as the base
ONLY the nonnegative root of the numberUNLIKE
The average of the set times the number of elements in the set

50. v625=
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25