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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 two statements in a data sufficiency problem will _______________.
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
61 -67
NEVER CONTRADICT ONE ANOTHER

2. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
11 -13 -17 -19
Prime
The average of an EVEN number of consecutive integers will NEVER be an integer.

3. In an evenly spaced set - the sum of the terms is equal to ____.
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
The average of the set times the number of elements in the set
A PERFECT SQUARE

4. v625=
N is a divisor of x+y
11 -13 -17 -19
25
13

5. Prime Numbers:3x
N is a divisor of x+y
31 -37
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

6. Prime Numbers:8x
The sum of any two primes will be even - unless one of the two primes is 2.
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.
83 -89
A PERFECT SQUARE

7. The average of an ODD number of consecutive integers will ________ be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.
13
ONLY the nonnegative root of the numberUNLIKE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

8. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
31 -37
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation

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

10. All perfect squares have a(n) _________ number of total factors.
61 -67
Prime factorization
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
ODD

11. 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.
A PERFECT SQUARE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Put the coefficient under the radical to get a better approximation

12. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
A MULTIPLE
25
[(last - first) / increment] + 1

13. 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?
16
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
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.

14. N! is _____ of all integers from 1 to N.
Either a multiple of N or a non-multiple of N
A MULTIPLE
Put the coefficient under the radical to get a better approximation
83 -89

15. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The sum of any two primes will be even - unless one of the two primes is 2.
31 -37
15
ONLY the nonnegative root of the numberUNLIKE

16. v169=
The PRODUCT of n consecutive integers is divisible by n!.
1.4
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13

17. In an evenly spaced set - the ____ and the ____ are equal.
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
31 -37

18. Prime Numbers:6x
61 -67
A MULTIPLE
53 -59
N is a divisor of x+y

19. Prime Numbers:4x
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.
23 -29
61 -67
41 -43 -47

20. 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

21. How to find the sum of consecutive integers:
A PERFECT SQUARE
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.
1.4
71 -73 -79

22. If 2 cannot be one of the primes in the sum - the sum must be _____.
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
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

23. If N is a divisor of x and y - then _______.
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.
2.5
N is a divisor of x+y

24. Prime Numbers:7x
A non-multiple of N.
71 -73 -79
In an evenly spaced set - the average and the median are equal.
N is a divisor of x+y

25. v225=
15
Prime
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.

26. v2˜
15
1.4
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.

27. Prime Numbers:5x
53 -59
14
EVEN
A PERFECT SQUARE

28. Prime Numbers:0x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
PERFECT CUBES
11 -13 -17 -19
2 -3 -5 -7

29. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
A PERFECT SQUARE
PERFECT CUBES
FACTOR
3·3n = 3^{n+1}

30. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A non-multiple of N.
1. The smallest or largest element 2. The increment 3. The number of items in the set

31. The prime factorization of a perfect square contains only ______ powers of primes.
The average of an EVEN number of consecutive integers will NEVER be an integer.
2 -3 -5 -7
EVEN
In an evenly spaced set - the average and the median are equal.

32. 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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an EVEN number of consecutive integers will NEVER be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

33. v3˜
13
1.7
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.

34. Prime Numbers:9x
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.
97
11 -13 -17 -19

35. v5˜
2.5
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
EVEN

36. Any integer with an EVEN number of total factors cannot be ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2 -3 -5 -7
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.

37. In an evenly spaced set - the mean and median are equal to the _____ of _________.
53 -59
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

38. 3n + 3n + 3n = _____ = ______
Never 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
3·3n = 3^{n+1}
The same sign as the base

39. Prime Numbers:1x
61 -67
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.

40. 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 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.
1.7
ONLY the nonnegative root of the numberUNLIKE

41. v256=
14
97
41 -43 -47
16

42. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Prime factorization
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1. The smallest or largest element 2. The increment 3. The number of items in the set
ONLY the nonnegative root of the numberUNLIKE

43. In an evenly spaced set - the average can be found by finding ________.
NEVER CONTRADICT ONE ANOTHER
3·3n = 3^{n+1}
The middle number
53 -59

44. The average of an EVEN number of consecutive integers will ________ be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime factorization
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.

45. If estimating a root with a coefficient - _____ .
The same sign as the base
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER
Put the coefficient under the radical to get a better approximation

46. Prime factors of _____ must come in pairs of three.
The PRODUCT of n consecutive integers is divisible by n!.
A MULTIPLE
PERFECT CUBES
1.7

47. For ODD ROOTS - the root has ______.
23 -29
The same sign as the base
1.4
The sum of any two primes will be even - unless one of the two primes is 2.

48. The sum of any two primes will be ____ - unless ______.
If 2 cannot be one of the primes in the sum - the sum must be even.
The sum of any two primes will be even - unless one of the two primes is 2.
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.

49. Prime Numbers:2x
83 -89
53 -59
23 -29
The middle number

50. Let N be an integer. If you add two non-multiples of N - the result could be _______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A PERFECT SQUARE
The average of the set times the number of elements in the set
Either a multiple of N or a non-multiple of N