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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. All perfect squares have a(n) _________ number of total factors.
ODD
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation

2. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
FACTOR
Prime
The same sign as the base
13

3. The two statements in a data sufficiency problem will _______________.
NEVER CONTRADICT ONE ANOTHER
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
1.7
[(last - first) / increment] + 1

4. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The same sign as the base
N is a divisor of x+y
1. The smallest or largest element 2. The increment 3. The number of items in the set
71 -73 -79

5. The prime factorization of __________ contains only EVEN powers of primes.
Either a multiple of N or a non-multiple of N
23 -29
14
A PERFECT SQUARE

6. N! is _____ of all integers from 1 to N.
83 -89
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
The sum of any two primes will be even - unless one of the two primes is 2.
A MULTIPLE

7. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
1. The smallest or largest element 2. The increment 3. The number of items in the set
Prime
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
The average of the set times the number of elements in the set

8. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
ODD
In an evenly spaced set - the average and the median are equal.
If 2 cannot be one of the primes in the sum - the sum must be even.

9. The prime factorization of a perfect square contains only ______ powers of primes.
EVEN
NEVER CONTRADICT ONE ANOTHER
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE

10. If N is a divisor of x and y - then _______.
[(last - first) / increment] + 1
N is a divisor of x+y
1.4
The average of an ODD number of consecutive integers will ALWAYS be an integer.

11. 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. The smallest or largest element 2. The increment 3. The number of items in the set
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 sum of any two primes will be even - unless one of the two primes is 2.
A PERFECT SQUARE

12. v256=
14
16
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.
11 -13 -17 -19

13. The PRODUCT of n consecutive integers is divisible by ____.
The PRODUCT of n consecutive integers is divisible by n!.
Never prime
Either a multiple of N or a non-multiple of N
A MULTIPLE

14. Prime Numbers:4x
EVEN
The same sign as the base
41 -43 -47
1.7

15. v196=
A PERFECT SQUARE
14
1.4
A non-multiple of N.

16. v3˜
2 -3 -5 -7
A PERFECT SQUARE
1.7
Either a multiple of N or a non-multiple of N

17. Prime Numbers:8x
83 -89
EVEN
The PRODUCT of n consecutive integers is divisible by n!.
In an evenly spaced set - the average and the median are equal.

18. v5˜
11 -13 -17 -19
97
2.5
[(last - first) / increment] + 1

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

20. Prime Numbers:0x
2 -3 -5 -7
FACTOR
2.5
The sum of any two primes will be even - unless one of the two primes is 2.

21. Positive integers with more than two factors are ____.
Never prime
EVEN
23 -29
In an evenly spaced set - the average and the median are equal.

22. v225=
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
A PERFECT SQUARE
15
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

23. For ODD ROOTS - the root has ______.
2.5
The same sign as the base
A PERFECT SQUARE
3·3n = 3^{n+1}

24. Prime Numbers:3x
14
ONLY the nonnegative root of the numberUNLIKE
[(last - first) / increment] + 1
31 -37

25. How to find the sum of consecutive integers:
15
NEVER CONTRADICT ONE ANOTHER
The average of an EVEN number of consecutive integers will NEVER 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.

26. Prime Numbers:6x
A PERFECT SQUARE
The average of an EVEN number of consecutive integers will NEVER be an integer.
61 -67
1.7

27. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.
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.
ODD
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 SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

28. The average of an EVEN number of consecutive integers will ________ be an integer.
2 -3 -5 -7
1.7
Prime
The average of an EVEN number of consecutive integers will NEVER be an integer.

29. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.
13
ODD
A non-multiple of N.
The average of the set times the number of elements in the set

30. Prime Numbers:7x
11 -13 -17 -19
71 -73 -79
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

31. Let N be an integer. If you add two non-multiples of N - the result could be _______.
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.
Either a multiple of N or a non-multiple of N
1.4
25

32. If 2 cannot be one of the primes in the sum - the sum must be _____.
11 -13 -17 -19
In an evenly spaced set - the average and the median are equal.
If 2 cannot be one of the primes in the sum - the sum must be even.
FACTOR

33. v169=
13
A PERFECT SQUARE
The PRODUCT of n consecutive integers is divisible by n!.
[(last - first) / increment] + 1

34. Prime Numbers:5x
14
2 -3 -5 -7
A non-multiple of N.
53 -59

35. In an evenly spaced set - the ____ and the ____ are equal.
71 -73 -79
A PERFECT SQUARE
1.4
In an evenly spaced set - the average and the median are equal.

36. v2˜
ODD
1.4
Put the coefficient under the radical to get a better approximation
11 -13 -17 -19

37. ³v216 =
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
PERFECT CUBES
[(last - first) / increment] + 1
83 -89

38. Prime Numbers:9x
A PERFECT SQUARE
ODD
A PERFECT SQUARE
97

39. If the problem states/assumes that a number is an integer - check to see if you can use _______.
Prime factorization
1.7
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
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.

40. Prime Numbers:1x
A PERFECT SQUARE
11 -13 -17 -19
41 -43 -47
1. The smallest or largest element 2. The increment 3. The number of items in the set

41. Prime Numbers:2x
16
23 -29
The middle number
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

42. 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.
If 2 cannot be one of the primes in the sum - the sum must be even.
The average of an EVEN number of consecutive integers will NEVER be an integer.
Never prime

43. Positive integers with only two factors must be ___.
EVEN
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.
Prime

44. The average of an ODD number of consecutive integers will ________ be an integer.
Either a multiple of N or a non-multiple of N
83 -89
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.

45. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
1.7
Put the coefficient under the radical to get a better approximation
71 -73 -79
ONLY the nonnegative root of the numberUNLIKE

46. Any integer with an ODD number of total factors must be _______.
PERFECT CUBES
Either a multiple of N or a non-multiple of N
16
A PERFECT SQUARE

47. 3n + 3n + 3n = _____ = ______
3·3n = 3^{n+1}
The average of an ODD number of consecutive integers will ALWAYS be an integer.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6

48. Prime factors of _____ must come in pairs of three.
PERFECT CUBES
A PERFECT SQUARE
A MULTIPLE
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

49. v625=
25
23 -29
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
Prime

50. The formula for finding the number of consecutive multiples in a set is _______.
[(last - first) / increment] + 1
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
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.
41 -43 -47