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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. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
11 -13 -17 -19
97
FACTOR
Put the coefficient under the radical to get a better approximation

2. In an evenly spaced set - the mean and median are equal to the _____ of _________.
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
[(last - first) / increment] + 1
14

3. Any integer with an ODD number of total factors must be _______.
EVEN
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N
3·3n = 3^{n+1}

4. Prime Numbers:7x
71 -73 -79
A PERFECT SQUARE
16
11 -13 -17 -19

5. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
13
ONLY the nonnegative root of the numberUNLIKE
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

6. The two statements in a data sufficiency problem will _______________.
Never prime
N is a divisor of x+y
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
NEVER CONTRADICT ONE ANOTHER

7. 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.
The same sign as the base
Never prime
Either a multiple of N or a non-multiple of N

8. 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
13
The average of the set times the number of elements in the set
1.4

9. N! is _____ of all integers from 1 to N.
A MULTIPLE
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.
ODD

10. The PRODUCT of n consecutive integers is divisible by ____.
ODD
The average of an ODD number of consecutive integers will ALWAYS be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
EVEN

11. Positive integers with only two factors must be ___.
3·3n = 3^{n+1}
31 -37
Prime
N is a divisor of x+y

12. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The sum of any two primes will be even - unless one of the two primes is 2.
Prime
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

13. If the problem states/assumes that a number is an integer - check to see if you can use _______.
41 -43 -47
11 -13 -17 -19
Prime factorization
61 -67

14. Prime Numbers:9x
41 -43 -47
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
97

15. v5˜
2.5
The middle number
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

16. Prime Numbers:8x
83 -89
3·3n = 3^{n+1}
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

17. v3˜
The average of an EVEN number of consecutive integers will NEVER be an integer.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
1.7
Never prime

18. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
N is a divisor of x+y

19. 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
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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

20. The average of an EVEN number of consecutive integers will ________ be an integer.
16
13
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.

21. v256=
16
61 -67
If 2 cannot be one of the primes in the sum - the sum must be even.
Put the coefficient under the radical to get a better approximation

22. Prime Numbers:6x
PERFECT CUBES
N is a divisor of x+y
61 -67
In an evenly spaced set - the average and the median are equal.

23. In an evenly spaced set - the sum of the terms is equal to ____.
The same sign as the base
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
PERFECT CUBES
The average of the set times the number of elements in the set

24. v2˜
23 -29
11 -13 -17 -19
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1.4

25. Prime factors of _____ must come in pairs of three.
Never prime
PERFECT CUBES
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
3·3n = 3^{n+1}

26. v169=
23 -29
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
13
14

27. All perfect squares have a(n) _________ number of total factors.
The same sign as the base
13
3·3n = 3^{n+1}
ODD

28. 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

29. v196=
23 -29
NEVER CONTRADICT ONE ANOTHER
14
In an evenly spaced set - the average and the median are equal.

30. The average of an ODD number of consecutive integers will ________ be an integer.
The sum of any two primes will be even - unless one of the two primes is 2.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
97
NEVER CONTRADICT ONE ANOTHER

31. For ODD ROOTS - the root has ______.
The same sign as the base
97
The average of the set times the number of elements in the set
11 -13 -17 -19

32. In an evenly spaced set - the ____ and the ____ are equal.
71 -73 -79
In an evenly spaced set - the average and the median are equal.
97
The same sign as the base

33. If N is a divisor of x and y - then _______.
11 -13 -17 -19
N is a divisor of x+y
ONLY the nonnegative root of the numberUNLIKE
41 -43 -47

34. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
NEVER CONTRADICT ONE ANOTHER
3·3n = 3^{n+1}
25
1. The smallest or largest element 2. The increment 3. The number of items in the set

35. Prime Numbers:2x
11 -13 -17 -19
53 -59
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
23 -29

36. Prime Numbers:5x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The PRODUCT of n consecutive integers is divisible by n!.
53 -59
2.5

37. Prime Numbers:1x
In an evenly spaced set - the average and the median are equal.
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.
11 -13 -17 -19
The average of an ODD number of consecutive integers will ALWAYS be an integer.

38. ³v216 =
The average of an EVEN number of consecutive integers will NEVER be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
16
1.4

39. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The average of an ODD number of consecutive integers will ALWAYS be an integer.
EVEN
Either a multiple of N or a non-multiple of N

40. 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.
A PERFECT SQUARE
The average of the set times the number of elements in the set
[(last - first) / increment] + 1

41. 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.
A PERFECT SQUARE
41 -43 -47
The PRODUCT of n consecutive integers is divisible by n!.

42. Positive integers with more than two factors are ____.
53 -59
11 -13 -17 -19
Never prime
A non-multiple of N.

43. The prime factorization of a perfect square contains only ______ powers of primes.
31 -37
EVEN
Prime factorization
2.5

44. If 2 cannot be one of the primes in the sum - the sum must be _____.
The same sign as the base
41 -43 -47
Either a multiple of N or a non-multiple of N
If 2 cannot be one of the primes in the sum - the sum must be even.

45. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A non-multiple of N.
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.

46. 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?
61 -67
PERFECT CUBES
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.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

47. Any integer with an EVEN number of total factors cannot be ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
1. The smallest or largest element 2. The increment 3. The number of items in the set

48. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE
16
53 -59

49. Prime Numbers:4x
16
41 -43 -47
1.4
The average of the set times the number of elements in the set

50. v625=
2 -3 -5 -7
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
25