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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. Let N be an integer. If you add two non-multiples of N - the result could be _______.
41 -43 -47
Prime
The middle number
Either a multiple of N or a non-multiple of N

2. The prime factorization of __________ contains only EVEN powers of primes.
3·3n = 3^{n+1}
[(last - first) / increment] + 1
A PERFECT SQUARE
The average of an EVEN number of consecutive integers will NEVER be an integer.

3. Prime Numbers:4x
41 -43 -47
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ONLY the nonnegative root of the numberUNLIKE
If 2 cannot be one of the primes in the sum - the sum must be even.

4. 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.
FACTOR
EVEN
97

5. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result 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.
[(last - first) / increment] + 1
A non-multiple of N.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

6. 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.
Put the coefficient under the radical to get a better approximation
13
A PERFECT SQUARE

7. 3n + 3n + 3n = _____ = ______
16
3·3n = 3^{n+1}
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.
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.

8. If 2 cannot be one of the primes in the sum - the sum must be _____.
Prime factorization
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.
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.
If 2 cannot be one of the primes in the sum - the sum must be even.

9. The two statements in a data sufficiency problem will _______________.
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
NEVER CONTRADICT ONE ANOTHER
14

10. The average of an ODD number of consecutive integers will ________ be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
A non-multiple of N.
11 -13 -17 -19
The average of an ODD number of consecutive integers will ALWAYS be an integer.

11. v256=
A PERFECT SQUARE
15
16
If 2 cannot be one of the primes in the sum - the sum must be even.

12. The average of an EVEN number of consecutive integers will ________ be an integer.
Put the coefficient under the radical to get a better approximation
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 EVEN number of consecutive integers will NEVER be an integer.
2.5

13. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
A MULTIPLE
2.5
15

14. Any integer with an ODD number of total factors must be _______.
[(last - first) / increment] + 1
A PERFECT SQUARE
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.
Never prime

15. 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 factorization
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.

16. Prime Numbers:2x
31 -37
14
23 -29
1. The smallest or largest element 2. The increment 3. The number of items in the set

17. v5˜
N is a divisor of x+y
2.5
The average of an EVEN number of consecutive integers will NEVER be an integer.
14

18. 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
The middle number
16
61 -67

19. Prime Numbers:5x
Never prime
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER
53 -59

20. v196=
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
71 -73 -79
14
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.

21. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
Never prime
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.

22. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
N is a divisor of x+y
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
In an evenly spaced set - the average and the median are equal.

23. v3˜
61 -67
1.7
97
The middle number

24. If N is a divisor of x and y - then _______.
The average of an EVEN number of consecutive integers will NEVER be an integer.
3·3n = 3^{n+1}
N is a divisor of x+y
A PERFECT SQUARE

25. Positive integers with more than two factors are ____.
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.
15
The sum of any two primes will be even - unless one of the two primes is 2.
Never prime

26. Prime Numbers:8x
2 -3 -5 -7
83 -89
The same sign as the base
Prime

27. In an evenly spaced set - the mean and median are equal to the _____ of _________.
2.5
The PRODUCT of n consecutive integers is divisible by n!.
16
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

28. v225=
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
15
A PERFECT SQUARE

29. v169=
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
97
13

30. The PRODUCT of n consecutive integers is divisible by ____.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.7
The PRODUCT of n consecutive integers is divisible by n!.

31. N! is _____ of all integers from 1 to N.
A MULTIPLE
71 -73 -79
1.4
14

32. 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
97
In an evenly spaced set - the average and the median are equal.
Prime factorization

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

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.
71 -73 -79
The sum of any two primes will be even - unless one of the two primes is 2.
Prime

35. v625=
53 -59
25
3·3n = 3^{n+1}
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.

36. Prime Numbers:3x
2.5
14
31 -37
[(last - first) / increment] + 1

37. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
15
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.

38. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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.
ONLY the nonnegative root of the numberUNLIKE
The PRODUCT of n consecutive integers is divisible by n!.
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.

39. Any integer with an EVEN number of total factors cannot be ______.
83 -89
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
N is a divisor of x+y
A PERFECT SQUARE

40. 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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41. Prime Numbers:1x
The same sign as the base
Either a multiple of N or a non-multiple of N
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.

42. Prime Numbers:0x
Never prime
97
2 -3 -5 -7
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.

43. Positive integers with only two factors must be ___.
[(last - first) / increment] + 1
2 -3 -5 -7
Prime
1. The smallest or largest element 2. The increment 3. The number of items in the set

44. Prime Numbers:7x
EVEN
71 -73 -79
23 -29
13

45. Prime Numbers:6x
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
61 -67
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

46. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
If 2 cannot be one of the primes in the sum - the sum must be even.
53 -59
3·3n = 3^{n+1}
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

47. The sum of any two primes will be ____ - unless ______.
A non-multiple of N.
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.
1.7
The sum of any two primes will be even - unless one of the two primes is 2.

48. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
In an evenly spaced set - the average and the median are equal.
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
23 -29
FACTOR

49. 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 average of an EVEN number of consecutive integers will NEVER be an integer.
Prime
31 -37
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. For ODD ROOTS - the root has ______.
1.4
The same sign as the base
The middle number
1. The smallest or largest element 2. The increment 3. The number of items in the set