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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. 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

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
ONLY the nonnegative root of the numberUNLIKE
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
Put the coefficient under the radical to get a better approximation
The average of the set times the number of elements in the set

3. The prime factorization of __________ contains only EVEN powers of primes.
[(last - first) / increment] + 1
A PERFECT SQUARE
97
Never prime

4. v5˜
The same sign as the base
1.7
2.5
A MULTIPLE

5. ³v216 =
Never prime
PERFECT CUBES
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

6. The PRODUCT of n consecutive integers is divisible by ____.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The PRODUCT of n consecutive integers is divisible by n!.
13
NEVER CONTRADICT ONE ANOTHER

7. If N is a divisor of x and y - then _______.
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.
25
N is a divisor of x+y
The average of an ODD number of consecutive integers will ALWAYS be an integer.

8. Prime Numbers:2x
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
23 -29
41 -43 -47

9. In an evenly spaced set - the sum of the terms is equal to ____.
3·3n = 3^{n+1}
13
23 -29
The average of the set times the number of elements in the set

10. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
71 -73 -79
31 -37

11. If 2 cannot be one of the primes in the sum - the sum must be _____.
If 2 cannot be one of the primes in the sum - the sum must be even.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
31 -37
14

12. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
Prime
13
15

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

14. 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
15
71 -73 -79
The sum of any two primes will be even - unless one of the two primes is 2.

15. The sum of any two primes will be ____ - unless ______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The sum of any two primes will be even - unless one of the two primes is 2.
14
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.

16. Prime Numbers:4x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
41 -43 -47
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.

17. v256=
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
16
A PERFECT SQUARE
23 -29

18. If the problem states/assumes that a number is an integer - check to see if you can use _______.
A non-multiple of N.
The middle number
23 -29
Prime factorization

19. v225=
53 -59
FACTOR
15
Either a multiple of N or a non-multiple of N

20. Positive integers with more than two factors are ____.
EVEN
The same sign as the base
Never prime
2 -3 -5 -7

21. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
EVEN
In an evenly spaced set - the average and the median are equal.
A PERFECT SQUARE

22. Prime Numbers:7x
N is a divisor of x+y
A MULTIPLE
97
71 -73 -79

23. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The sum of any two primes will be even - unless one of the two primes is 2.
PERFECT CUBES
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N

24. Any integer with an EVEN number of total factors cannot be ______.
71 -73 -79
41 -43 -47
1.4
A PERFECT SQUARE

25. Positive integers with only two factors must be ___.
Prime
15
EVEN
N is a divisor of x+y

26. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
71 -73 -79
The average of the set times the number of elements in the set

27. Prime Numbers:6x
3·3n = 3^{n+1}
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
61 -67

28. Prime Numbers:9x
13
A non-multiple of N.
23 -29
97

29. In an evenly spaced set - the ____ and the ____ are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
53 -59
In an evenly spaced set - the average and the median are equal.

30. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A PERFECT SQUARE
11 -13 -17 -19
71 -73 -79
A non-multiple of N.

31. Prime Numbers:8x
61 -67
1.4
3·3n = 3^{n+1}
83 -89

32. v625=
3·3n = 3^{n+1}
In an evenly spaced set - the average and the median are equal.
16
25

33. Prime Numbers:1x
EVEN
11 -13 -17 -19
N is a divisor of x+y
Never prime

34. Prime Numbers:0x
The sum of any two primes will be even - unless one of the two primes is 2.
EVEN
2 -3 -5 -7
97

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

36. 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.
Never prime
Either a multiple of N or a non-multiple of N
83 -89

37. The prime factorization of a perfect square contains only ______ powers of primes.
14
EVEN
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.
Put the coefficient under the radical to get a better approximation

38. Prime Numbers:5x
EVEN
53 -59
NEVER CONTRADICT ONE ANOTHER
A non-multiple of N.

39. v3˜
Prime factorization
1.7
15
A non-multiple of N.

40. 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?
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.
1.4
31 -37
PERFECT CUBES

41. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1
ONLY the nonnegative root of the numberUNLIKE
1.4

42. v196=
ODD
53 -59
31 -37
14

43. 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 non-multiple of N.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
16
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.

44. All perfect squares have a(n) _________ number of total factors.
FACTOR
23 -29
71 -73 -79
ODD

45. v2˜
Never prime
EVEN
1.4
ODD

46. N! is _____ of all integers from 1 to N.
NEVER CONTRADICT ONE ANOTHER
11 -13 -17 -19
A MULTIPLE
In an evenly spaced set - the average and the median are equal.

47. For ODD ROOTS - the root has ______.
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
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The same sign as the base

48. The formula for finding the number of consecutive multiples in a set is _______.
23 -29
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.
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.

49. In an evenly spaced set - the average can be found by finding ________.
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 mean and median are equal to the average of the first and the last number.
ONLY the nonnegative root of the numberUNLIKE
The middle number

50. How to find the sum of consecutive integers:
NEVER CONTRADICT ONE ANOTHER
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.
EVEN