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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. Positive integers with more than two factors are ____.
Never prime
41 -43 -47
Put the coefficient under the radical to get a better approximation
2.5

2. The formula for finding the number of consecutive multiples in a set is _______.
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
[(last - first) / increment] + 1
1. The smallest or largest element 2. The increment 3. The number of items in the set

3. v5˜
2.5
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
25

4. The two statements in a data sufficiency problem will _______________.
A non-multiple of N.
PERFECT CUBES
16
NEVER CONTRADICT ONE ANOTHER

5. Positive integers with only two factors must be ___.
[(last - first) / increment] + 1
Prime
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

6. v625=
14
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
25

7. In an evenly spaced set - the sum of the terms is equal to ____.
FACTOR
The average of an ODD number of consecutive integers will ALWAYS be an integer.
53 -59
The average of the set times the number of elements in the set

8. If estimating a root with a coefficient - _____ .
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
Put the coefficient under the radical to get a better approximation
31 -37

9. 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.
Prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
13

10. Any integer with an ODD number of total 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 PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
15

11. N! is _____ of all integers from 1 to N.
FACTOR
A MULTIPLE
2.5
The sum of any two primes will be even - unless one of the two primes is 2.

12. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
A MULTIPLE
Never prime
ODD

13. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
In an evenly spaced set - the average and the median are equal.
A MULTIPLE
13

14. 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
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
In an evenly spaced set - the average and the median are equal.
N is a divisor of x+y

15. Prime Numbers:5x
16
53 -59
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1

16. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A MULTIPLE
Either a multiple of N or a non-multiple of N
The same sign as the base

17. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
23 -29
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
Prime

18. Prime Numbers:2x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13
41 -43 -47
23 -29

19. 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.
[(last - first) / increment] + 1
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.

20. 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.
1. The smallest or largest element 2. The increment 3. The number of items in the set
15
The average of an EVEN number of consecutive integers will NEVER be an integer.

21. v3˜
1.7
41 -43 -47
11 -13 -17 -19
The middle number

22. Prime Numbers:0x
2 -3 -5 -7
53 -59
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime

23. v169=
A non-multiple of N.
13
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
3·3n = 3^{n+1}

24. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
ODD
[(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.

25. 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.
The middle number
EVEN
If 2 cannot be one of the primes in the sum - the sum must be even.

26. Prime Numbers:8x
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.
83 -89
25

27. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
A PERFECT SQUARE
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
13

28. Any integer with an EVEN number of total factors cannot be ______.
PERFECT CUBES
A PERFECT SQUARE
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.
FACTOR

29. All perfect squares have a(n) _________ number of total factors.
Never prime
11 -13 -17 -19
ODD
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

30. v2˜
1.4
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 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
25

31. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
In an evenly spaced set - the average and the median are equal.
Prime
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
FACTOR

32. v256=
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.
[(last - first) / increment] + 1
16
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

33. The average of an EVEN number of consecutive integers will ________ be an integer.
11 -13 -17 -19
The average of an EVEN number of consecutive integers will NEVER be an integer.
FACTOR
The same sign as the base

34. 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?
EVEN
If 2 cannot be one of the primes in the sum - the sum must be 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.
15

35. v196=
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
1.4
14

36. 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

37. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
1. The smallest or largest element 2. The increment 3. The number of items in the set
[(last - first) / increment] + 1
41 -43 -47
A non-multiple of N.

38. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ONLY the nonnegative root of the numberUNLIKE
N is a divisor of x+y

39. How to find the sum of consecutive integers:
The same sign as the base
Prime
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 sum of any two primes will be even - unless one of the two primes is 2.

40. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
In an evenly spaced set - the average and the median are equal.
23 -29
1.4
1. The smallest or largest element 2. The increment 3. The number of items in the set

41. For ODD ROOTS - the root has ______.
The same sign as the base
1.4
If 2 cannot be one of the primes in the sum - the sum must be even.
Put the coefficient under the radical to get a better approximation

42. Prime Numbers:9x
ONLY the nonnegative root of the numberUNLIKE
15
Either a multiple of N or a non-multiple of N
97

43. In an evenly spaced set - the average can be found by finding ________.
The middle number
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 average of the set times the number of elements in the set
16

44. Prime Numbers:4x
A PERFECT SQUARE
A non-multiple of N.
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.

45. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
15
31 -37
Prime

46. The PRODUCT of n consecutive integers is divisible by ____.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
31 -37
The PRODUCT of n consecutive integers is divisible by n!.
Either a multiple of N or a non-multiple of N

47. Prime factors of _____ must come in pairs of three.
15
PERFECT CUBES
The middle number
A non-multiple of N.

48. 3n + 3n + 3n = _____ = ______
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
3·3n = 3^{n+1}

49. Prime Numbers:7x
1.4
71 -73 -79
83 -89
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

50. v225=
Prime
15
In an evenly spaced set - the average and the median are equal.
The sum of any two primes will be even - unless one of the two primes is 2.