## Test your basic knowledge |

# GMAT Number Properties

**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:5x**

**2. v216 =**

**3. 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**

**4. For ODD ROOTS - the root has ______.**

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

**6. v3**

**7. v256=**

**8. The prime factorization of __________ contains only EVEN powers of primes.**

**9. Prime Numbers:7x**

**10. Prime factors of _____ must come in pairs of three.**

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

**12. v2**

**13. Positive integers with more than two factors are ____.**

**14. 3n + 3n + 3n = _____ = ______**

**15. Prime Numbers:6x**

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

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

**18. Prime Numbers:9x**

**19. How to find the sum of consecutive integers:**

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

**21. N! is _____ of all integers from 1 to N.**

**22. Let N be an integer. If you add two non-multiples of N - the result could be _______.**

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

**24. 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?**

**25. Prime Numbers:0x**

**26. v625=**

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

**28. The PRODUCT of n consecutive integers is divisible by ____.**

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

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

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

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

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

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

**35. Prime Numbers:4x**

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

**37. Prime Numbers:1x**

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

**39. Prime Numbers:3x**

**40. Prime Numbers:8x**

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

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

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

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

**45. v5**

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

**47. Positive integers with only two factors must be ___.**

**48. 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**

**49. v169=**

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