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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. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
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
FACTOR

2. If 2 cannot be one of the primes in the sum - the sum must be _____.
25
83 -89
N is a divisor of x+y
If 2 cannot be one of the primes in the sum - the sum must be even.

3. For ODD ROOTS - the root has ______.
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
11 -13 -17 -19

4. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
Either a multiple of N or a non-multiple of N
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

5. Prime Numbers:3x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
31 -37
Prime

6. All perfect squares have a(n) _________ number of total factors.
31 -37
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 PRODUCT of n consecutive integers is divisible by n!.

7. Prime Numbers:0x
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.
A PERFECT SQUARE

8. If estimating a root with a coefficient - _____ .
1. The smallest or largest element 2. The increment 3. The number of items in the set
25
ONLY the nonnegative root of the numberUNLIKE
Put the coefficient under the radical to get a better approximation

9. Positive integers with more than two factors are ____.
13
Never prime
2 -3 -5 -7
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.

10. v625=
41 -43 -47
25
A PERFECT SQUARE
71 -73 -79

11. Prime Numbers:1x
11 -13 -17 -19
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
PERFECT CUBES

12. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
ODD
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
53 -59
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

13. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
11 -13 -17 -19
3·3n = 3^{n+1}
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
FACTOR

14. The two statements in a data sufficiency problem will _______________.
15
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
NEVER CONTRADICT ONE ANOTHER
Prime

15. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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.
ONLY the nonnegative root of the numberUNLIKE
Never prime

16. v2˜
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29
1.4
The average of an ODD number of consecutive integers will ALWAYS be an integer.

17. v256=
The average of an ODD number of consecutive integers will ALWAYS be an integer.
16
71 -73 -79
EVEN

18. Let N be an integer. If you add two non-multiples of N - the result could be _______.
[(last - first) / increment] + 1
Either a multiple of N or a non-multiple of N
The middle number
1.7

19. In an evenly spaced set - the ____ and the ____ are equal.
Never prime
NEVER CONTRADICT ONE ANOTHER
In an evenly spaced set - the average and the median are equal.
23 -29

20. In an evenly spaced set - the sum of the terms is equal to ____.
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The average of the set times the number of elements in the set
13

21. Positive integers with only two factors must be ___.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime

22. 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.
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
41 -43 -47
PERFECT CUBES

23. v196=
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
14
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

24. The PRODUCT of n consecutive integers is divisible by ____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
61 -67
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The PRODUCT of n consecutive integers is divisible by n!.

25. In an evenly spaced set - the average can be found by finding ________.
EVEN
The middle number
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.
PERFECT CUBES

26. Prime Numbers:9x
A PERFECT SQUARE
The average of the set times the number of elements in the set
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
97

27. ³v216 =
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
ONLY the nonnegative root of the numberUNLIKE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A MULTIPLE

28. v169=
A PERFECT SQUARE
3·3n = 3^{n+1}
13
NEVER CONTRADICT ONE ANOTHER

29. N! is _____ of all integers from 1 to N.
25
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.
A MULTIPLE
41 -43 -47

30. The prime factorization of __________ contains only EVEN powers of primes.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
61 -67
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

31. 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.
Never prime
3·3n = 3^{n+1}
The sum of any two primes will be even - unless one of the two primes is 2.

32. If N is a divisor of x and y - then _______.
The middle number
The same sign as the base
N is a divisor of x+y
A MULTIPLE

33. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
2.5
97
NEVER CONTRADICT ONE ANOTHER

34. Prime Numbers:7x
71 -73 -79
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

35. The average of an ODD number of consecutive integers will ________ be an integer.
11 -13 -17 -19
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime factorization
25

36. The prime factorization of a perfect square contains only ______ powers of primes.
ODD
31 -37
Never prime
EVEN

37. Prime Numbers:2x
The PRODUCT of n consecutive integers is divisible by n!.
23 -29
Prime
16

38. 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
71 -73 -79
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
1.4
1.7

39. Prime Numbers:5x
PERFECT CUBES
53 -59
11 -13 -17 -19
1.7

40. How to find the sum of consecutive integers:
The same sign as the base
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.
3·3n = 3^{n+1}
23 -29

41. v5˜
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.
2.5
A PERFECT SQUARE
11 -13 -17 -19

42. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Prime factorization
ONLY the nonnegative root of the numberUNLIKE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
FACTOR

43. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
31 -37
1. The smallest or largest element 2. The increment 3. The number of items in the set
71 -73 -79

44. v225=
15
41 -43 -47
97
The same sign as the base

45. Any integer with an EVEN number of total factors cannot be ______.
A PERFECT SQUARE
If 2 cannot be one of the primes in the sum - the sum must be even.
25
41 -43 -47

46. 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.
A MULTIPLE
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.
[(last - first) / increment] + 1

47. 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

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48. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
13
15
ONLY the nonnegative root of the numberUNLIKE

49. If the problem states/assumes that a number is an integer - check to see if you can use _______.
1.7
A MULTIPLE
Prime factorization
The average of the set times the number of elements in the set

50. The average of an EVEN number of consecutive integers will ________ be an integer.
25
The average of an EVEN number of consecutive integers will NEVER be an integer.
2 -3 -5 -7
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.