# 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. 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

2. Prime Numbers:7x

3. Prime factors of _____ must come in pairs of three.

4. The prime factorization of a perfect square contains only ______ powers of primes.

5. Prime Numbers:1x

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7. In an evenly spaced set - the mean and median are equal to the _____ of _________.

8. v5

9. The PRODUCT of n consecutive integers is divisible by ____.

10. The sum of any two primes will be ____ - unless ______.

11. Let N be an integer. If you add a multiple of N to a non-multiple of N - the result is ________.

12. Positive integers with only two factors must be ___.

13. v2

14. Prime Numbers:2x

15. How to solve: Is the integer z divisible by 6? (1) gcd(z -12) = 3 (2) gcd(z -15) = 15

16. v225=

17. In an evenly spaced set - the average can be found by finding ________.

18. The average of an EVEN number of consecutive integers will ________ be an integer.

19. All evenly spaced sets are fully defined if:1. _____ 2. _____ 3. _____ are known.

20. N! is _____ of all integers from 1 to N.

21. v3

22. Positive integers with more than two factors are ____.

23. Any integer with an ODD number of total factors must be _______.

24. 3n + 3n + 3n = _____ = ______

25. If N is a divisor of x and y - then _______.

26. All perfect squares have a(n) _________ number of total factors.

27. In an evenly spaced set - the ____ and the ____ are equal.

28. Prime Numbers:0x

29. 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

30. v625=

31. 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?

32. On data sufficiency - ALWAYS _______ algebraic expressions when you can. ESPECIALLY for divisibility.

33. 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

34. v169=

35. Any integer with an EVEN number of total factors cannot be ______.

36. The formula for finding the number of consecutive multiples in a set is _______.

37. If the problem states/assumes that a number is an integer - check to see if you can use _______.

38. The prime factorization of __________ contains only EVEN powers of primes.

39. Prime Numbers:5x

40. If 2 cannot be one of the primes in the sum - the sum must be _____.

41. The SUM of n consecutive integers is divisible by n if ____ - but not if ______.

42. Prime Numbers:8x

43. In an evenly spaced set - the sum of the terms is equal to ____.

44. Prime Numbers:6x

45. The two statements in a data sufficiency problem will _______________.

46. When we take an EVEN ROOT - a radical sign means ________. This is _____ even exponents.

47. v196=

48. The average of an ODD number of consecutive integers will ________ be an integer.

49. v256=

50. Prime Numbers:4x