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GMAT Number Properties

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. If N is a divisor of x and y - then _______.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If 2 cannot be one of the primes in the sum - the sum must be even.
N is a divisor of x+y
A non-multiple of N.

2. All perfect squares have a(n) _________ number of total factors.
ODD
Never prime
2.5
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5

3. 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
In an evenly spaced set - the average and the median are equal.
53 -59
If 2 cannot be one of the primes in the sum - the sum must be even.

4. Prime Numbers:6x
33n = 3^{n+1}
If 2 cannot be one of the primes in the sum - the sum must be even.
61 -67
13

5. In an evenly spaced set - the mean and median are equal to the _____ of _________.
Put the coefficient under the radical to get a better approximation
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
In an evenly spaced set - the average and the median are equal.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

6. 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
61 -67
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.
N is a divisor of x+y
2.5

7. v169=
ONLY the nonnegative root of the numberUNLIKE
13
The middle number
PERFECT CUBES

8. Let N be an integer. If you add two non-multiples of N - the result could be _______.
97
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.
Either a multiple of N or a non-multiple of N

9. v256=
A non-multiple of N.
16
71 -73 -79
61 -67

10. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
Never prime
23 -29
[(last - first) / increment] + 1

11. v2
1.4
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6
The average of an EVEN number of consecutive integers will NEVER be an integer.
PERFECT CUBES

12. In an evenly spaced set - the average can be found by finding ________.
In an evenly spaced set - the average and the median are equal.
83 -89
The middle number
13

13. The prime factorization of __________ contains only EVEN powers of primes.
Never prime
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
A PERFECT SQUARE

14. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
97
14
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

15. In an evenly spaced set - the ____ and the ____ are equal.
33n = 3^{n+1}
71 -73 -79
In an evenly spaced set - the average and the median are equal.
11 -13 -17 -19

16. Any integer with an EVEN number of total factors cannot be ______.
23 -29
83 -89
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.

17. v225=
Never prime
13
23 -29
15

18. The formula for finding the number of consecutive multiples in a set is _______.
31 -37
The average of the set times the number of elements in the set
[(last - first) / increment] + 1
The average of an ODD number of consecutive integers will ALWAYS be an integer.

19. The two statements in a data sufficiency problem will _______________.
25
NEVER CONTRADICT ONE ANOTHER
23 -29
53 -59

20. 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.
A MULTIPLE
ODD
EVEN

21. 3n + 3n + 3n = _____ = ______
13
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
33n = 3^{n+1}

22. v216 =
14
25
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6
PERFECT CUBES

23. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an EVEN number of consecutive integers will NEVER be an integer.
23 -29
61 -67
A PERFECT SQUARE

24. v3
1.4
Prime factorization
NEVER CONTRADICT ONE ANOTHER
1.7

25. Prime Numbers:0x
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7
N is a divisor of x+y
25

26. Prime Numbers:4x
FACTOR
41 -43 -47
83 -89
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

27. N! is _____ of all integers from 1 to N.
25
A MULTIPLE
NEVER CONTRADICT ONE ANOTHER
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6

28. 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 --2 2 3 --3 3 3 5 ---------5
ODD
Either a multiple of N or a non-multiple of N
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2 3 = 6 - so v216 = v6 = 6

29. Prime Numbers:5x
53 -59
The same sign as the base
83 -89
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

30. Prime Numbers:9x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A non-multiple of N.
EVEN
97

31. Positive integers with more than two factors are ____.
Never prime
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.
71 -73 -79

32. The sum of any two primes will be ____ - unless ______.
25
The sum of any two primes will be even - unless one of the two primes is 2.
1. The smallest or largest element 2. The increment 3. The number of items in the set
97

33. The PRODUCT of n consecutive integers is divisible by ____.
31 -37
The PRODUCT of n consecutive integers is divisible by n!.
NEVER CONTRADICT ONE ANOTHER
A MULTIPLE

34. v196=
14
1.4
83 -89
Prime

35. Positive integers with only two factors must be ___.
Prime
31 -37
13
11 -13 -17 -19

36. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
A PERFECT SQUARE
FACTOR
15
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5

37. Prime Numbers:1x
11 -13 -17 -19
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.
A PERFECT SQUARE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

38. The prime factorization of a perfect square contains only ______ powers of primes.
53 -59
Prime
1.7
EVEN

39. v625=
61 -67
25
Either a multiple of N or a non-multiple of N
Never prime

40. Any integer with an ODD number of total factors must be _______.
A PERFECT SQUARE
Never prime
1.4
NEVER CONTRADICT ONE ANOTHER

41. v5
2.5
33n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A MULTIPLE

42. 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?
2.5
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.
Set up prime columns. -- z 6 12 15 2 --2 2 3 --3 3 3 5 ---------5
Put the coefficient under the radical to get a better approximation

43. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
PERFECT CUBES
15
Either a multiple of N or a non-multiple of N
A non-multiple of N.

44. Prime Numbers:8x
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
13
ODD
83 -89

45. Prime Numbers:2x
2.5
FACTOR
23 -29
N is a divisor of x+y

46. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
31 -37
1. The smallest or largest element 2. The increment 3. The number of items in the set
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
11 -13 -17 -19

47. Prime Numbers:7x
71 -73 -79
13
ODD
The average of an EVEN number of consecutive integers will NEVER be an integer.

48. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
The average of the set times the number of elements in the set
PERFECT CUBES
EVEN
ONLY the nonnegative root of the numberUNLIKE

49. If 2 cannot be one of the primes in the sum - the sum must be _____.
The sum of any two primes will be even - unless one of the two primes is 2.
31 -37
If 2 cannot be one of the primes in the sum - the sum must be even.
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.

50. The average of an ODD number of consecutive integers will ________ be an integer.
41 -43 -47
23 -29
2.5
The average of an ODD number of consecutive integers will ALWAYS be an integer.

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GMAT Number Properties

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