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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. Any integer with an ODD number of total factors must be _______.
The sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE

2. For ODD ROOTS - the root has ______.
Either a multiple of N or a non-multiple of N
Prime factorization
A PERFECT SQUARE
The same sign as the base

3. v225=
2.5
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
A PERFECT SQUARE

4. The sum of any two primes will be ____ - unless ______.
If 2 cannot be one of the primes in the sum - the sum must be even.
[(last - first) / increment] + 1
97
The sum of any two primes will be even - unless one of the two primes is 2.

5. ³v216 =
The average of an EVEN number of consecutive integers will NEVER be an integer.
61 -67
The middle number
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

6. 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?
The average of an EVEN number of consecutive integers will NEVER be an integer.
ONLY the nonnegative root of the numberUNLIKE
53 -59
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.

7. Prime Numbers:7x
71 -73 -79
A PERFECT SQUARE
N is a divisor of x+y
61 -67

8. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
2.5
FACTOR
11 -13 -17 -19
The average of an ODD number of consecutive integers will ALWAYS be an integer.

9. Positive integers with only two factors must be ___.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE
14
Prime

10. Prime Numbers:2x
A PERFECT SQUARE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A MULTIPLE
23 -29

11. v3˜
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.
1.7
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.
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.

12. Prime Numbers:3x
83 -89
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
31 -37

13. v2˜
FACTOR
The same sign as the base
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

14. Prime Numbers:1x
Prime factorization
83 -89
11 -13 -17 -19
In an evenly spaced set - the average and the median are equal.

15. The prime factorization of a perfect square contains only ______ powers of primes.
53 -59
15
FACTOR
EVEN

16. In an evenly spaced set - the sum of the terms is equal to ____.
2 -3 -5 -7
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
The average of the set times the number of elements in the set

17. The average of an EVEN number of consecutive integers will ________ be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
The average of an EVEN number of consecutive integers will NEVER be an integer.
1.4
A non-multiple of N.

18. Prime factors of _____ must come in pairs of three.
The middle number
The average of the set times the number of elements in the set
PERFECT CUBES
A PERFECT SQUARE

19. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A MULTIPLE
A non-multiple of N.

20. Prime Numbers:8x
83 -89
15
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.
61 -67

21. Prime Numbers:0x
97
1.4
2 -3 -5 -7
71 -73 -79

22. v5˜
The sum of any two primes will be even - unless one of the two primes is 2.
2.5
14
ONLY the nonnegative root of the numberUNLIKE

23. All perfect squares have a(n) _________ number of total factors.
The average of an EVEN number of consecutive integers will NEVER be an integer.
1.7
ODD
NEVER CONTRADICT ONE ANOTHER

24. Prime Numbers:5x
2 -3 -5 -7
71 -73 -79
53 -59
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. If estimating a root with a coefficient - _____ .
25
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.
Put the coefficient under the radical to get a better approximation
61 -67

26. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
A PERFECT SQUARE
Prime
[(last - first) / increment] + 1
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

27. The prime factorization of __________ contains only EVEN powers of primes.
Prime factorization
A PERFECT SQUARE
2 -3 -5 -7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

28. The two statements in a data sufficiency problem will _______________.
97
NEVER CONTRADICT ONE ANOTHER
N is a divisor of x+y
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

29. Prime Numbers:6x
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.
Either a multiple of N or a non-multiple of N
61 -67

30. In an evenly spaced set - the average can be found by finding ________.
2.5
Prime factorization
The middle number
The same sign as the base

31. v196=
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime
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.

32. 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
2 -3 -5 -7
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

33. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25
61 -67

34. v169=
ONLY the nonnegative root of the numberUNLIKE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
13
Prime factorization

35. v256=
Put the coefficient under the radical to get a better approximation
16
A PERFECT SQUARE
2.5

36. The formula for finding the number of consecutive multiples in a set is _______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ONLY the nonnegative root of the numberUNLIKE
[(last - first) / increment] + 1
83 -89

37. 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.
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
A MULTIPLE

38. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
N is a divisor of x+y
41 -43 -47
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.
ONLY the nonnegative root of the numberUNLIKE

39. In an evenly spaced set - the ____ and the ____ are equal.
NEVER CONTRADICT ONE ANOTHER
31 -37
83 -89
In an evenly spaced set - the average and the median are equal.

40. 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
61 -67
A non-multiple of N.

41. Prime Numbers:4x
1.4
41 -43 -47
14
25

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
A non-multiple of N.
ONLY the nonnegative root of the numberUNLIKE
41 -43 -47

43. N! is _____ of all integers from 1 to N.
61 -67
N is a divisor of x+y
15
A MULTIPLE

44. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
13

45. Prime Numbers:9x
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
97
71 -73 -79

46. Positive integers with more than two factors are ____.
11 -13 -17 -19
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime
14

47. 3n + 3n + 3n = _____ = ______
FACTOR
3·3n = 3^{n+1}
23 -29
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. In an evenly spaced set - the mean and median are equal to the _____ of _________.
83 -89
71 -73 -79
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.7

49. 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.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ODD
1. The smallest or largest element 2. The increment 3. The number of items in the set

50. v625=
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
If 2 cannot be one of the primes in the sum - the sum must be even.
41 -43 -47
25