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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. 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
23 -29
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

2. Prime Numbers:2x
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN
A PERFECT SQUARE
23 -29

3. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
41 -43 -47
2 -3 -5 -7
The same sign as the base

4. The prime factorization of __________ contains only EVEN powers of primes.
2.5
A PERFECT SQUARE
Prime
A non-multiple of N.

5. 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
1. The smallest or largest element 2. The increment 3. The number of items 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
The same sign as the base
14

6. v225=
15
97
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
PERFECT CUBES

7. Positive integers with more than two factors are ____.
The PRODUCT of n consecutive integers is divisible by n!.
PERFECT CUBES
Never prime
The same sign as the base

8. v3˜
3·3n = 3^{n+1}
1.7
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.

9. Prime Numbers:1x
[(last - first) / increment] + 1
11 -13 -17 -19
In an evenly spaced set - the average and the median are equal.
ONLY the nonnegative root of the numberUNLIKE

10. If estimating a root with a coefficient - _____ .
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
In an evenly spaced set - the average and the median are equal.
Prime
Put the coefficient under the radical to get a better approximation

11. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

12. If the problem states/assumes that a number is an integer - check to see if you can use _______.
71 -73 -79
The PRODUCT of n consecutive integers is divisible by n!.
31 -37
Prime factorization

13. v256=
14
31 -37
16
11 -13 -17 -19

14. The two statements in a data sufficiency problem will _______________.
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
2.5
NEVER CONTRADICT ONE ANOTHER

15. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
A MULTIPLE
The middle number
Prime factorization

16. In an evenly spaced set - the mean and median are equal to the _____ of _________.
EVEN
61 -67
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
97

17. 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.
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The sum of any two primes will be even - unless one of the two primes is 2.

18. The PRODUCT of n consecutive integers is divisible by ____.
25
A PERFECT SQUARE
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.

19. In an evenly spaced set - the average can be found by finding ________.
If 2 cannot be one of the primes in the sum - the sum must be even.
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
The middle number

20. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
ONLY the nonnegative root of the numberUNLIKE
ODD
71 -73 -79
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

21. ³v216 =
NEVER CONTRADICT ONE ANOTHER
61 -67
Never prime
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

22. N! is _____ of all integers from 1 to N.
A MULTIPLE
13
16
In an evenly spaced set - the average and the median are equal.

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

24. Prime Numbers:8x
16
1.7
The same sign as the base
83 -89

25. 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
Never prime
23 -29
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

26. All perfect squares have a(n) _________ number of total factors.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The same sign as the base
ODD
61 -67

27. Prime Numbers:6x
A MULTIPLE
1.4
[(last - first) / increment] + 1
61 -67

28. 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.
1.4
Either a multiple of N or a non-multiple of N
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. Prime Numbers:9x
Prime
23 -29
PERFECT CUBES
97

30. Prime Numbers:0x
1.4
2 -3 -5 -7
11 -13 -17 -19
41 -43 -47

31. v2˜
1.4
A PERFECT SQUARE
A PERFECT SQUARE
15

32. 3n + 3n + 3n = _____ = ______
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
3·3n = 3^{n+1}
Prime factorization

33. v169=
FACTOR
13
The middle number
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.

34. If N is a divisor of x and y - then _______.
2.5
13
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
N is a divisor of x+y

35. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
1. The smallest or largest element 2. The increment 3. The number of items in the set
PERFECT CUBES
25
[(last - first) / increment] + 1

36. If 2 cannot be one of the primes in the sum - the sum must be _____.
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.
If 2 cannot be one of the primes in the sum - the sum must be even.
A MULTIPLE

37. v625=
1. The smallest or largest element 2. The increment 3. The number of items in the set
25
FACTOR
3·3n = 3^{n+1}

38. Positive integers with only two factors must be ___.
Never prime
Prime
1.7
A PERFECT SQUARE

39. Prime Numbers:7x
97
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
71 -73 -79
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

40. v196=
The PRODUCT of n consecutive integers is divisible by n!.
61 -67
The average of the set times the number of elements in the set
14

41. Prime Numbers:5x
11 -13 -17 -19
53 -59
The PRODUCT of n consecutive integers is divisible by n!.
The average of the set times the number of elements in the set

42. Prime Numbers:3x
1.4
Prime factorization
31 -37
FACTOR

43. For ODD ROOTS - the root has ______.
The same sign as the base
16
If 2 cannot be one of the primes in the sum - the sum must be even.
EVEN

44. 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?
23 -29
The PRODUCT of n consecutive integers is divisible by n!.
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.
FACTOR

45. The average of an ODD number of consecutive integers will ________ be an integer.
ONLY the nonnegative root of the numberUNLIKE
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.
ODD

46. The prime factorization of a perfect square contains only ______ powers of primes.
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
EVEN
[(last - first) / increment] + 1

47. Prime Numbers:4x
97
41 -43 -47
61 -67
EVEN

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
Put the coefficient under the radical to get a better approximation
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.

49. Let N be an integer. If you add two non-multiples of N - the result could be _______.
13
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Either a multiple of N or a non-multiple of N
11 -13 -17 -19

50. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
14
23 -29
61 -67