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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. Prime Numbers:3x
Either a multiple of N or a non-multiple of N
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}
31 -37

2. 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
41 -43 -47
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
FACTOR
A PERFECT SQUARE

3. 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?
[(last - first) / increment] + 1
Put the coefficient under the radical to get a better approximation
97
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.

4. v225=
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.
1.7
15
EVEN

5. Prime Numbers:0x
ONLY the nonnegative root of the numberUNLIKE
2 -3 -5 -7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
71 -73 -79

6. v256=
FACTOR
53 -59
If 2 cannot be one of the primes in the sum - the sum must be even.
16

7. The prime factorization of __________ contains only EVEN powers of primes.
ODD
31 -37
A PERFECT SQUARE
14

8. Prime factors of _____ must come in pairs of three.
25
23 -29
83 -89
PERFECT CUBES

9. Any integer with an EVEN number of total factors cannot be ______.
53 -59
If 2 cannot be one of the primes in the sum - the sum must be even.
Put the coefficient under the radical to get a better approximation
A PERFECT SQUARE

10. Prime Numbers:4x
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
41 -43 -47
In an evenly spaced set - the average and the median are equal.
97

11. In an evenly spaced set - the ____ and the ____ are equal.
11 -13 -17 -19
In an evenly spaced set - the average and the median are equal.
1.7
The PRODUCT of n consecutive integers is divisible by n!.

12. In an evenly spaced set - the average can be found by finding ________.
The middle number
If 2 cannot be one of the primes in the sum - the sum must be even.
The same sign as the base
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.

13. v3˜
15
1.7
25
The same sign as the base

14. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.
ONLY the nonnegative root of the numberUNLIKE
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
25
EVEN

15. v5˜
Prime factorization
2.5
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.
1.4

16. N! is _____ of all integers from 1 to N.
[(last - first) / increment] + 1
EVEN
41 -43 -47
A MULTIPLE

17. The formula for finding the number of consecutive multiples in a set is _______.
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹
A non-multiple of N.
1.4
[(last - first) / increment] + 1

18. The sum of any two primes will be ____ - unless ______.
23 -29
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
The sum of any two primes will be even - unless one of the two primes is 2.

19. Prime Numbers:8x
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.
83 -89
13
The average of an EVEN number of consecutive integers will NEVER be an integer.

20. The two statements in a data sufficiency problem will _______________.
The sum of any two primes will be even - unless one of the two primes is 2.
NEVER CONTRADICT ONE ANOTHER
The PRODUCT of n consecutive integers is divisible by n!.
Never prime

21. v196=
In an evenly spaced set - the average and the median are equal.
ODD
14
The same sign as the base

22. 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
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
31 -37
A PERFECT SQUARE
16

23. Prime Numbers:1x
11 -13 -17 -19
A non-multiple of N.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
3·3n = 3^{n+1}

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

25. For ODD ROOTS - the root has ______.
The same sign as the base
97
Never prime
23 -29

26. 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.
The middle number
14
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

27. If estimating a root with a coefficient - _____ .
Put the coefficient under the radical to get a better approximation
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.
ODD

28. v625=
A PERFECT SQUARE
25
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.
The middle number

29. Let N be an integer. If you add two non-multiples of N - the result could be _______.
13
1.4
Either a multiple of N or a non-multiple of N
53 -59

30. All perfect squares have a(n) _________ number of total factors.
ODD
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation
A non-multiple of N.

31. The average of an ODD number of consecutive integers will ________ be an integer.
83 -89
ODD
The average of an ODD number of consecutive integers will ALWAYS be an integer.
Never prime

32. If 2 cannot be one of the primes in the sum - the sum must be _____.
ODD
31 -37
If 2 cannot be one of the primes in the sum - the sum must be even.
1.7

33. The prime factorization of a perfect square contains only ______ powers of primes.
The PRODUCT of n consecutive integers is divisible by n!.
EVEN
A PERFECT SQUARE
The sum of any two primes will be even - unless one of the two primes is 2.

34. In an evenly spaced set - the mean and median are equal to the _____ of _________.
ODD
The average of an ODD number of consecutive integers will ALWAYS be an integer.
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
25

35. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.
The SUM of n consecutive integers is divisible by n if n is odd - but not if n is even.
1. The smallest or largest element 2. The increment 3. The number of items in the set
41 -43 -47
If 2 cannot be one of the primes in the sum - the sum must be even.

36. ³v216 =
The average of the set times the number of elements in the set
1.7
Break the number into prime powers: 216 = 2 2 2 3 3 * 3 = 2³ · 3³ = 6³ - so ³v216 = ³v6³ = 6
83 -89

37. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15
The average of the set times the number of elements in the set
The same sign as the base
Prime factorization
Set up prime columns. -- z 6 12 15 2 --2¹ 2² 3 --3¹ 3¹ 3¹ 5 ---------5¹

38. v2˜
1.4
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 average of the set times the number of elements in the set
In an evenly spaced set - the average and the median are equal.

39. Prime Numbers:7x
16
71 -73 -79
[(last - first) / increment] + 1
In an evenly spaced set - the average and the median are equal.

40. v169=
Prime factorization
13
1.4
The same sign as the base

41. Positive integers with only two factors must be ___.
71 -73 -79
N is a divisor of x+y
3·3n = 3^{n+1}
Prime

42. Prime Numbers:2x
23 -29
25
ODD
The middle number

43. Prime Numbers:5x
2.5
FACTOR
EVEN
53 -59

44. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.
ONLY the nonnegative root of the numberUNLIKE
A PERFECT SQUARE
2.5
FACTOR

45. How to find the sum of consecutive integers:
In an evenly spaced set - the mean and median are equal to the average of the first and the last number.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The average of an ODD number of consecutive integers will ALWAYS 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.

46. If the problem states/assumes that a number is an integer - check to see if you can use _______.
31 -37
Prime factorization
FACTOR
[(last - first) / increment] + 1

47. Any integer with an ODD number of total factors must be _______.
71 -73 -79
25
A PERFECT SQUARE
Put the coefficient under the radical to get a better approximation

48. The PRODUCT of n consecutive integers is divisible by ____.
If gcd(k1 -n) ? 1 or gcd(k2 -n) ? 1 - this proves insufficiency.
The PRODUCT of n consecutive integers is divisible by n!.
3·3n = 3^{n+1}
A MULTIPLE

49. If N is a divisor of x and y - then _______.
1.4
N is a divisor of x+y
The average of the set times the number of elements in the set
Prime

50. Positive integers with more than two factors are ____.
Never prime
Put the coefficient under the radical to get a better approximation
The average of an ODD number of consecutive integers will ALWAYS be an integer.
3·3n = 3^{n+1}