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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. 3n + 3n + 3n = _____ = ______
11 -13 -17 -19
3·3n = 3^{n+1}
41 -43 -47
15

2. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
83 -89
EVEN
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. v625=
FACTOR
25
Put the coefficient under the radical to get a better approximation
The average of the set times the number of elements in the set

4. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
1.4
15
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

5. Prime Numbers:0x
13
2 -3 -5 -7
The same sign as the base
ODD

6. Prime Numbers:1x
11 -13 -17 -19
3·3n = 3^{n+1}
The average of an EVEN number of consecutive integers will NEVER be an integer.
71 -73 -79

7. v256=
41 -43 -47
16
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
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.

8. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
PERFECT CUBES
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
FACTOR
In an evenly spaced set - the average and the median are equal.

9. 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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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
13

10. The average of an EVEN number of consecutive integers will ________ be an integer.
A non-multiple of N.
The average of an EVEN number of consecutive integers will NEVER be an integer.
3·3n = 3^{n+1}
83 -89

11. Positive integers with only two factors must be ___.
41 -43 -47
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

12. Prime Numbers:8x
PERFECT CUBES
NEVER CONTRADICT ONE ANOTHER
83 -89
15

13. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
16
Either a multiple of N or a non-multiple of N
11 -13 -17 -19

14. Prime Numbers:2x
11 -13 -17 -19
41 -43 -47
23 -29
ONLY the nonnegative root of the numberUNLIKE

15. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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
Never prime

16. Prime Numbers:7x
In an evenly spaced set - the average and the median are equal.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
71 -73 -79
The average of an ODD number of consecutive integers will ALWAYS be an integer.

17. How to find the sum of consecutive integers:
A non-multiple of N.
53 -59
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

18. Prime Numbers:9x
The sum of any two primes will be even - unless one of the two primes is 2.
The middle number
97
Prime

19. In an evenly spaced set - the sum of the terms is equal to ____.
EVEN
61 -67
The average of the set times the number of elements in the set
ODD

20. If the problem states/assumes that a number is an integer - check to see if you can use _______.
[(last - first) / increment] + 1
Prime factorization
Put the coefficient under the radical to get a better approximation
25

21. 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.
71 -73 -79
If 2 cannot be one of the primes in the sum - the sum must be even.
14

22. If 2 cannot be one of the primes in the sum - the sum must be _____.
71 -73 -79
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
14
If 2 cannot be one of the primes in the sum - the sum must be even.

23. All perfect squares have a(n) _________ number of total factors.
71 -73 -79
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.
ODD

24. The formula for finding the number of consecutive multiples in a set is _______.
NEVER CONTRADICT ONE ANOTHER
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Put the coefficient under the radical to get a better approximation
[(last - first) / increment] + 1

25. 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

26. v196=
The average of the set times the number of elements in the set
71 -73 -79
14
2 -3 -5 -7

27. v5˜
71 -73 -79
2.5
The same sign as the base
Put the coefficient under the radical to get a better approximation

28. v225=
41 -43 -47
A non-multiple of N.
15
Put the coefficient under the radical to get a better approximation

29. In an evenly spaced set - the ____ and the ____ are equal.
15
41 -43 -47
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the average and the median are equal.

30. The prime factorization of a perfect square contains only ______ powers of primes.
13
2 -3 -5 -7
EVEN
The average of the set times the number of elements in the set

31. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
71 -73 -79
A non-multiple of N.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

32. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
Never prime
A non-multiple of N.

33. Prime Numbers:5x
1.4
53 -59
3·3n = 3^{n+1}
Prime

34. If N is a divisor of x and y - then _______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
N is a divisor of x+y
25
3·3n = 3^{n+1}

35. v169=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
13
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.

36. 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?
The sum of any two primes will be even - unless one of the two primes is 2.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
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.
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.

37. Positive integers with more than two factors are ____.
Never prime
A MULTIPLE
A PERFECT SQUARE
83 -89

38. Prime Numbers:4x
41 -43 -47
2 -3 -5 -7
2.5
The PRODUCT of n consecutive integers is divisible by n!.

39. The sum of any two primes will be ____ - unless ______.
16
A MULTIPLE
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.

40. N! is _____ of all integers from 1 to N.
1.7
PERFECT CUBES
16
A MULTIPLE

41. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
2.5
97
In an evenly spaced set - the average and the median are equal.

42. v2˜
The middle number
Never prime
1.4
Put the coefficient under the radical to get a better approximation

43. In an evenly spaced set - the average can be found by finding ________.
The middle number
2 -3 -5 -7
41 -43 -47
A PERFECT SQUARE

44. If estimating a root with a coefficient - _____ .
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
PERFECT CUBES

45. For ODD ROOTS - the root has ______.
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 same sign as the base
13

46. Any integer with an ODD number of total factors must be _______.
1.4
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
23 -29

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
The middle 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
53 -59
Put the coefficient under the radical to get a better approximation

48. 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
41 -43 -47
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.
11 -13 -17 -19
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

49. Prime Numbers:3x
Never prime
Prime
13
31 -37

50. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
13
53 -59
71 -73 -79
1. The smallest or largest element 2. The increment 3. The number of items in the set