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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. Prime Numbers:6x
FACTOR
71 -73 -79
61 -67
31 -37

2. Positive integers with more than two factors are ____.
53 -59
Never prime
1.7
15

3. In an evenly spaced set - the average can be found by finding ________.
The middle number
In an evenly spaced set - the average and the median are equal.
Prime
PERFECT CUBES

4. v625=
25
ONLY the nonnegative root of the numberUNLIKE
PERFECT CUBES
15

5. Prime Numbers:3x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
ODD
31 -37
1. The smallest or largest element 2. The increment 3. The number of items in the set

6. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
FACTOR
ONLY the nonnegative root of the numberUNLIKE
13
53 -59

7. Prime Numbers:4x
ONLY the nonnegative root of the numberUNLIKE
41 -43 -47
1.4
A PERFECT SQUARE

8. v225=
2.5
15
[(last - first) / increment] + 1
Prime

9. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 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
[(last - first) / increment] + 1
Either a multiple of N or a non-multiple of N
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

10. 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
23 -29
97
The average of the set times the number of elements in the set
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

11. All perfect squares have a(n) _________ number of total factors.
ODD
The middle number
1.7
FACTOR

12. The average of an ODD number of consecutive integers will ________ be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an ODD number of consecutive integers will ALWAYS 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.
ODD

13. Prime Numbers:5x
A PERFECT SQUARE
The middle number
53 -59
1.7

14. Prime Numbers:7x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Prime factorization
71 -73 -79
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. 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.
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 PRODUCT of n consecutive integers is divisible by n!.
Never prime

16. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
N is a divisor of x+y
41 -43 -47
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

17. Prime Numbers:8x
83 -89
97
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE

18. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
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 non-multiple of N.

19. The prime factorization of a perfect square contains only ______ powers of primes.
NEVER CONTRADICT ONE ANOTHER
The same sign as the base
EVEN
14

20. Prime Numbers:1x
11 -13 -17 -19
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
31 -37

21. If N is a divisor of x and y - then _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
FACTOR
N is a divisor of x+y
Prime

22. The average of an EVEN number of consecutive integers will ________ be an integer.
23 -29
1.4
16
The average of an EVEN number of consecutive integers will NEVER be an integer.

23. The two statements in a data sufficiency problem will _______________.
83 -89
NEVER CONTRADICT ONE ANOTHER
31 -37
2.5

24. Prime Numbers:2x
53 -59
23 -29
PERFECT CUBES
16

25. v2˜
Prime
The middle number
The same sign as the base
1.4

26. If estimating a root with a coefficient - _____ .
The middle number
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.
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.

27. Prime factors of _____ must come in pairs of three.
ONLY the nonnegative root of the numberUNLIKE
2.5
In an evenly spaced set - the average and the median are equal.
PERFECT CUBES

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

29. ³v216 =
23 -29
2 -3 -5 -7
11 -13 -17 -19
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

30. In an evenly spaced set - the mean and median are equal to the _____ of _________.
61 -67
97
13
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

31. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
A PERFECT SQUARE
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
31 -37

32. v196=
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.
2.5
In an evenly spaced set - the average and the median are equal.

33. v169=
13
PERFECT CUBES
Either a multiple of N or a non-multiple of N
FACTOR

34. 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.
PERFECT CUBES
The average of the set times the number of elements in the set
The PRODUCT of n consecutive integers is divisible by n!.

35. Any integer with an ODD number of total factors must be _______.
61 -67
ODD
A PERFECT SQUARE
3·3n = 3^{n+1}

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

37. 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
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
53 -59

38. 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
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.
53 -59
Prime factorization

39. If 2 cannot be one of the primes in the sum - the sum must be _____.
Prime
If 2 cannot be one of the primes in the sum - the sum must be 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.
13

40. 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?
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.
31 -37
Either a multiple of N or a non-multiple of N
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.

41. For ODD ROOTS - the root has ______.
If 2 cannot be one of the primes in the sum - the sum must be even.
83 -89
11 -13 -17 -19
The same sign as the base

42. 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

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43. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37
15
13

44. v5˜
The same sign as the base
Prime factorization
2.5
Either a multiple of N or a non-multiple of N

45. Let N be an integer. If you add two non-multiples of N - the result could be _______.
23 -29
The average of an EVEN number of consecutive integers will NEVER be an integer.
Either a multiple of N or a non-multiple of N
25

46. N! is _____ of all integers from 1 to N.
A MULTIPLE
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.
61 -67
FACTOR

47. v3˜
1.7
71 -73 -79
A PERFECT SQUARE
25

48. v256=
97
Either a multiple of N or a non-multiple of N
53 -59
16

49. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
2.5
14
The average of the set times the number of elements in the set

50. Prime Numbers:9x
Prime
13
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
97