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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. Let N be an integer. If you add two non-multiples of N - the result could be _______.
53 -59
A PERFECT SQUARE
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Either a multiple of N or a non-multiple of N

2. v225=
A PERFECT SQUARE
A MULTIPLE
71 -73 -79
15

3. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
97
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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

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 PRODUCT of n consecutive integers is divisible by ____.
53 -59
NEVER CONTRADICT ONE ANOTHER
N is a divisor of x+y
The PRODUCT of n consecutive integers is divisible by n!.

6. The sum of any two primes will be ____ - unless ______.
3·3n = 3^{n+1}
13
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The sum of any two primes will be even - unless one of the two primes is 2.

7. If N is a divisor of x and y - then _______.
N is a divisor of x+y
A MULTIPLE
The sum of any two primes will be even - unless one of the two primes is 2.
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

8. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
The average of an ODD number of consecutive integers will ALWAYS be an integer.
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37

9. 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
The sum of any two primes will be even - unless one of the two primes is 2.
1.7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
11 -13 -17 -19

10. v625=
The PRODUCT of n consecutive integers is divisible by n!.
41 -43 -47
25
15

11. The two statements in a data sufficiency problem will _______________.
A MULTIPLE
Never prime
NEVER CONTRADICT ONE ANOTHER
Put the coefficient under the radical to get a better approximation

12. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
16
1. The smallest or largest element 2. The increment 3. The number of items in the set
Put the coefficient under the radical to get a better approximation
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

13. v5˜
71 -73 -79
2.5
25
23 -29

14. Any integer with an ODD number of total factors must be _______.
The middle number
The average of an EVEN number of consecutive integers will NEVER be an integer.
53 -59
A PERFECT SQUARE

15. The prime factorization of a perfect square contains only ______ powers of primes.
Never prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
The same sign as the base
EVEN

16. v256=
16
13
41 -43 -47
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

17. If estimating a root with a coefficient - _____ .
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!.
Put the coefficient under the radical to get a better approximation
Never prime

18. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
A MULTIPLE
ONLY the nonnegative root of the numberUNLIKE
25
83 -89

19. Prime Numbers:1x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD
The middle number
11 -13 -17 -19

20. Prime Numbers:9x
97
Prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
FACTOR

21. Prime Numbers:2x
15
Prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
23 -29

22. Prime Numbers:7x
The same sign as the base
A MULTIPLE
71 -73 -79
61 -67

23. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
The PRODUCT of n consecutive integers is divisible by n!.
53 -59
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
FACTOR

24. Prime Numbers:0x
ODD
In an evenly spaced set - the average and the median are equal.
61 -67
2 -3 -5 -7

25. Prime Numbers:4x
41 -43 -47
16
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ODD

26. In an evenly spaced set - the ____ and the ____ are equal.
PERFECT CUBES
In an evenly spaced set - the average and the median are equal.
A MULTIPLE
16

27. The prime factorization of __________ contains only EVEN powers of primes.
31 -37
A PERFECT SQUARE
In an evenly spaced set - the average and the median are equal.
3·3n = 3^{n+1}

28. Positive integers with more than two factors are ____.
Never prime
The middle number
A PERFECT SQUARE
41 -43 -47

29. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
A MULTIPLE
A non-multiple of N.
N is a divisor of x+y
A PERFECT SQUARE

30. The average of an EVEN number of consecutive integers will ________ be an integer.
11 -13 -17 -19
3·3n = 3^{n+1}
The average of an EVEN number of consecutive integers will NEVER be an integer.
2.5

31. 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?
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.
71 -73 -79
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 PRODUCT of n consecutive integers is divisible by n!.

32. 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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Put the coefficient under the radical to get a better approximation
71 -73 -79

33. 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
14
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
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

34. v2˜
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.
3·3n = 3^{n+1}
1.4
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

35. In an evenly spaced set - the mean and median are equal to the _____ of _________.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
1.4
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE

36. All perfect squares have a(n) _________ number of total factors.
A PERFECT SQUARE
ODD
A non-multiple of N.
3·3n = 3^{n+1}

37. In an evenly spaced set - the average can be found by finding ________.
In an evenly spaced set - the average and the median are equal.
The middle number
FACTOR
Prime

38. Any integer with an EVEN number of total factors cannot be ______.
1.4
If 2 cannot be one of the primes in the sum - the sum must be even.
13
A PERFECT SQUARE

39. Prime factors of _____ must come in pairs of three.
14
71 -73 -79
PERFECT CUBES
2 -3 -5 -7

40. Prime Numbers:6x
NEVER CONTRADICT ONE ANOTHER
61 -67
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

41. Prime Numbers:8x
83 -89
2 -3 -5 -7
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.

42. Prime Numbers:3x
61 -67
A PERFECT SQUARE
A non-multiple of N.
31 -37

43. Positive integers with only two factors must be ___.
83 -89
Prime
The sum of any two primes will be even - unless one of the two primes is 2.
2 -3 -5 -7

44. N! is _____ of all integers from 1 to N.
Never prime
A MULTIPLE
EVEN
1. The smallest or largest element 2. The increment 3. The number of items in the set

45. For ODD ROOTS - the root has ______.
23 -29
Put the coefficient under the radical to get a better approximation
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

46. v3˜
1.7
97
The average of the set times the number of elements in the set
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

47. The average of an ODD number of consecutive integers will ________ be an integer.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
83 -89
The average of an ODD number of consecutive integers will ALWAYS be an integer.

48. How to find the sum of consecutive integers:
In an evenly spaced set - the average and the median are equal.
2.5
A PERFECT SQUARE
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.

49. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
Prime
A non-multiple of N.
If 2 cannot be one of the primes in the sum - the sum must be even.

50. If the problem states/assumes that a number is an integer - check to see if you can use _______.
A PERFECT SQUARE
41 -43 -47
Prime factorization
14