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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. If 2 cannot be one of the primes in the sum - the sum must be _____.
Prime factorization
53 -59
[(last - first) / increment] + 1
If 2 cannot be one of the primes in the sum - the sum must be even.

2. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
Never prime
In an evenly spaced set - the average and the median are equal.
[(last - first) / increment] + 1
ONLY the nonnegative root of the numberUNLIKE

3. 3n + 3n + 3n = _____ = ______
13
3·3n = 3^{n+1}
A PERFECT SQUARE
NEVER CONTRADICT ONE ANOTHER

4. The two statements in a data sufficiency problem will _______________.
In an evenly spaced set - the average and the median are equal.
83 -89
NEVER CONTRADICT ONE ANOTHER
A PERFECT SQUARE

5. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
23 -29
The middle number
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Never prime

6. How to find the sum of consecutive integers:
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
23 -29
[(last - first) / increment] + 1

7. For ODD ROOTS - the root has ______.
41 -43 -47
61 -67
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 same sign as the base

8. In an evenly spaced set - the ____ and the ____ are equal.
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
13
In an evenly spaced set - the average and the median are equal.

9. If N is a divisor of x and y - then _______.
Never prime
61 -67
N is a divisor of x+y
41 -43 -47

10. v3˜
13
1.7
14
EVEN

11. Any integer with an EVEN number of total factors cannot be ______.
The sum of any two primes will be even - unless one of the two primes is 2.
1.7
A PERFECT SQUARE
ONLY the nonnegative root of the numberUNLIKE

12. v5˜
61 -67
23 -29
2.5
53 -59

13. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
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.
ODD
83 -89
A non-multiple of N.

14. 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
A MULTIPLE
2.5
15

15. The prime factorization of a perfect square contains only ______ powers of primes.
The average of an EVEN number of consecutive integers will NEVER be an integer.
EVEN
A non-multiple of N.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

16. 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 -3 -5 -7
Prime factorization
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.
71 -73 -79

17. In an evenly spaced set - the average can be found by finding ________.
13
The middle number
97
3·3n = 3^{n+1}

18. Prime Numbers:6x
15
41 -43 -47
Never prime
61 -67

19. 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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20. ³v216 =
If 2 cannot be one of the primes in the sum - the sum must be even.
14
23 -29
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

21. Positive integers with only two factors must be ___.
A PERFECT SQUARE
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.
Prime
ONLY the nonnegative root of the numberUNLIKE

22. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
11 -13 -17 -19
97
The middle number
1. The smallest or largest element 2. The increment 3. The number of items in the set

23. In an evenly spaced set - the sum of the terms is equal to ____.
FACTOR
25
The average of the set times the number of elements in the set
53 -59

24. 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 middle number
Put the coefficient under the radical to get a better approximation
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
[(last - first) / increment] + 1

25. In an evenly spaced set - the mean and median are equal to the _____ of _________.
The average of the set times the number of elements in the set
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
A non-multiple of N.
25

26. Prime Numbers:4x
41 -43 -47
53 -59
Prime factorization
ONLY the nonnegative root of the numberUNLIKE

27. All perfect squares have a(n) _________ number of total factors.
ODD
2.5
83 -89
Either a multiple of N or a non-multiple of N

28. The sum of any two primes will be ____ - unless ______.
15
13
Prime
The sum of any two primes will be even - unless one of the two primes is 2.

29. Prime Numbers:7x
71 -73 -79
53 -59
13
2 -3 -5 -7

30. v196=
53 -59
14
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
If 2 cannot be one of the primes in the sum - the sum must be even.

31. If the problem states/assumes that a number is an integer - check to see if you can use _______.
If 2 cannot be one of the primes in the sum - the sum must be even.
13
Prime factorization
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

32. 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 -3 -5 -7
15
31 -37

33. v625=
1.7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
25
The average of the set times the number of elements in the set

34. Prime Numbers:1x
A non-multiple of N.
A PERFECT SQUARE
11 -13 -17 -19
2.5

35. 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.
11 -13 -17 -19
NEVER CONTRADICT ONE ANOTHER
The PRODUCT of n consecutive integers is divisible by n!.

36. v169=
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 middle number
13
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.

37. Prime Numbers:8x
13
15
2.5
83 -89

38. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
1. The smallest or largest element 2. The increment 3. The number of items in the set
FACTOR
97
11 -13 -17 -19

39. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
Prime
1.7
The same sign as the base

40. The prime factorization of __________ contains only EVEN powers of primes.
The average of an EVEN number of consecutive integers will NEVER be an integer.
83 -89
FACTOR
A PERFECT SQUARE

41. Prime Numbers:2x
14
23 -29
16
[(last - first) / increment] + 1

42. The average of an ODD number of consecutive integers will ________ 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.
14
The average of an ODD number of consecutive integers will ALWAYS be an integer.
A PERFECT SQUARE

43. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
A PERFECT SQUARE
53 -59

44. Prime Numbers:0x
61 -67
[(last - first) / increment] + 1
2 -3 -5 -7
ODD

45. Prime Numbers:5x
31 -37
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.
N is a divisor of x+y
53 -59

46. Prime Numbers:9x
3·3n = 3^{n+1}
83 -89
In an evenly spaced set - the average and the median are equal.
97

47. Prime factors of _____ must come in pairs of three.
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.
14
31 -37
PERFECT CUBES

48. v256=
Never prime
16
The sum of any two primes will be even - unless one of the two primes is 2.
FACTOR

49. 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
Either a multiple of N or a non-multiple of N
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 middle number
53 -59

50. Positive integers with more than two factors are ____.
Never prime
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
53 -59
25