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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 _______.
1.7
11 -13 -17 -19
Either a multiple of N or a non-multiple of N
The sum of any two primes will be even - unless one of the two primes is 2.

2. If N is a divisor of x and y - then _______.
25
41 -43 -47
N is a divisor of x+y
16

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
1.4
The middle number
A MULTIPLE
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

4. The sum of any two primes will be ____ - unless ______.
1.4
The sum of any two primes will be even - unless one of the two primes is 2.
A non-multiple of N.
23 -29

5. v5˜
2.5
Prime
Prime factorization
The PRODUCT of n consecutive integers is divisible by n!.

6. The prime factorization of __________ contains only EVEN powers of primes.
1.7
61 -67
14
A PERFECT SQUARE

7. How to find the sum of consecutive integers:
25
The average of the set times the number of elements in the set
1. The smallest or largest element 2. The increment 3. The number of items in the set
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.

8. N! is _____ of all integers from 1 to N.
14
3·3n = 3^{n+1}
A MULTIPLE
The PRODUCT of n consecutive integers is divisible by n!.

9. Prime Numbers:8x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
83 -89
31 -37
15

10. 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
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
71 -73 -79
83 -89
61 -67

11. Prime Numbers:5x
53 -59
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
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.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

12. v3˜
The PRODUCT of n consecutive integers is divisible by n!.
ONLY the nonnegative root of the numberUNLIKE
Never prime
1.7

13. The average of an ODD number of consecutive integers will ________ be an integer.
The middle number
The average of an ODD number of consecutive integers will ALWAYS be an integer.
FACTOR
2.5

14. Prime Numbers:1x
The middle number
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
11 -13 -17 -19
EVEN

15. In an evenly spaced set - the ____ and the ____ are equal.
In an evenly spaced set - the average and the median are equal.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE
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.

16. In an evenly spaced set - the average can be found by finding ________.
Never prime
53 -59
The middle number
A non-multiple of N.

17. Any integer with an EVEN number of total factors cannot be ______.
The middle number
A PERFECT SQUARE
Prime factorization
31 -37

18. Positive integers with only two factors must be ___.
Prime
2 -3 -5 -7
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
ODD

19. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
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
If 2 cannot be one of the primes in the sum - the sum must be even.

20. If the problem states/assumes that a number is an integer - check to see if you can use _______.
A MULTIPLE
61 -67
Prime factorization
The middle number

21. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
3·3n = 3^{n+1}
15
The PRODUCT of n consecutive integers is divisible by n!.

22. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
31 -37
97
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Prime

23. 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

24. v225=
The middle number
The average of an ODD number of consecutive integers will ALWAYS be an integer.
15
Either a multiple of N or a non-multiple of N

25. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
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
ONLY the nonnegative root of the numberUNLIKE
71 -73 -79
NEVER CONTRADICT ONE ANOTHER

26. The prime factorization of a perfect square contains only ______ powers of primes.
41 -43 -47
15
The PRODUCT of n consecutive integers is divisible by n!.
EVEN

27. For ODD ROOTS - the root has ______.
The same sign as the base
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.
In an evenly spaced set - the average and the median are equal.
3·3n = 3^{n+1}

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 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
Either a multiple of N or a non-multiple of N
A PERFECT SQUARE
FACTOR

29. Positive integers with more than two factors are ____.
Never prime
A PERFECT SQUARE
A PERFECT SQUARE
53 -59

30. Prime Numbers:0x
2 -3 -5 -7
The PRODUCT of n consecutive integers is divisible by n!.
31 -37
1.7

31. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
13
16
71 -73 -79
FACTOR

32. 3n + 3n + 3n = _____ = ______
Never prime
3·3n = 3^{n+1}
53 -59
The average of an ODD number of consecutive integers will ALWAYS be an integer.

33. v625=
A PERFECT SQUARE
25
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

34. Prime Numbers:9x
ODD
23 -29
97
41 -43 -47

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.
2.5
41 -43 -47
The middle number

36. If 2 cannot be one of the primes in the sum - the sum must be _____.
ONLY the nonnegative root of the numberUNLIKE
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.
EVEN

37. Prime Numbers:3x
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A PERFECT SQUARE
PERFECT CUBES
31 -37

38. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
2.5
1. The smallest or largest element 2. The increment 3. The number of items in the set
The average of an EVEN number of consecutive integers will NEVER be an integer.

39. Prime Numbers:2x
3·3n = 3^{n+1}
23 -29
A MULTIPLE
The average of the set times the number of elements in the set

40. The average of an EVEN number of consecutive integers will ________ be an integer.
The average of an ODD number of consecutive integers will ALWAYS be an integer.
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
The average of an EVEN number of consecutive integers will NEVER be an integer.

41. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
25
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

42. The two statements in a data sufficiency problem will _______________.
The average of an EVEN number of consecutive integers will NEVER be an integer.
NEVER CONTRADICT ONE ANOTHER
A non-multiple of N.
25

43. 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?
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.
14

44. v256=
16
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
14

45. The formula for finding the number of consecutive multiples in a set is _______.
3·3n = 3^{n+1}
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.
[(last - first) / increment] + 1
2 -3 -5 -7

46. Prime Numbers:7x
The average of an EVEN number of consecutive integers will NEVER be an integer.
71 -73 -79
A PERFECT SQUARE
13

47. ³v216 =
A MULTIPLE
61 -67
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.

48. All perfect squares have a(n) _________ number of total factors.
1.7
1.4
ODD
15

49. v169=
A PERFECT SQUARE
13
1.7
97

50. Prime Numbers:6x
2.5
The average of the set times the number of elements in the set
A PERFECT SQUARE
61 -67