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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. The prime factorization of __________ contains only EVEN powers of primes.
97
2 -3 -5 -7
1.4
A PERFECT SQUARE

2. In an evenly spaced set - the sum of the terms is equal to ____.
61 -67
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

3. Prime Numbers:0x
1.4
NEVER CONTRADICT ONE ANOTHER
ONLY the nonnegative root of the numberUNLIKE
2 -3 -5 -7

4. The sum of any two primes will be ____ - unless ______.
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.
A non-multiple of N.
11 -13 -17 -19

5. 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.
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
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

6. v625=
NEVER CONTRADICT ONE ANOTHER
25
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

7. v5˜
23 -29
ONLY the nonnegative root of the numberUNLIKE
The PRODUCT of n consecutive integers is divisible by n!.
2.5

8. Prime Numbers:4x
71 -73 -79
41 -43 -47
2 -3 -5 -7
2.5

9. v225=
31 -37
15
71 -73 -79
Put the coefficient under the radical to get a better approximation

10. In an evenly spaced set - the average can be found by finding ________.
3·3n = 3^{n+1}
97
The middle number
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

11. Prime Numbers:9x
15
1. The smallest or largest element 2. The increment 3. The number of items in the set
97
1.4

12. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
The middle number
41 -43 -47
Never prime

13. All perfect squares have a(n) _________ number of total factors.
The PRODUCT of n consecutive integers is divisible by n!.
PERFECT CUBES
ODD
2.5

14. 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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15. How to find the sum of consecutive integers:
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A MULTIPLE
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.

16. Prime Numbers:1x
16
A PERFECT SQUARE
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER

17. Prime Numbers:2x
EVEN
23 -29
Prime factorization
2.5

18. N! is _____ of all integers from 1 to N.
3·3n = 3^{n+1}
11 -13 -17 -19
ODD
A MULTIPLE

19. v256=
The average of an EVEN number of consecutive integers will NEVER be an integer.
3·3n = 3^{n+1}
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.
16

20. For ODD ROOTS - the root has ______.
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.
The average of an EVEN number of consecutive integers will NEVER be an integer.
The same sign as the base

21. v169=
13
ODD
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.

22. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
61 -67
The middle number
Prime factorization
A non-multiple of N.

23. 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
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
[(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.

24. If N is a divisor of x and y - then _______.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
N is a divisor of x+y
A non-multiple of N.

25. The average of an EVEN number of consecutive integers will ________ be an integer.
PERFECT CUBES
The average of an EVEN number of consecutive integers will NEVER be an integer.
The middle number
A PERFECT SQUARE

26. v196=
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
14
The average of an EVEN number of consecutive integers will NEVER be an integer.

27. Prime Numbers:6x
53 -59
Prime factorization
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

28. Any integer with an EVEN number of total factors cannot be ______.
ODD
A PERFECT SQUARE
23 -29
NEVER CONTRADICT ONE ANOTHER

29. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The same sign as the base
FACTOR
A non-multiple of N.
3·3n = 3^{n+1}

30. ³v216 =
Never prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
2.5

31. 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
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The same sign as the base
FACTOR

32. Positive integers with more than two factors are ____.
Put the coefficient under the radical to get a better approximation
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
2.5
Never prime

33. Prime Numbers:3x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
16
71 -73 -79
31 -37

34. The average of an ODD number of consecutive integers will ________ be an integer.
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
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.

35. Prime Numbers:8x
13
Prime factorization
61 -67
83 -89

36. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
3·3n = 3^{n+1}
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
FACTOR

37. v3˜
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.7
25
71 -73 -79

38. The prime factorization of a perfect square contains only ______ powers of primes.
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.
15
EVEN

39. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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.
14
1.7
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

40. Prime Numbers:5x
53 -59
3·3n = 3^{n+1}
23 -29
PERFECT CUBES

41. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the average and the median are equal.
2.5
The sum of any two primes will be even - unless one of the two primes is 2.

42. v2˜
1.4
83 -89
Prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

43. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
A PERFECT SQUARE
1.4
FACTOR

44. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
FACTOR
The sum of any two primes will be even - unless one of the two primes is 2.
16
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

45. 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?
1. The smallest or largest element 2. The increment 3. The number of items in the set
11 -13 -17 -19
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.
EVEN

46. 3n + 3n + 3n = _____ = ______
31 -37
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.
3·3n = 3^{n+1}

47. Prime factors of _____ must come in pairs of three.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
PERFECT CUBES
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

48. Positive integers with only two factors must be ___.
83 -89
A PERFECT SQUARE
23 -29
Prime

49. The formula for finding the number of consecutive multiples in a set is _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
11 -13 -17 -19
[(last - first) / increment] + 1
Prime factorization

50. If estimating a root with a coefficient - _____ .
61 -67
Put the coefficient under the radical to get a better approximation
23 -29
A MULTIPLE