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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. Positive integers with only two factors must be ___.
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.
14
11 -13 -17 -19
Prime

2. ³v216 =
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
31 -37

3. Prime Numbers:5x
31 -37
53 -59
1.4
A PERFECT SQUARE

4. 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

5. The prime factorization of a perfect square contains only ______ powers of primes.
83 -89
Prime
31 -37
EVEN

6. The average of an EVEN number of consecutive integers will ________ be an integer.
23 -29
41 -43 -47
The average of an EVEN number of consecutive integers will NEVER be an integer.
N is a divisor of x+y

7. Prime Numbers:9x
The average of an EVEN number of consecutive integers will NEVER be an integer.
97
The PRODUCT of n consecutive integers is divisible by n!.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

8. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
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.
Never prime

9. v256=
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
23 -29
16

10. N! is _____ of all integers from 1 to N.
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.
83 -89
23 -29

11. v196=
14
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.
N is a divisor of x+y

12. In an evenly spaced set - the average can be found by finding ________.
15
The middle number
Never prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

13. v169=
13
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.
ONLY the nonnegative root of the numberUNLIKE

14. Prime Numbers:1x
11 -13 -17 -19
16
A PERFECT SQUARE
Prime factorization

15. For ODD ROOTS - the root has ______.
13
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.
FACTOR

16. 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.
EVEN
ONLY the nonnegative root of the numberUNLIKE
2.5

17. In an evenly spaced set - the sum of the terms is equal to ____.
Prime
[(last - first) / increment] + 1
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.
The average of the set times the number of elements in the set

18. Any integer with an ODD number of total factors must be _______.
PERFECT CUBES
97
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set

19. How to find the sum of consecutive integers:
25
A MULTIPLE
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.

20. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
25
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
NEVER CONTRADICT ONE ANOTHER

21. v225=
A non-multiple of N.
15
ODD
3·3n = 3^{n+1}

22. The sum of any two primes will be ____ - unless ______.
The sum of any two primes will be even - unless one of the two primes is 2.
ODD
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.

23. 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 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
15
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 CONTRADICT ONE ANOTHER

24. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
15
1.4
ONLY the nonnegative root of the numberUNLIKE
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.

25. If estimating a root with a coefficient - _____ .
Never prime
Put the coefficient under the radical to get a better approximation
ODD
The same sign as the base

26. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The same sign as the base
1. The smallest or largest element 2. The increment 3. The number of items in the set
[(last - first) / increment] + 1
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

27. Prime Numbers:0x
2 -3 -5 -7
A PERFECT SQUARE
A PERFECT SQUARE
Prime

28. In an evenly spaced set - the ____ and the ____ are equal.
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the average and the median are equal.
The average of the set times the number of elements in the set
1.4

29. Prime Numbers:6x
Put the coefficient under the radical to get a better approximation
11 -13 -17 -19
53 -59
61 -67

30. Any integer with an EVEN number of total factors cannot be ______.
71 -73 -79
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
NEVER CONTRADICT ONE ANOTHER

31. v2˜
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.4
31 -37
Never prime

32. In an evenly spaced set - the mean and median are equal to the _____ of _________.
2 -3 -5 -7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Put the coefficient under the radical to get a better approximation
16

33. Prime Numbers:4x
In an evenly spaced set - the average and the median are equal.
Prime factorization
41 -43 -47
ONLY the nonnegative root of the numberUNLIKE

34. The average of an ODD number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
71 -73 -79
Never prime
97

35. 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.
3·3n = 3^{n+1}
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

36. If N is a divisor of x and y - then _______.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
15
N is a divisor of x+y
Put the coefficient under the radical to get a better approximation

37. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
23 -29
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.

38. Prime Numbers:8x
14
If 2 cannot be one of the primes in the sum - the sum must be even.
83 -89
Put the coefficient under the radical to get a better approximation

39. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
23 -29
97
A PERFECT SQUARE

40. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
Prime factorization
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.
2.5

41. The PRODUCT of n consecutive integers is divisible by ____.
A MULTIPLE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.

42. If the problem states/assumes that a number is an integer - check to see if you can use _______.
N is a divisor of x+y
41 -43 -47
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.

43. v5˜
15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of an EVEN number of consecutive integers will NEVER be an integer.
2.5

44. v625=
16
41 -43 -47
14
25

45. Prime Numbers:7x
71 -73 -79
97
16
2.5

46. v3˜
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13

47. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Either a multiple of N or a non-multiple of N
In an evenly spaced set - the average and the median are equal.
The PRODUCT of n consecutive integers is divisible by n!.
23 -29

48. Prime Numbers:2x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
23 -29
A MULTIPLE

49. 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 sum of any two primes will be even - unless one of the two primes is 2.
PERFECT CUBES
15

50. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.
15
A PERFECT SQUARE