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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. v169=
A PERFECT SQUARE
11 -13 -17 -19
Prime factorization
13

2. Prime Numbers:9x
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
97
A non-multiple of N.

3. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
In an evenly spaced set - the average and the median are equal.
61 -67
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

4. v196=
14
31 -37
PERFECT CUBES
41 -43 -47

5. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
3·3n = 3^{n+1}
A non-multiple of N.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

6. v3˜
53 -59
1. The smallest or largest element 2. The increment 3. The number of items in the set
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

7. The prime factorization of a perfect square contains only ______ powers of primes.
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
EVEN
A PERFECT SQUARE
1.4

8. Positive integers with more than two factors are ____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
25
FACTOR
Never prime

9. How to find the sum of consecutive integers:
13
2 -3 -5 -7
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.

10. Positive integers with only two factors must be ___.
16
ODD
Never prime
Prime

11. N! is _____ of all integers from 1 to N.
Put the coefficient under the radical to get a better approximation
Never prime
A MULTIPLE
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

12. The average of an ODD number of consecutive integers will ________ be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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.

13. 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

14. Any integer with an EVEN number of total factors cannot be ______.
EVEN
A PERFECT SQUARE
3·3n = 3^{n+1}
The same sign as the base

15. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
N is a divisor of x+y
3·3n = 3^{n+1}
23 -29

16. Prime Numbers:5x
1. The smallest or largest element 2. The increment 3. The number of items in the set
25
53 -59
71 -73 -79

17. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
Prime factorization
If 2 cannot be one of the primes in the sum - the sum must be even.
1.7

18. Prime Numbers:0x
Either a multiple of N or a non-multiple of N
2 -3 -5 -7
Prime
N is a divisor of x+y

19. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A non-multiple of N.
The average of the set times the number of elements in the set

20. v225=
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If 2 cannot be one of the primes in the sum - the sum must be even.
15
In an evenly spaced set - the average and the median are equal.

21. Any integer with an ODD number of total factors must be _______.
97
2.5
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. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Prime factorization
1. The smallest or largest element 2. The increment 3. The number of items in the set
3·3n = 3^{n+1}
The average of the set times the number of elements in the set

23. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last 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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
83 -89

24. v256=
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
16
13

25. In an evenly spaced set - the sum of the terms is equal to ____.
The average of the set times the number of elements in the set
The middle number
15
23 -29

26. If 2 cannot be one of the primes in the sum - the sum must be _____.
25
71 -73 -79
If 2 cannot be one of the primes in the sum - the sum must be even.
Never prime

27. ³v216 =
A PERFECT SQUARE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
EVEN
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

28. Prime factors of _____ must come in pairs of three.
11 -13 -17 -19
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
PERFECT CUBES
23 -29

29. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
61 -67
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is 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.
2 -3 -5 -7

30. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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
14

31. All perfect squares have a(n) _________ number of total factors.
53 -59
1.7
The PRODUCT of n consecutive integers is divisible by n!.
ODD

32. If N is a divisor of x and y - then _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
NEVER CONTRADICT ONE ANOTHER
16
N is a divisor of x+y

33. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
1.7
NEVER CONTRADICT ONE ANOTHER
83 -89

34. Prime Numbers:3x
FACTOR
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.
31 -37

35. The average of an EVEN number of consecutive integers will ________ be an integer.
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.
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

36. In an evenly spaced set - the ____ and the ____ are equal.
1.7
25
In an evenly spaced set - the average and the median are equal.
16

37. The two statements in a data sufficiency problem will _______________.
2 -3 -5 -7
23 -29
Put the coefficient under the radical to get a better approximation
NEVER CONTRADICT ONE ANOTHER

38. v2˜
1.4
2.5
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
11 -13 -17 -19

39. Prime Numbers:2x
In an evenly spaced set - the average and the median are equal.
23 -29
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 MULTIPLE

40. v5˜
1.4
16
The average of an ODD number of consecutive integers will ALWAYS be an integer.
2.5

41. 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
ONLY the nonnegative root of the numberUNLIKE
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

42. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Prime factorization
N is a divisor of x+y
15

43. 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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
13
FACTOR

44. Prime Numbers:7x
31 -37
NEVER CONTRADICT ONE ANOTHER
71 -73 -79
A MULTIPLE

45. Prime Numbers:4x
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
41 -43 -47
15

46. 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?
Never prime
3·3n = 3^{n+1}
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.

47. Prime Numbers:8x
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
31 -37
83 -89

48. In an evenly spaced set - the average can be found by finding ________.
A MULTIPLE
The middle number
If 2 cannot be one of the primes in the sum - the sum must be even.
N is a divisor of x+y

49. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
The middle number
14
NEVER CONTRADICT ONE ANOTHER

50. Prime Numbers:6x
61 -67
13
PERFECT CUBES
ONLY the nonnegative root of the numberUNLIKE