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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
The sum of any two primes will be even - unless one of the two primes is 2.
61 -67
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
25

2. ³v216 =
[(last - first) / increment] + 1
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

3. The average of an EVEN number of consecutive integers will ________ be an integer.
3·3n = 3^{n+1}
The average of an EVEN number of consecutive integers will NEVER be an integer.
ODD
Prime factorization

4. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
PERFECT CUBES
25
1.4

5. v256=
16
The PRODUCT of n consecutive integers is divisible by n!.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

6. 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
23 -29
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
31 -37

7. Positive integers with more than two factors are ____.
Never prime
ODD
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

8. 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
3·3n = 3^{n+1}
1. The smallest or largest element 2. The increment 3. The number of items in the set
A PERFECT SQUARE

9. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
Either a multiple of N or a non-multiple of N
13
11 -13 -17 -19

10. 3n + 3n + 3n = _____ = ______
A PERFECT SQUARE
1.7
31 -37
3·3n = 3^{n+1}

11. Prime Numbers:4x
A PERFECT SQUARE
Never prime
41 -43 -47
13

12. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
A MULTIPLE
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.
FACTOR

13. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
ODD
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 2 cannot be one of the primes in the sum - the sum must be even.
A non-multiple of N.

14. The two statements in a data sufficiency problem will _______________.
13
Never prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
NEVER CONTRADICT ONE ANOTHER

15. If estimating a root with a coefficient - _____ .
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The sum of any two primes will be even - unless one of the two primes is 2.
Put the coefficient under the radical to get a better approximation
EVEN

16. If the problem states/assumes that a number is an integer - check to see if you can use _______.
25
Prime factorization
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

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

18. v169=
ODD
Never prime
13
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

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 same sign as the base
1.4
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

20. If 2 cannot be one of the primes in the sum - the sum must be _____.
1.7
53 -59
ONLY the nonnegative root of the numberUNLIKE
If 2 cannot be one of the primes in the sum - the sum must be even.

21. Prime Numbers:8x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
83 -89
A PERFECT SQUARE
Never prime

22. v625=
41 -43 -47
ODD
25
In an evenly spaced set - the average and the median are equal.

23. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
In an evenly spaced set - the average and the median are equal.
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 n consecutive integers is divisible by n if n is odd - but not if n is even.
2 -3 -5 -7

24. In an evenly spaced set - the ____ and the ____ are equal.
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.
31 -37
11 -13 -17 -19

25. Positive integers with only two factors must be ___.
The sum of any two primes will be even - unless one of the two primes is 2.
Prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
14

26. Prime Numbers:1x
11 -13 -17 -19
1.4
Put the coefficient under the radical to get a better approximation
25

27. Prime Numbers:2x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
61 -67
97
23 -29

28. All perfect squares have a(n) _________ number of total factors.
ODD
A PERFECT SQUARE
61 -67
31 -37

29. The average of an ODD number of consecutive integers will ________ be an integer.
1.4
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A non-multiple of N.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

30. v3˜
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Never prime
1.7

31. v2˜
15
In an evenly spaced set - the average and the median are equal.
13
1.4

32. Prime Numbers:7x
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.
97

33. Any integer with an EVEN number of total factors cannot be ______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
97
11 -13 -17 -19

34. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
ODD
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Put the coefficient under the radical to get a better approximation
13

35. Prime Numbers:0x
The average of an EVEN number of consecutive integers will NEVER be an integer.
2 -3 -5 -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.
Put the coefficient under the radical to get a better approximation

36. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
23 -29
The middle number
31 -37

37. Prime Numbers:5x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
53 -59
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

38. 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.
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime
1.4

39. If N is a divisor of x and y - then _______.
The PRODUCT of n consecutive integers is divisible by n!.
53 -59
41 -43 -47
N is a divisor of x+y

40. v225=
2.5
15
14
The middle number

41. 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.
Prime factorization
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.

42. 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
PERFECT CUBES
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.

43. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1. The smallest or largest element 2. The increment 3. The number of items in the set
NEVER CONTRADICT ONE ANOTHER

44. N! is _____ of all integers from 1 to N.
1.7
[(last - first) / increment] + 1
A MULTIPLE
1.4

45. v196=
The average of an EVEN number of consecutive integers will NEVER be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
14
11 -13 -17 -19

46. 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.
Prime factorization
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime

47. The prime factorization of __________ contains only EVEN powers of primes.
11 -13 -17 -19
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
2.5

48. The prime factorization of a perfect square contains only ______ powers of primes.
2 -3 -5 -7
The same sign as the base
NEVER CONTRADICT ONE ANOTHER
EVEN

49. 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?
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.
31 -37
61 -67

50. Prime Numbers:3x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Put the coefficient under the radical to get a better approximation
31 -37
If 2 cannot be one of the primes in the sum - the sum must be even.