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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 only two factors must be ___.
53 -59
A PERFECT SQUARE
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.

2. Prime Numbers:8x
83 -89
ODD
15
16

3. The prime factorization of __________ contains only EVEN powers of primes.
The sum of any two primes will be even - unless one of the two primes is 2.
ODD
3·3n = 3^{n+1}
A PERFECT SQUARE

4. Prime Numbers:4x
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 same sign as the base
41 -43 -47
71 -73 -79

5. 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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6. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Either a multiple of N or a non-multiple of N
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
3·3n = 3^{n+1}

7. v225=
Put the coefficient under the radical to get a better approximation
1.4
A PERFECT SQUARE
15

8. Prime Numbers:9x
23 -29
97
A non-multiple of N.
A PERFECT SQUARE

9. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A non-multiple of N.
61 -67
16
83 -89

10. v625=
25
23 -29
14
Prime

11. Let N be an integer. If you add two non-multiples of N - the result could be _______.
23 -29
16
Either a multiple of N or a non-multiple of N
25

12. Any integer with an EVEN number of total factors cannot be ______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
41 -43 -47
FACTOR
A PERFECT SQUARE

13. The PRODUCT of n consecutive integers is divisible by ____.
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.
Either a multiple of N or a non-multiple of N
[(last - first) / increment] + 1

14. 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
Prime
1.4
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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

15. Positive integers with more than two factors are ____.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
EVEN
N is a divisor of x+y
Never prime

16. The average of an EVEN number of consecutive integers will ________ be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
13
The average of an EVEN number of consecutive integers will NEVER be an integer.
Never prime

17. The formula for finding the number of consecutive multiples in a set is _______.
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
[(last - first) / increment] + 1
97

18. If estimating a root with a coefficient - _____ .
If 2 cannot be one of the primes in the sum - the sum must be even.
31 -37
Put the coefficient under the radical to get a better approximation
1.4

19. Prime Numbers:0x
EVEN
ODD
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.

20. If 2 cannot be one of the primes in the sum - the sum must be _____.
Prime
53 -59
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If 2 cannot be one of the primes in the sum - the sum must be even.

21. The two statements in a data sufficiency problem will _______________.
ODD
The same sign as the base
13
NEVER CONTRADICT ONE ANOTHER

22. 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.
PERFECT CUBES
The sum of any two primes will be even - unless one of the two primes is 2.
11 -13 -17 -19

23. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
NEVER CONTRADICT ONE ANOTHER
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.
16

24. v5˜
1. The smallest or largest element 2. The increment 3. The number of items in the set
71 -73 -79
FACTOR
2.5

25. 3n + 3n + 3n = _____ = ______
ODD
14
N is a divisor of x+y
3·3n = 3^{n+1}

26. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The middle number
83 -89
The average of the set times the number of elements in the set

27. In an evenly spaced set - the ____ and the ____ are equal.
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.
A MULTIPLE
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 average and the median are equal.

28. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
EVEN
A non-multiple of N.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

29. The sum of any two primes will be ____ - unless ______.
The average of the set times the number of elements in the set
13
A non-multiple of N.
The sum of any two primes will be even - unless one of the two primes is 2.

30. Prime Numbers:3x
FACTOR
31 -37
Put the coefficient under the radical to get a better approximation
16

31. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
PERFECT CUBES
In an evenly spaced set - the average and the median are equal.
NEVER CONTRADICT ONE ANOTHER

32. For ODD ROOTS - the root has ______.
The middle number
11 -13 -17 -19
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set

33. 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
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
16

34. Prime factors of _____ must come in pairs of three.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
2 -3 -5 -7
PERFECT CUBES
3·3n = 3^{n+1}

35. v196=
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
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.

36. v169=
ONLY the nonnegative root of the numberUNLIKE
If 2 cannot be one of the primes in the sum - the sum must be even.
13
2 -3 -5 -7

37. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
1. The smallest or largest element 2. The increment 3. The number of items in the set
53 -59
FACTOR
ONLY the nonnegative root of the numberUNLIKE

38. Prime Numbers:5x
61 -67
1.4
53 -59
13

39. v2˜
The average of an EVEN number of consecutive integers will NEVER 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.
1.4
A PERFECT SQUARE

40. The average of an ODD number of consecutive integers will ________ be an integer.
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ODD
NEVER CONTRADICT ONE ANOTHER

41. 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.
Either a multiple of N or a non-multiple of N
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE

42. N! is _____ of all integers from 1 to N.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
EVEN
A MULTIPLE
71 -73 -79

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

44. All perfect squares have a(n) _________ number of total factors.
Put the coefficient under the radical to get a better approximation
ODD
2.5
A MULTIPLE

45. In an evenly spaced set - the mean and median are equal to the _____ of _________.
14
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

46. 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?
53 -59
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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.

47. In an evenly spaced set - the average can be found by finding ________.
The middle number
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The sum of any two primes will be even - unless one of the two primes is 2.
11 -13 -17 -19

48. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
If 2 cannot be one of the primes in the sum - the sum must be even.
1. The smallest or largest element 2. The increment 3. The number of items in the set
ONLY the nonnegative root of the numberUNLIKE
16

49. Prime Numbers:2x
23 -29
3·3n = 3^{n+1}
1. The smallest or largest element 2. The increment 3. The number of items in the set
A non-multiple of N.

50. v3˜
1.7
The middle number
PERFECT CUBES
31 -37