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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. The formula for finding the number of consecutive multiples in a set is _______.
PERFECT CUBES
[(last - first) / increment] + 1
FACTOR
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

2. v225=
In an evenly spaced set - the average and the median are equal.
83 -89
2 -3 -5 -7
15

3. Any integer with an EVEN number of total factors cannot be ______.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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
Prime

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.
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE
EVEN
61 -67

6. 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
2.5
A PERFECT SQUARE
A PERFECT SQUARE

7. v196=
2 -3 -5 -7
NEVER CONTRADICT ONE ANOTHER
Prime factorization
14

8. If 2 cannot be one of the primes in the sum - the sum must be _____.
83 -89
If 2 cannot be one of the primes in the sum - the sum must be even.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A non-multiple of N.

9. The prime factorization of __________ contains only EVEN powers of primes.
41 -43 -47
A PERFECT SQUARE
Prime factorization
The average of an EVEN number of consecutive integers will NEVER be an integer.

10. Prime Numbers:1x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.
PERFECT CUBES
11 -13 -17 -19

11. Prime Numbers:4x
The middle number
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
PERFECT CUBES
41 -43 -47

12. 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.
13
A PERFECT SQUARE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

13. Positive integers with more than two factors are ____.
16
83 -89
Never prime
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

14. N! is _____ of all integers from 1 to N.
71 -73 -79
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The PRODUCT of n consecutive integers is divisible by n!.
A MULTIPLE

15. If estimating a root with a coefficient - _____ .
N is a divisor of x+y
Put the coefficient under the radical to get a better approximation
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.
FACTOR

16. v625=
13
16
If 2 cannot be one of the primes in the sum - the sum must be even.
25

17. The average of an EVEN number of consecutive integers will ________ be an integer.
11 -13 -17 -19
The average of an EVEN number of consecutive integers will NEVER be an integer.
In an evenly spaced set - the average and the median are equal.
1. The smallest or largest element 2. The increment 3. The number of items in the set

18. ³v216 =
NEVER CONTRADICT ONE ANOTHER
A non-multiple of N.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

19. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
A PERFECT SQUARE
The average of an EVEN number of consecutive integers will NEVER be an integer.
ONLY the nonnegative root of the numberUNLIKE
41 -43 -47

20. Any integer with an ODD number of total factors must be _______.
In an evenly spaced set - the average and the median are equal.
53 -59
A PERFECT SQUARE
The average of an ODD number of consecutive integers will ALWAYS be an integer.

21. In an evenly spaced set - the average can be found by finding ________.
The middle number
53 -59
Prime
The same sign as the base

22. Prime Numbers:5x
53 -59
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1.7
97

23. How to find the sum of consecutive integers:
A MULTIPLE
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.
A PERFECT SQUARE

24. Prime Numbers:6x
NEVER CONTRADICT ONE ANOTHER
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 PRODUCT of n consecutive integers is divisible by n!.
61 -67

25. Prime Numbers:0x
2 -3 -5 -7
83 -89
The average of an ODD number of consecutive integers will ALWAYS be an integer.
ODD

26. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
41 -43 -47
PERFECT CUBES
NEVER CONTRADICT ONE ANOTHER
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

27. Positive integers with only two factors must be ___.
Prime
A PERFECT SQUARE
3·3n = 3^{n+1}
[(last - first) / increment] + 1

28. v2˜
1.4
41 -43 -47
31 -37
The PRODUCT of n consecutive integers is divisible by n!.

29. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
23 -29
41 -43 -47
A PERFECT SQUARE
FACTOR

30. For ODD ROOTS - the root has ______.
FACTOR
Either a multiple of N or a non-multiple of N
The same sign as the base
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

31. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
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
Either a multiple of N or a non-multiple of N
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

32. Prime factors of _____ must come in pairs of three.
13
A non-multiple of N.
PERFECT CUBES
The same sign as the base

33. In an evenly spaced set - the sum of the terms is equal to ____.
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of an ODD number of consecutive integers will ALWAYS be 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.
The average of the set times the number of elements in the set

34. The two statements in a data sufficiency problem will _______________.
71 -73 -79
Prime
FACTOR
NEVER CONTRADICT ONE ANOTHER

35. v5˜
97
A PERFECT SQUARE
1.4
2.5

36. 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
In an evenly spaced set - the average and the median are equal.
Prime factorization
1. The smallest or largest element 2. The increment 3. The number of items in the set

37. Prime Numbers:2x
71 -73 -79
A PERFECT SQUARE
23 -29
16

38. If N is a divisor of x and y - then _______.
11 -13 -17 -19
16
N is a divisor of x+y
ONLY the nonnegative root of the numberUNLIKE

39. 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?
A non-multiple of 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.
25
N is a divisor of x+y

40. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+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.
1.4
A MULTIPLE

41. v3˜
ONLY the nonnegative root of the numberUNLIKE
3·3n = 3^{n+1}
1.7
25

42. Prime Numbers:9x
97
The same sign as the base
11 -13 -17 -19
A non-multiple of N.

43. v169=
13
A PERFECT SQUARE
1.4
[(last - first) / increment] + 1

44. Prime Numbers:7x
71 -73 -79
23 -29
11 -13 -17 -19
FACTOR

45. Prime Numbers:8x
Never prime
[(last - first) / increment] + 1
83 -89
Either a multiple of N or a non-multiple of N

46. Prime Numbers:3x
31 -37
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
The PRODUCT of n consecutive integers is divisible by n!.

47. 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
A PERFECT SQUARE
Prime factorization
71 -73 -79

48. 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
A non-multiple of N.
15
N is a divisor of x+y

49. 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
[(last - first) / increment] + 1
If 2 cannot be one of the primes in the sum - the sum must be even.
In an evenly spaced set - the average and the median are equal.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

50. v256=
16
PERFECT CUBES
14
1. The smallest or largest element 2. The increment 3. The number of items in the set