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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. v196=
Never prime
ODD
14
61 -67

2. Let N be an integer. If you add two non-multiples of N - the result could be _______.
Never prime
Either a multiple of N or a non-multiple of N
2.5
13

3. v256=
16
Never prime
The same sign as the base
53 -59

4. Prime factors of _____ must come in pairs of three.
Prime
PERFECT CUBES
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The middle number

5. v169=
23 -29
Never prime
13
1.4

6. Prime Numbers:0x
Prime
2 -3 -5 -7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
ONLY the nonnegative root of the numberUNLIKE

7. In an evenly spaced set - the sum of the terms is equal to ____.
The same sign as the base
16
The average of the set times the number of elements in the set
Either a multiple of N or a non-multiple of N

8. Any integer with an EVEN number of total factors cannot be ______.
If 2 cannot be one of the primes in the sum - the sum must be even.
A PERFECT SQUARE
1.4
[(last - first) / increment] + 1

9. The prime factorization of __________ contains only EVEN powers of primes.
The middle number
The average of an EVEN number of consecutive integers will NEVER be an integer.
A PERFECT SQUARE
Either a multiple of N or a non-multiple of N

10. Prime Numbers:3x
A PERFECT SQUARE
2 -3 -5 -7
1. The smallest or largest element 2. The increment 3. The number of items in the set
31 -37

11. v5˜
1.7
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
2.5
A non-multiple of N.

12. If N is a divisor of x and y - then _______.
15
The average of the set times the number of elements in the set
N is a divisor of x+y
The same sign as the base

13. In an evenly spaced set - the average can be found by finding ________.
97
ONLY the nonnegative root of the numberUNLIKE
A MULTIPLE
The middle number

14. 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?
Prime factorization
The middle number
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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

15. Positive integers with more than two factors are ____.
Never prime
41 -43 -47
25
In an evenly spaced set - the average and the median are equal.

16. Any integer with an ODD number of total factors must be _______.
The same sign as the base
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.
11 -13 -17 -19

17. The sum of any two primes will be ____ - unless ______.
The middle number
The average of an EVEN number of consecutive integers will NEVER be an integer.
A non-multiple of N.
The sum of any two primes will be even - unless one of the two primes is 2.

18. 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
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.
83 -89
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

19. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
ODD
Either a multiple of N or a non-multiple of N
Prime factorization
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

20. v3˜
1.7
97
16
N is a divisor of x+y

21. If 2 cannot be one of the primes in the sum - the sum must be _____.
11 -13 -17 -19
ONLY the nonnegative root of the numberUNLIKE
Either a multiple of N or a non-multiple of N
If 2 cannot be one of the primes in the sum - the sum must be even.

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

23. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
41 -43 -47
N is a divisor of x+y
A PERFECT SQUARE

24. The average of an ODD number of consecutive integers will ________ be an integer.
16
A PERFECT SQUARE
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

25. Prime Numbers:6x
61 -67
13
2.5
31 -37

26. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
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

27. 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
3·3n = 3^{n+1}
Prime
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
2 -3 -5 -7

28. All perfect squares have a(n) _________ number of total factors.
ODD
97
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.

29. How to find the sum of consecutive integers:
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A MULTIPLE
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.
Put the coefficient under the radical to get a better approximation

30. The average of an EVEN number of consecutive integers will ________ be an integer.
The PRODUCT of n consecutive integers is divisible by n!.
The average of an EVEN number of consecutive integers will NEVER be an integer.
97
Prime factorization

31. Prime Numbers:4x
41 -43 -47
2 -3 -5 -7
25
The PRODUCT of n consecutive integers is divisible by n!.

32. v625=
Prime factorization
25
2 -3 -5 -7
A PERFECT SQUARE

33. 3n + 3n + 3n = _____ = ______
23 -29
NEVER CONTRADICT ONE ANOTHER
83 -89
3·3n = 3^{n+1}

34. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
16
3·3n = 3^{n+1}
FACTOR
97

35. Prime Numbers:9x
A PERFECT SQUARE
A non-multiple of N.
Never prime
97

36. For ODD ROOTS - the root has ______.
The same sign as the base
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.
16

37. The two statements in a data sufficiency problem will _______________.
[(last - first) / increment] + 1
61 -67
NEVER CONTRADICT ONE ANOTHER
11 -13 -17 -19

38. 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.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The sum of any two primes will be even - unless one of the two primes is 2.
ODD

39. v225=
15
The same sign as the base
The average of an EVEN number of consecutive integers will NEVER be an integer.
A MULTIPLE

40. Prime Numbers:1x
11 -13 -17 -19
Never prime
13
A PERFECT SQUARE

41. Prime Numbers:8x
83 -89
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Either a multiple of N or a non-multiple of N
Prime

42. 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
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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
Never prime
41 -43 -47

43. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
Put the coefficient under the radical to get a better approximation
71 -73 -79
2.5
1. The smallest or largest element 2. The increment 3. The number of items in the set

44. v2˜
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
1.4
FACTOR
Prime factorization

45. Prime Numbers:2x
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
N is a divisor of x+y
3·3n = 3^{n+1}
23 -29

46. Positive integers with only two factors must be ___.
1.4
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
Prime
ONLY the nonnegative root of the numberUNLIKE

47. 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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48. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
PERFECT CUBES
A PERFECT SQUARE
A non-multiple of N.
ONLY the nonnegative root of the numberUNLIKE

49. N! is _____ of all integers from 1 to N.
A PERFECT SQUARE
1. The smallest or largest element 2. The increment 3. The number of items in the set
EVEN
A MULTIPLE

50. In an evenly spaced set - the ____ and the ____ are equal.
1.4
If 2 cannot be one of the primes in the sum - the sum must be even.
15
In an evenly spaced set - the average and the median are equal.