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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 prime factorization of a perfect square contains only ______ powers of primes.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
EVEN

2. The sum of any two primes will be ____ - unless ______.
Prime
The average of the set times the number of elements in the set
23 -29
The sum of any two primes will be even - unless one of the two primes is 2.

3. Prime Numbers:0x
2 -3 -5 -7
EVEN
A MULTIPLE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

4. N! is _____ of all integers from 1 to N.
The same sign as the base
53 -59
A MULTIPLE
1.7

5. v169=
97
83 -89
13
1.4

6. Prime Numbers:7x
1.4
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ODD
71 -73 -79

7. 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
71 -73 -79
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Either a multiple of N or a non-multiple of N
1.4

8. 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.
The PRODUCT of n consecutive integers is divisible by n!.
2.5
97

9. All perfect squares have a(n) _________ number of total factors.
61 -67
ODD
2 -3 -5 -7
ONLY the nonnegative root of the numberUNLIKE

10. If 2 cannot be one of the primes in the sum - the sum must be _____.
A PERFECT SQUARE
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

11. v225=
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.
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.
1.4
15

12. Any integer with an ODD number of total factors must be _______.
Never prime
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
Prime factorization

13. Prime Numbers:6x
16
61 -67
A PERFECT SQUARE
1.7

14. v256=
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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
16

15. The formula for finding the number of consecutive multiples in a set is _______.
ONLY the nonnegative root of the numberUNLIKE
31 -37
[(last - first) / increment] + 1
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.

16. In an evenly spaced set - the sum of the terms is equal to ____.
In an evenly spaced set - the average and the median are equal.
The average of the set times the number of elements in the set
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime

17. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an EVEN number of consecutive integers will NEVER be an integer.
16
A non-multiple of N.

18. How to find the sum of consecutive integers:
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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
16

19. If N is a divisor of x and y - then _______.
N is a divisor of x+y
A PERFECT SQUARE
The average of an EVEN number of consecutive integers will NEVER 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.

20. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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 MULTIPLE
NEVER CONTRADICT ONE ANOTHER
ONLY the nonnegative root of the numberUNLIKE

21. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Prime factorization
3·3n = 3^{n+1}
1. The smallest or largest element 2. The increment 3. The number of items in the set
97

22. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
The average of the set times the number of elements in the set
3·3n = 3^{n+1}
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Either a multiple of N or a non-multiple of N

23. v196=
31 -37
3·3n = 3^{n+1}
14
61 -67

24. Any integer with an EVEN number of total factors cannot be ______.
[(last - first) / increment] + 1
53 -59
FACTOR
A PERFECT SQUARE

25. The two statements in a data sufficiency problem will _______________.
The PRODUCT of n consecutive integers is divisible by n!.
NEVER CONTRADICT ONE ANOTHER
The same sign as the base
11 -13 -17 -19

26. v625=
16
NEVER CONTRADICT ONE ANOTHER
25
The sum of any two primes will be even - unless one of the two primes is 2.

27. 3n + 3n + 3n = _____ = ______
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.
3·3n = 3^{n+1}
13
Either a multiple of N or a non-multiple of N

28. v3˜
1.7
The average of the set times the number of elements in the set
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
If 2 cannot be one of the primes in the sum - the sum must be even.

29. The average of an EVEN number of consecutive integers will ________ 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.
14
The average of an EVEN number of consecutive integers will NEVER be an integer.
The PRODUCT of n consecutive integers is divisible by n!.

30. The prime factorization of __________ contains only EVEN powers of primes.
1. The smallest or largest element 2. The increment 3. The number of items in the set
71 -73 -79
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

31. Prime Numbers:5x
A PERFECT SQUARE
Prime
53 -59
A PERFECT SQUARE

32. In an evenly spaced set - the average can be found by finding ________.
The middle number
61 -67
A non-multiple of N.
NEVER CONTRADICT ONE ANOTHER

33. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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.
The middle number
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

34. Prime Numbers:9x
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
A PERFECT SQUARE
97

35. Prime Numbers:2x
N is a divisor of x+y
11 -13 -17 -19
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.
23 -29

36. Positive integers with more than two factors are ____.
Never prime
ONLY the nonnegative root of the numberUNLIKE
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

37. 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

38. Positive integers with only two factors must be ___.
EVEN
61 -67
53 -59
Prime

39. 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.
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
2 -3 -5 -7

40. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
N is a divisor of x+y
16
Prime factorization

41. Prime factors of _____ must come in pairs of three.
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES
A PERFECT SQUARE
1.4

42. Prime Numbers:1x
The same sign as the base
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.
15
11 -13 -17 -19

43. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Never prime
The same sign as the base
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 n consecutive integers is divisible by n if n is odd - but not if n is even.

44. Prime Numbers:8x
23 -29
Put the coefficient under the radical to get a better approximation
83 -89
ONLY the nonnegative root of the numberUNLIKE

45. In an evenly spaced set - the ____ and the ____ are equal.
N is a divisor of x+y
The same sign as the base
13
In an evenly spaced set - the average and the median are equal.

46. The average of an ODD number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
[(last - first) / increment] + 1
2 -3 -5 -7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

47. v2˜
1.4
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
ODD
The same sign as the base

48. Prime Numbers:4x
31 -37
N is a divisor of x+y
41 -43 -47
83 -89

49. v5˜
Put the coefficient under the radical to get a better approximation
2.5
14
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

50. If estimating a root with a coefficient - _____ .
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The middle number