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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. v225=
71 -73 -79
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
15

2. If 2 cannot be one of the primes in the sum - the sum must be _____.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47
The middle number
If 2 cannot be one of the primes in the sum - the sum must be even.

3. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
FACTOR
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Either a multiple of N or 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.

4. v196=
FACTOR
14
ONLY the nonnegative root of the numberUNLIKE
The PRODUCT of n consecutive integers is divisible by n!.

5. v3˜
1.7
23 -29
61 -67
ONLY the nonnegative root of the numberUNLIKE

6. Any integer with an EVEN number of total factors cannot 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.
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
A PERFECT SQUARE
ODD

7. The PRODUCT of n consecutive integers is divisible by ____.
2 -3 -5 -7
1.4
The PRODUCT of n consecutive integers is divisible by n!.
13

8. Prime Numbers:6x
The average of an ODD number of consecutive integers will ALWAYS be an integer.
41 -43 -47
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
61 -67

9. Any integer with an ODD number of total factors must be _______.
ODD
16
23 -29
A PERFECT SQUARE

10. How to find the sum of consecutive integers:
1.7
25
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

11. v625=
25
13
1.7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

12. All perfect squares have a(n) _________ number of total factors.
The sum of any two primes will be even - unless one of the two primes is 2.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD
71 -73 -79

13. If N is a divisor of x and y - then _______.
N is a divisor of x+y
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
A PERFECT SQUARE

14. Let N be an integer. If you add two non-multiples of N - the result could be _______.
The average of the set times the number of elements in the set
61 -67
Either a multiple of N or a non-multiple of N
N is a divisor of x+y

15. The two statements in a data sufficiency problem will _______________.
41 -43 -47
PERFECT CUBES
NEVER CONTRADICT ONE ANOTHER
3·3n = 3^{n+1}

16. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
1.7
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.
The average of the set times the number of elements in the set

17. 3n + 3n + 3n = _____ = ______
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
3·3n = 3^{n+1}
A MULTIPLE
EVEN

18. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 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 2 cannot be one of the primes in the sum - the sum must be even.
41 -43 -47

19. N! is _____ of all integers from 1 to N.
EVEN
11 -13 -17 -19
A MULTIPLE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

20. Prime Numbers:4x
15
3·3n = 3^{n+1}
41 -43 -47
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

21. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The middle number
FACTOR
A non-multiple of N.
15

22. Prime Numbers:3x
25
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
31 -37
The middle number

23. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
14
16
A non-multiple of N.
N is a divisor of x+y

24. 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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25. If the problem states/assumes that a number is an integer - check to see if you can use _______.
The middle number
[(last - first) / increment] + 1
Prime factorization
Put the coefficient under the radical to get a better approximation

26. The prime factorization of __________ contains only EVEN powers of primes.
A PERFECT SQUARE
16
In an evenly spaced set - the average and the median are equal.
23 -29

27. In an evenly spaced set - the average can be found by finding ________.
1.7
31 -37
The average of the set times the number of elements in the set
The middle number

28. 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.
13
14
2.5

29. Prime Numbers:0x
ONLY the nonnegative root of the numberUNLIKE
NEVER CONTRADICT ONE ANOTHER
2 -3 -5 -7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

30. v5˜
15
2.5
1.7
FACTOR

31. v2˜
1.4
2 -3 -5 -7
14
PERFECT CUBES

32. Prime Numbers:2x
The average of an EVEN number of consecutive integers will NEVER be an integer.
23 -29
1.7
3·3n = 3^{n+1}

33. Prime Numbers:7x
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Prime
71 -73 -79
61 -67

34. 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
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
Never prime
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

35. 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.
13
2.5

36. ³v216 =
The PRODUCT of n consecutive integers is divisible by n!.
13
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

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

38. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
The sum of any two primes will be even - unless one of the two primes is 2.
41 -43 -47
The same sign as the base

39. In an evenly spaced set - the mean and median are equal to the _____ of _________.
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 PERFECT SQUARE
2.5
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

40. Positive integers with only two factors must be ___.
53 -59
16
If 2 cannot be one of the primes in the sum - the sum must be even.
Prime

41. The sum of any two primes will be ____ - unless ______.
ODD
The sum of any two primes will be even - unless one of the two primes is 2.
If 2 cannot be one of the primes in the sum - the sum must be even.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

42. Positive integers with more than two factors are ____.
Never prime
The sum of any two primes will be even - unless one of the two primes is 2.
Put the coefficient under the radical to get a better approximation
97

43. The average of an EVEN number of consecutive integers will ________ be an integer.
Prime
The average of an EVEN number of consecutive integers will NEVER be an integer.
The middle number
Put the coefficient under the radical to get a better approximation

44. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
3·3n = 3^{n+1}
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
53 -59

45. Prime Numbers:8x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The same sign as the base
83 -89
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.

46. v169=
41 -43 -47
13
The average of the set times the number of elements in the set
The average of an ODD number of consecutive integers will ALWAYS be an integer.

47. For ODD ROOTS - the root has ______.
The same sign as the base
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
ONLY the nonnegative root of the numberUNLIKE

48. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
N is a divisor of x+y
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.

49. v256=
16
11 -13 -17 -19
If 2 cannot be one of the primes in the sum - the sum must be even.
13

50. The average of an ODD number of consecutive integers will ________ be an integer.
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
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Prime
If 2 cannot be one of the primes in the sum - the sum must be even.