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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. v625=
NEVER CONTRADICT ONE ANOTHER
25
Put the coefficient under the radical to get a better approximation
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.

2. 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
PERFECT CUBES
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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

3. The two statements in a data sufficiency problem will _______________.
2.5
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.
NEVER CONTRADICT ONE ANOTHER
Either a multiple of N or a non-multiple of N

4. Prime Numbers:2x
71 -73 -79
61 -67
23 -29
1. The smallest or largest element 2. The increment 3. The number of items in the set

5. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
1.4
A non-multiple of N.
The same sign as the base
NEVER CONTRADICT ONE ANOTHER

6. 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
13
The PRODUCT of n consecutive integers is divisible by n!.
EVEN

7. Any integer with an EVEN number of total factors cannot be ______.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
83 -89
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.

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

9. Prime Numbers:7x
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
71 -73 -79
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

10. In an evenly spaced set - the ____ and the ____ are equal.
The same sign as the base
1.7
In an evenly spaced set - the average and the median are equal.
61 -67

11. In an evenly spaced set - the average can be found by finding ________.
23 -29
53 -59
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.

12. Prime Numbers:3x
The average of an EVEN number of consecutive integers will NEVER be an integer.
31 -37
A PERFECT SQUARE
1.4

13. For ODD ROOTS - the root has ______.
NEVER CONTRADICT ONE ANOTHER
The same sign as the base
53 -59
2 -3 -5 -7

14. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
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. The smallest or largest element 2. The increment 3. The number of items in the set
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
[(last - first) / increment] + 1

15. The average of an ODD number of consecutive integers will ________ be an integer.
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE
41 -43 -47

16. Prime Numbers:1x
13
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
16
11 -13 -17 -19

17. v169=
97
13
11 -13 -17 -19
The sum of any two primes will be even - unless one of the two primes is 2.

18. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
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
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set

19. If 2 cannot be one of the primes in the sum - the sum must be _____.
Prime
83 -89
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.

20. Prime factors of _____ must come in pairs of three.
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 an EVEN number of consecutive integers will NEVER be an integer.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
PERFECT CUBES

21. The PRODUCT of n consecutive integers is divisible by ____.
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 PRODUCT of n consecutive integers is divisible by n!.
PERFECT CUBES
83 -89

22. 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?
EVEN
FACTOR
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.
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.

23. The prime factorization of __________ contains only EVEN powers of primes.
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 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.

24. v5˜
Put the coefficient under the radical to get a better approximation
ODD
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
2.5

25. v2˜
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.4
15
61 -67

26. The average of an EVEN number of consecutive integers will ________ be an integer.
14
ONLY the nonnegative root of the numberUNLIKE
The average of an EVEN number of consecutive integers will NEVER be an integer.
Prime

27. v225=
15
2.5
23 -29
The average of an EVEN number of consecutive integers will NEVER be an integer.

28. v196=
The average of an EVEN number of consecutive integers will NEVER be an integer.
Put the coefficient under the radical to get a better approximation
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.

29. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
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.
FACTOR
16

30. 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
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

31. In an evenly spaced set - the mean and median are equal to the _____ of _________.
PERFECT CUBES
83 -89
A MULTIPLE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

32. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
11 -13 -17 -19
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
41 -43 -47
61 -67

33. 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.
Prime factorization
The same sign as the base
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

34. If estimating a root with a coefficient - _____ .
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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
2.5

35. If N is a divisor of x and y - then _______.
41 -43 -47
ONLY the nonnegative root of the numberUNLIKE
N is a divisor of x+y
Either a multiple of N or a non-multiple of N

36. All perfect squares have a(n) _________ number of total factors.
ODD
Either a multiple of N or a non-multiple of N
ONLY the nonnegative root of the numberUNLIKE
The middle number

37. N! is _____ of all integers from 1 to N.
A MULTIPLE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Put the coefficient under the radical to get a better approximation
61 -67

38. How to find the sum of consecutive integers:
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.
11 -13 -17 -19
61 -67
PERFECT CUBES

39. Let N be an integer. If you add two non-multiples of N - the result could be _______.
A MULTIPLE
97
25
Either a multiple of N or a non-multiple of N

40. Prime Numbers:9x
ODD
23 -29
97
Put the coefficient under the radical to get a better approximation

41. Positive integers with only two factors must be ___.
Prime
In an evenly spaced set - the average and the median are equal.
2 -3 -5 -7
Either a multiple of N or a non-multiple of N

42. 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.
In an evenly spaced set - the average and the median are equal.
[(last - first) / increment] + 1
A non-multiple of N.

43. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
A PERFECT SQUARE
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
ONLY the nonnegative root of the numberUNLIKE

44. Prime Numbers:8x
15
83 -89
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. Any integer with an ODD number of total factors must be _______.
Either a multiple of N or a non-multiple of N
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE

46. Prime Numbers:5x
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.
The same sign as the base
Put the coefficient under the radical to get a better approximation

47. Positive integers with more than two factors are ____.
A PERFECT SQUARE
97
In an evenly spaced set - the average and the median are equal.
Never prime

48. ³v216 =
25
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
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 mean and median are equal to the average of the first and the last number.

49. v256=
The sum of any two primes will be even - unless one of the two primes is 2.
16
PERFECT CUBES
23 -29

50. Prime Numbers:0x
A PERFECT SQUARE
2 -3 -5 -7
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE