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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 a perfect square contains only ______ powers of primes.
The average of the set times the number of elements in the set
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
The same sign as the base

2. N! is _____ of all integers from 1 to N.
[(last - first) / increment] + 1
11 -13 -17 -19
A MULTIPLE
61 -67

3. In an evenly spaced set - the sum of the terms is equal to ____.
71 -73 -79
The average of the set times the number of elements in the set
The sum of any two primes will be even - unless one of the two primes is 2.
23 -29

4. 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
In an evenly spaced set - the average and the median are equal.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ONLY the nonnegative root of the numberUNLIKE
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

5. Prime Numbers:8x
ONLY the nonnegative root of the numberUNLIKE
83 -89
A PERFECT SQUARE
The middle number

6. v225=
PERFECT CUBES
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 average of an EVEN number of consecutive integers will NEVER be an integer.

7. v2˜
1.4
97
53 -59
NEVER CONTRADICT ONE ANOTHER

8. Prime Numbers:1x
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.
11 -13 -17 -19
The same sign as the base

9. For ODD ROOTS - the root has ______.
83 -89
N is a divisor of x+y
The same sign as the base
A PERFECT SQUARE

10. v3˜
The middle number
11 -13 -17 -19
1.7
The same sign as the base

11. Prime Numbers:3x
16
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
31 -37
71 -73 -79

12. v169=
A non-multiple of N.
FACTOR
EVEN
13

13. Any integer with an EVEN number of total factors cannot be ______.
23 -29
The PRODUCT of n consecutive integers is divisible by n!.
16
A PERFECT SQUARE

14. Prime Numbers:4x
25
41 -43 -47
Prime
31 -37

15. All perfect squares have a(n) _________ number of total factors.
61 -67
A PERFECT SQUARE
ODD
2 -3 -5 -7

16. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
13
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
53 -59

17. 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.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ODD
11 -13 -17 -19

18. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
14
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

19. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
1.4
14
FACTOR
EVEN

20. v625=
N is a divisor of x+y
41 -43 -47
EVEN
25

21. v196=
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
14
3·3n = 3^{n+1}
23 -29

22. If estimating a root with a coefficient - _____ .
The average of the set times the number of elements in the set
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER

23. Prime Numbers:9x
97
Either a multiple of N or a non-multiple of N
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.

24. If N is a divisor of x and y - then _______.
1.4
N is a divisor of x+y
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.

25. Prime Numbers:5x
The average of the set times the number of elements in the set
53 -59
13
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

26. The PRODUCT of n consecutive integers is divisible by ____.
ONLY the nonnegative root of the numberUNLIKE
2.5
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The PRODUCT of n consecutive integers is divisible by n!.

27. Let N be an integer. If you add two non-multiples of N - the result could be _______.
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N
41 -43 -47
A non-multiple of N.

28. Prime factors of _____ must come in pairs of three.
2.5
Prime
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.

29. The prime factorization of __________ contains only EVEN powers of primes.
The average of the set times the number of elements in the set
A PERFECT SQUARE
53 -59
14

30. v256=
41 -43 -47
PERFECT CUBES
61 -67
16

31. v5˜
A PERFECT SQUARE
EVEN
2.5
A PERFECT SQUARE

32. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N
11 -13 -17 -19
3·3n = 3^{n+1}

33. The formula for finding the number of consecutive multiples in a set is _______.
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
The sum of any two primes will be even - unless one of the two primes is 2.

34. Prime Numbers:0x
23 -29
Either a multiple of N or a non-multiple of N
2 -3 -5 -7
In an evenly spaced set - the average and the median are equal.

35. 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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
14
EVEN

36. 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

37. 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 non-multiple of N.
The middle number
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.
83 -89

38. Positive integers with more than two factors are ____.
3·3n = 3^{n+1}
Put the coefficient under the radical to get a better approximation
Never 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.

39. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
2.5
1.7
Put the coefficient under the radical to get a better approximation

40. How to find the sum of consecutive integers:
97
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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.
N is a divisor of x+y

41. The sum of any two primes will be ____ - unless ______.
61 -67
2 -3 -5 -7
The sum of any two primes will be even - unless one of the two primes is 2.
If 2 cannot be one of the primes in the sum - the sum must be even.

42. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Prime factorization
1. The smallest or largest element 2. The increment 3. The number of items in the set
61 -67
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

43. 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 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
PERFECT CUBES

44. The average of an EVEN number of consecutive integers will ________ be an integer.
ODD
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.
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

45. The average of an ODD number of consecutive integers will ________ be an integer.
NEVER CONTRADICT ONE ANOTHER
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.
If 2 cannot be one of the primes in the sum - the sum must be even.

46. In an evenly spaced set - the average can be found by finding ________.
The same sign as the base
The middle number
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE

47. 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
31 -37
11 -13 -17 -19
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
A non-multiple of N.

48. 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.
53 -59
16
The average of an EVEN number of consecutive integers will NEVER be an integer.

49. 3n + 3n + 3n = _____ = ______
A MULTIPLE
3·3n = 3^{n+1}
1.4
2 -3 -5 -7

50. Prime Numbers:6x
83 -89
61 -67
16
The average of the set times the number of elements in the set